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Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog

The LIGO Scientific Collaboration, the Virgo Collaboration, R. Abbott, T. D. Abbott, S. Abraham, F. Acernese, K. Ackley, A. Adams, C. Adams, R. X. Adhikari, V. B. Adya, C. Affeldt, M. Agathos, K. Agatsuma, N. Aggarwal, O. D. Aguiar, L. Aiello, A. Ain, P. Ajith, G. Allen, A. Allocca, P. A. Altin, A. Amato, S. Anand, A. Ananyeva, S. B. Anderson, W. G. Anderson, S. V. Angelova, S. Ansoldi, J. M. Antelis, S. Antier, S. Appert, K. Arai, M. C. Araya, J. S. Areeda, M. Arène, N. Arnaud, S. M. Aronson, K. G. Arun, Y. Asali, S. Ascenzi, G. Ashton, S. M. Aston, P. Astone, F. Aubin, P. Aufmuth, K. AultONeal, C. Austin, V. Avendano, S. Babak, F. Badaracco, M. K. M. Bader, S. Bae, A. M. Baer, S. Bagnasco, J. Baird, M. Ball, G. Ballardin, S. W. Ballmer, A. Bals, A. Balsamo, G. Baltus, S. Banagiri, D. Bankar, R. S. Bankar, J. C. Barayoga, C. Barbieri, B. C. Barish, D. Barker, P. Barneo, S. Barnum, F. Barone, B. Barr, L. Barsotti, M. Barsuglia, D. Barta, J. Bartlett, I. Bartos, R. Bassiri, A. Basti, M. Bawaj, J. C. Bayley, M. Bazzan, B. R. Becher, B. Bécsy, V. M. Bedakihale, M. Bejger, I. Belahcene, D. Beniwal, M. G. Benjamin, R. Benkel, T. F. Bennett, J. D. Bentley, F. Bergamin, B. K. Berger, G. Bergmann, S. Bernuzzi, C. P. L. Berry, D. Bersanetti, A. Bertolini, J. Betzwieser, R. Bhandare, A. V. Bhandari, D. Bhattacharjee, J. Bidler, I. A. Bilenko, G. Billingsley, R. Birney, O. Birnholtz, S. Biscans, M. Bischi, S. Biscoveanu, A. Bisht, M. Bitossi, M. -A. Bizouard, J. K. Blackburn, J. Blackman, C. D. Blair, D. G. Blair, R. M. Blair, O. Blanch, F. Bobba, N. Bode, M. Boer, Y. Boetzel, G. Bogaert, M. Boldrini, F. Bondu, E. Bonilla, R. Bonnand, P. Booker, B. A. Boom, S. Borhanian, R. Bork, V. Boschi, N. Bose, S. Bose, V. Bossilkov, V. Boudart, Y. Bouffanais, A. Bozzi, C. Bradaschia, P. R. Brady, A. Bramley, M. Branchesi, J. E. Brau, M. Breschi, T. Briant, J. H. Briggs, F. Brighenti, A. Brillet, M. Brinkmann, P. Brockill, A. F. Brooks, J. Brooks, D. D. Brown, S. Brunett, G. Bruno, R. Bruntz, A. Buikema, T. Bulik, H. J. Bulten, A. Buonanno, D. Buskulic, R. L. Byer, M. Cabero, L. Cadonati, M. Caesar, G. Cagnoli, C. Cahillane, J. Calderón Bustillo, J. D. Callaghan, T. A. Callister, E. Calloni, J. B. Camp, M. Canepa, K. C. Cannon, H. Cao, J. Cao, G. Carapella, F. Carbognani, M. F. Carney, M. Carpinelli, G. Carullo, T. L. Carver, J. Casanueva Diaz, C. Casentini, S. Caudill, M. Cavaglià, F. Cavalier, R. Cavalieri, G. Cella, P. Cerdá-Durán, E. Cesarini, W. Chaibi, K. Chakravarti, C. -L. Chan, C. Chan, K. Chandra, P. Chanial, S. Chao, P. Charlton, E. A. Chase, E. Chassande-Mottin, D. Chatterjee, M. Chaturvedi, K. Chatziioannou, A. Chen, H. Y. Chen, X. Chen, Y. Chen, H. -P. Cheng, C. K. Cheong, H. Y. Chia, F. Chiadini, R. Chierici, A. Chincarini, A. Chiummo, G. Cho, H. S. Cho, M. Cho, S. Choate, N. Christensen, Q. Chu, S. Chua, K. W. Chung, S. Chung, G. Ciani, P. Ciecielag, M. Cieślar, M. Cifaldi, A. A. Ciobanu, R. Ciolfi, F. Cipriano, A. Cirone, F. Clara, E. N. Clark, J. A. Clark, L. Clarke, P. Clearwater, S. Clesse, F. Cleva, E. Coccia, P. -F. Cohadon, D. E. Cohen, M. Colleoni, C. G. Collette, C. Collins, M. Colpi, M. Constancio, L. Conti, S. J. Cooper, P. Corban, T. R. Corbitt, I. Cordero-Carrión, S. Corezzi, K. R. Corley, N. Cornish, D. Corre, A. Corsi, S. Cortese, C. A. Costa, R. Cotesta, M. W. Coughlin, S. B. Coughlin, J. -P. Coulon, S. T. Countryman, P. Couvares, P. B. Covas, D. M. Coward, M. J. Cowart, D. C. Coyne, R. Coyne, J. D. E. Creighton, T. D. Creighton, M. Croquette, S. G. Crowder, J. R. Cudell, T. J. Cullen, A. Cumming, R. Cummings, L. Cunningham, E. Cuoco, M. Curylo, T. Dal Canton, G. Dálya, A. Dana, L. M. DaneshgaranBajastani, B. D'Angelo, S. L. Danilishin, S. D'Antonio, K. Danzmann, C. Darsow-Fromm, A. Dasgupta, L. E. H. Datrier, V. Dattilo, I. Dave, M. Davier, G. S. Davies, D. Davis, E. J. Daw, R. Dean, D. DeBra, M. Deenadayalan, J. Degallaix, M. De Laurentis, S. Deléglise, V. Del Favero, F. De Lillo, N. De Lillo, W. Del Pozzo, L. M. DeMarchi, F. De Matteis, V. D'Emilio, N. Demos, T. Denker, T. Dent, A. Depasse, R. De Pietri, R. De Rosa, C. De Rossi, R. DeSalvo, O. de Varona, A. Dhani, S. Dhurandhar, M. C. Díaz, M. Diaz-Ortiz, N. A. Didio, T. Dietrich, L. Di Fiore, C. DiFronzo, C. Di Giorgio, F. Di Giovanni, M. Di Giovanni, T. Di Girolamo, A. Di Lieto, B. Ding, S. Di Pace, I. Di Palma, F. Di Renzo, A. K. Divakarla, A. Dmitriev, Z. Doctor, L. D'Onofrio, F. Donovan, K. L. Dooley, S. Doravari, I. Dorrington, T. P. Downes, M. Drago, J. C. Driggers, Z. Du, J. -G. Ducoin, R. Dudi, P. Dupej, O. Durante, D. D'Urso, P. -A. Duverne, S. E. Dwyer, P. J. Easter, G. Eddolls, B. Edelman, T. B. Edo, O. Edy, A. Effler, J. Eichholz, S. S. Eikenberry, M. Eisenmann, R. A. Eisenstein, A. Ejlli, L. Errico, R. C. Essick, H. Estellés, D. Estevez, Z. B. Etienne, T. Etzel, M. Evans, T. M. Evans, B. E. Ewing, V. Fafone, H. Fair, S. Fairhurst, X. Fan, A. M. Farah, S. Farinon, B. Farr, W. M. Farr, E. J. Fauchon-Jones, M. Favata, M. Fays, M. Fazio, J. Feicht, M. M. Fejer, F. Feng, E. Fenyvesi, D. L. Ferguson, A. Fernandez-Galiana, I. Ferrante, T. A. Ferreira, F. Fidecaro, P. Figura, I. Fiori, D. Fiorucci, M. Fishbach, R. P. Fisher, J. M. Fishner, R. Fittipaldi, M. Fitz-Axen, V. Fiumara, R. Flaminio, E. Floden, E. Flynn, H. Fong, J. A. Font, P. W. F. Forsyth, J. -D. Fournier, S. Frasca, F. Frasconi, Z. Frei, A. Freise, R. Frey, V. Frey, P. Fritschel, V. V. Frolov, G. G. Fronzé, P. Fulda, M. Fyffe, H. A. Gabbard, B. U. Gadre, S. M. Gaebel, J. R. Gair, J. Gais, S. Galaudage, R. Gamba, D. Ganapathy, A. Ganguly, S. G. Gaonkar, B. Garaventa, C. García-Quirós, F. Garufi, B. Gateley, S. Gaudio, V. Gayathri, G. Gemme, A. Gennai, D. George, J. George, R. N. George, L. Gergely, S. Ghonge, Abhirup Ghosh, Archisman Ghosh, S. Ghosh, B. Giacomazzo, L. Giacoppo, J. A. Giaime, K. D. Giardina, D. R. Gibson, C. Gier, K. Gill, P. Giri, J. Glanzer, A. E. Gleckl, P. Godwin, E. Goetz, R. Goetz, N. Gohlke, B. Goncharov, G. González, A. Gopakumar, S. E. Gossan, M. Gosselin, R. Gouaty, B. Grace, A. Grado, M. Granata, V. Granata, A. Grant, S. Gras, P. Grassia, C. Gray, R. Gray, G. Greco, A. C. Green, R. Green, E. M. Gretarsson, H. L. Griggs, G. Grignani, A. Grimaldi, E. Grimes, S. J. Grimm, H. Grote, S. Grunewald, P. Gruning, J. G. Guerrero, G. M. Guidi, A. R. Guimaraes, G. Guixé, H. K. Gulati, Y. Guo, Anchal Gupta, Anuradha Gupta, P. Gupta, E. K. Gustafson, R. Gustafson, F. Guzman, L. Haegel, O. Halim, E. D. Hall, E. Z. Hamilton, G. Hammond, M. Haney, M. M. Hanke, J. Hanks, C. Hanna, M. D. Hannam, O. A. Hannuksela, O. Hannuksela, H. Hansen, T. J. Hansen, J. Hanson, T. Harder, T. Hardwick, K. Haris, J. Harms, G. M. Harry, I. W. Harry, D. Hartwig, R. K. Hasskew, C. -J. Haster, K. Haughian, F. J. Hayes, J. Healy, A. Heidmann, M. C. Heintze, J. Heinze, J. Heinzel, H. Heitmann, F. Hellman, P. Hello, A. F. Helmling-Cornell, G. Hemming, M. Hendry, I. S. Heng, E. Hennes, J. Hennig, M. H. Hennig, F. Hernandez Vivanco, M. Heurs, S. Hild, P. Hill, A. S. Hines, S. Hochheim, E. Hofgard, D. Hofman, J. N. Hohmann, A. M. Holgado, N. A. Holland, I. J. Hollows, Z. J. Holmes, K. Holt, D. E. Holz, P. Hopkins, C. Horst, J. Hough, E. J. Howell, C. G. Hoy, D. Hoyland, Y. Huang, M. T. Hübner, A. D. Huddart, E. A. Huerta, B. Hughey, V. Hui, S. Husa, S. H. Huttner, B. M. Hutzler, R. Huxford, T. Huynh-Dinh, B. Idzkowski, A. Iess, S. Imperato, H. Inchauspe, C. Ingram, G. Intini, M. Isi, B. R. Iyer, V. JaberianHamedan, T. Jacqmin, S. J. Jadhav, S. P. Jadhav, A. L. James, K. Jani, K. Janssens, N. N. Janthalur, P. Jaranowski, D. Jariwala, R. Jaume, A. C. Jenkins, M. Jeunon, J. Jiang, G. R. Johns, N. K. Johnson-McDaniel, A. W. Jones, D. I. Jones, J. D. Jones, P. Jones, R. Jones, R. J. G. Jonker, L. Ju, J. Junker, C. V. Kalaghatgi, V. Kalogera, B. Kamai, S. Kandhasamy, G. Kang, J. B. Kanner, S. J. Kapadia, D. P. Kapasi, C. Karathanasis, S. Karki, R. Kashyap, M. Kasprzack, W. Kastaun, S. Katsanevas, E. Katsavounidis, W. Katzman, K. Kawabe, F. Kéfélian, D. Keitel, J. S. Key, S. Khadka, F. Y. Khalili, I. Khan, S. Khan, E. A. Khazanov, N. Khetan, M. Khursheed, N. Kijbunchoo, C. Kim, G. J. Kim, J. C. Kim, K. Kim, W. S. Kim, Y. -M. Kim, C. Kimball, P. J. King, M. Kinley-Hanlon, R. Kirchhoff, J. S. Kissel, L. Kleybolte, S. Klimenko, T. D. Knowles, E. Knyazev, P. Koch, S. M. Koehlenbeck, G. Koekoek, S. Koley, M. Kolstein, K. Komori, V. Kondrashov, A. Kontos, N. Koper, M. Korobko, W. Z. Korth, M. Kovalam, D. B. Kozak, C. Krämer, V. Kringel, N. V. Krishnendu, A. Królak, G. Kuehn, A. Kumar, P. Kumar, Rahul Kumar, Rakesh Kumar, K. Kuns, S. Kwang, B. D. Lackey, D. Laghi, E. Lalande, T. L. Lam, A. Lamberts, M. Landry, B. B. Lane, R. N. Lang, J. Lange, B. Lantz, R. K. Lanza, I. La Rosa, A. Lartaux-Vollard, P. D. Lasky, M. Laxen, A. Lazzarini, C. Lazzaro, P. Leaci, S. Leavey, Y. K. Lecoeuche, H. M. Lee, H. W. Lee, J. Lee, K. Lee, J. Lehmann, E. Leon, N. Leroy, N. Letendre, Y. Levin, A. Li, J. Li, K. J. L. Li, T. G. F. Li, X. Li, F. Linde, S. D. Linker, J. N. Linley, T. B. Littenberg, J. Liu, X. Liu, M. Llorens-Monteagudo, R. K. L. Lo, A. Lockwood, L. T. London, A. Longo, M. Lorenzini, V. Loriette, M. Lormand, G. Losurdo, J. D. Lough, C. O. Lousto, G. Lovelace, H. Lück, D. Lumaca, A. P. Lundgren, Y. Ma, R. Macas, M. MacInnis, D. M. Macleod, I. A. O. MacMillan, A. Macquet, I. Magaña Hernandez, F. Magaña-Sandoval, C. Magazzù, R. M. Magee, E. Majorana, I. Maksimovic, S. Maliakal, A. Malik, N. Man, V. Mandic, V. Mangano, G. L. Mansell, M. Manske, M. Mantovani, M. Mapelli, F. Marchesoni, F. Marion, S. Márka, Z. Márka, C. Markakis, A. S. Markosyan, A. Markowitz, E. Maros, A. Marquina, S. Marsat, F. Martelli, I. W. Martin, R. M. Martin, M. Martinez, V. Martinez, D. V. Martynov, H. Masalehdan, K. Mason, E. Massera, A. Masserot, T. J. Massinger, M. Masso-Reid, S. Mastrogiovanni, A. Matas, M. Mateu-Lucena, F. Matichard, M. Matiushechkina, N. Mavalvala, E. Maynard, J. J. McCann, R. McCarthy, D. E. McClelland, S. McCormick, L. McCuller, S. C. McGuire, C. McIsaac, J. McIver, D. J. McManus, T. McRae, S. T. McWilliams, D. Meacher, G. D. Meadors, M. Mehmet, A. K. Mehta, A. Melatos, D. A. Melchor, G. Mendell, A. Menendez-Vazquez, R. A. Mercer, L. Mereni, K. Merfeld, E. L. Merilh, J. D. Merritt, M. Merzougui, S. Meshkov, C. Messenger, C. Messick, R. Metzdorff, P. M. Meyers, F. Meylahn, A. Mhaske, A. Miani, H. Miao, I. Michaloliakos, C. Michel, H. Middleton, L. Milano, A. L. Miller, M. Millhouse, J. C. Mills, E. Milotti, M. C. Milovich-Goff, O. Minazzoli, Y. Minenkov, Ll. M. Mir, A. Mishkin, C. Mishra, T. Mistry, S. Mitra, V. P. Mitrofanov, G. Mitselmakher, R. Mittleman, G. Mo, K. Mogushi, S. R. P. Mohapatra, S. R. Mohite, I. Molina, M. Molina-Ruiz, M. Mondin, M. Montani, C. J. Moore, D. Moraru, F. Morawski, G. Moreno, S. Morisaki, B. Mours, C. M. Mow-Lowry, S. Mozzon, F. Muciaccia, Arunava Mukherjee, D. Mukherjee, Soma Mukherjee, Subroto Mukherjee, N. Mukund, A. Mullavey, J. Munch, E. A. Muñiz, P. G. Murray, S. L. Nadji, A. Nagar, I. Nardecchia, L. Naticchioni, R. K. Nayak, B. F. Neil, J. Neilson, G. Nelemans, T. J. N. Nelson, M. Nery, A. Neunzert, K. Y. Ng, S. Ng, C. Nguyen, P. Nguyen, T. Nguyen, S. A. Nichols, S. Nissanke, F. Nocera, M. Noh, C. North, D. Nothard, L. K. Nuttall, J. Oberling, B. D. O'Brien, J. O'Dell, G. Oganesyan, G. H. Ogin, J. J. Oh, S. H. Oh, F. Ohme, H. Ohta, M. A. Okada, C. Olivetto, P. Oppermann, R. J. Oram, B. O'Reilly, R. G. Ormiston, N. Ormsby, L. F. Ortega, R. O'Shaughnessy, S. Ossokine, C. Osthelder, D. J. Ottaway, H. Overmier, B. J. Owen, A. E. Pace, G. Pagano, M. A. Page, G. Pagliaroli, A. Pai, S. A. Pai, J. R. Palamos, O. Palashov, C. Palomba, H. Pan, P. K. Panda, T. H. Pang, C. Pankow, F. Pannarale, B. C. Pant, F. Paoletti, A. Paoli, A. Paolone, W. Parker, D. Pascucci, A. Pasqualetti, R. Passaquieti, D. Passuello, M. Patel, B. Patricelli, E. Payne, T. C. Pechsiri, M. Pedraza, M. Pegoraro, A. Pele, S. Penn, A. Perego, C. J. Perez, C. Périgois, A. Perreca, S. Perriès, J. Petermann, D. Petterson, H. P. Pfeiffer, K. A. Pham, K. S. Phukon, O. J. Piccinni, M. Pichot, M. Piendibene, F. Piergiovanni, L. Pierini, V. Pierro, G. Pillant, F. Pilo, L. Pinard, I. M. Pinto, K. Piotrzkowski, M. Pirello, M. Pitkin, E. Placidi, W. Plastino, C. Pluchar, R. Poggiani, E. Polini, D. Y. T. Pong, S. Ponrathnam, P. Popolizio, E. K. Porter, A. Poverman, J. Powell, M. Pracchia, A. K. Prajapati, K. Prasai, R. Prasanna, G. Pratten, T. Prestegard, M. Principe, G. A. Prodi, L. Prokhorov, P. Prosposito, A. Puecher, M. Punturo, F. Puosi, P. Puppo, M. Pürrer, H. Qi, V. Quetschke, P. J. Quinonez, R. Quitzow-James, F. J. Raab, G. Raaijmakers, H. Radkins, N. Radulesco, P. Raffai, H. Rafferty, S. X. Rail, S. Raja, C. Rajan, B. Rajbhandari, M. Rakhmanov, K. E. Ramirez, T. D. Ramirez, A. Ramos-Buades, J. Rana, K. Rao, P. Rapagnani, U. D. Rapol, B. Ratto, V. Raymond, M. Razzano, J. Read, T. Regimbau, L. Rei, S. Reid, D. H. Reitze, P. Rettegno, F. Ricci, C. J. Richardson, J. W. Richardson, L. Richardson, P. M. Ricker, G. Riemenschneider, K. Riles, M. Rizzo, N. A. Robertson, F. Robinet, A. Rocchi, J. A. Rocha, S. Rodriguez, R. D. Rodriguez-Soto, L. Rolland, J. G. Rollins, V. J. Roma, M. Romanelli, R. Romano, C. L. Romel, A. Romero, I. M. Romero-Shaw, J. H. Romie, S. Ronchini, C. A. Rose, D. Rose, K. Rose, D. Rosińska, S. G. Rosofsky, M. P. Ross, S. Rowan, S. J. Rowlinson, Santosh Roy, Soumen Roy, P. Ruggi, K. Ryan, S. Sachdev, T. Sadecki, M. Sakellariadou, O. S. Salafia, L. Salconi, M. Saleem, A. Samajdar, E. J. Sanchez, J. H. Sanchez, L. E. Sanchez, N. Sanchis-Gual, J. R. Sanders, K. A. Santiago, E. Santos, T. R. Saravanan, N. Sarin, B. Sassolas, B. S. Sathyaprakash, O. Sauter, R. L. Savage, V. Savant, D. Sawant, S. Sayah, D. Schaetzl, P. Schale, M. Scheel, J. Scheuer, A. Schindler-Tyka, P. Schmidt, R. Schnabel, R. M. S. Schofield, A. Schönbeck, E. Schreiber, B. W. Schulte, B. F. Schutz, O. Schwarm, E. Schwartz, J. Scott, S. M. Scott, M. Seglar-Arroyo, E. Seidel, D. Sellers, A. S. Sengupta, N. Sennett, D. Sentenac, V. Sequino, A. Sergeev, Y. Setyawati, T. Shaffer, M. S. Shahriar, S. Sharifi, A. Sharma, P. Sharma, P. Shawhan, H. Shen, M. Shikauchi, R. Shink, D. H. Shoemaker, D. M. Shoemaker, K. Shukla, S. ShyamSundar, M. Sieniawska, D. Sigg, L. P. Singer, D. Singh, N. Singh, A. Singha, A. Singhal, A. M. Sintes, V. Sipala, V. Skliris, B. J. J. Slagmolen, T. J. Slaven-Blair, J. Smetana, J. R. Smith, R. J. E. Smith, S. N. Somala, E. J. Son, S. Soni, B. Sorazu, V. Sordini, F. Sorrentino, N. Sorrentino, R. Soulard, T. Souradeep, E. Sowell, A. P. Spencer, M. Spera, A. K. Srivastava, V. Srivastava, K. Staats, C. Stachie, D. A. Steer, J. Steinhoff, M. Steinke, J. Steinlechner, S. Steinlechner, D. Steinmeyer, G. Stolle-McAllister, D. J. Stops, M. Stover, K. A. Strain, G. Stratta, A. Strunk, R. Sturani, A. L. Stuver, J. Südbeck, S. Sudhagar, V. Sudhir, H. G. Suh, T. Z. Summerscales, H. Sun, L. Sun, S. Sunil, A. Sur, J. Suresh, P. J. Sutton, B. L. Swinkels, M. J. Szczepańczyk, M. Tacca, S. C. Tait, C. Talbot, A. J. Tanasijczuk, D. B. Tanner, D. Tao, A. Tapia, E. N. Tapia San Martin, J. D. Tasson, R. Taylor, R. Tenorio, L. Terkowski, M. P. Thirugnanasambandam, L. Thomas, M. Thomas, P. Thomas, J. E. Thompson, S. R. Thondapu, K. A. Thorne, E. Thrane, Shubhanshu Tiwari, Srishti Tiwari, V. Tiwari, K. Toland, A. E. Tolley, M. Tonelli, Z. Tornasi, A. Torres-Forné, C. I. Torrie, I. Tosta e Melo, D. Töyrä, A. T. Tran, A. Trapananti, F. Travasso, G. Traylor, M. C. Tringali, A. Tripathee, A. Trovato, R. J. Trudeau, D. S. Tsai, K. W. Tsang, M. Tse, R. Tso, L. Tsukada, D. Tsuna, T. Tsutsui, M. Turconi, A. S. Ubhi, R. P. Udall, K. Ueno, D. Ugolini, C. S. Unnikrishnan, A. L. Urban, S. A. Usman, A. C. Utina, H. Vahlbruch, G. Vajente, A. Vajpeyi, G. Valdes, M. Valentini, V. Valsan, N. van Bakel, M. van Beuzekom, J. F. J. van den Brand, C. Van Den Broeck, D. C. Vander-Hyde, L. van der Schaaf, J. V. van Heijningen, M. Vardaro, A. F. Vargas, V. Varma, S. Vass, M. Vasúth, A. Vecchio, G. Vedovato, J. Veitch, P. J. Veitch, K. Venkateswara, J. Venneberg, G. Venugopalan, D. Verkindt, Y. Verma, D. Veske, F. Vetrano, A. Viceré, A. D. Viets, A. Vijaykumar, V. Villa-Ortega, J. -Y. Vinet, S. Vitale, T. Vo, H. Vocca, C. Vorvick, S. P. Vyatchanin, A. R. Wade, L. E. Wade, M. Wade, R. M. Wald, R. C. Walet, M. Walker, G. S. Wallace, L. Wallace, S. Walsh, J. Z. Wang, S. Wang, W. H. Wang, Y. F. Wang, R. L. Ward, J. Warner, M. Was, N. Y. Washington, J. Watchi, B. Weaver, L. Wei, M. Weinert, A. J. Weinstein, R. Weiss, F. Wellmann, L. Wen, P. Weßels, J. W. Westhouse, K. Wette, J. T. Whelan, D. D. White, L. V. White, B. F. Whiting, C. Whittle, D. M. Wilken, D. Williams, M. J. Williams, A. R. Williamson, J. L. Willis, B. Willke, D. J. Wilson, M. H. Wimmer, W. Winkler, C. C. Wipf, G. Woan, J. Woehler, J. K. Wofford, I. C. F. Wong, J. Wrangel, J. L. Wright, D. S. Wu, D. M. Wysocki, L. Xiao, H. Yamamoto, L. Yang, Y. Yang, Z. Yang, M. J. Yap, D. W. Yeeles, A. Yoon, Hang Yu, Haocun Yu, S. H. R. Yuen, A. Zadrożny, M. Zanolin, T. Zelenova, J. -P. Zendri, M. Zevin, J. Zhang, L. Zhang, R. Zhang, T. Zhang, C. Zhao, G. Zhao, M. Zhou, Z. Zhou, X. J. Zhu, A. B. Zimmerman, M. E. Zucker, J. Zweizig

TL;DR

This work conducts a comprehensive suite of general relativity tests using binary black hole mergers from GWTC-2, combining residual, IMR-consistency, generation- and propagation-focused tests, remnant-ringdown analyses, echo searches, and polarization content. By employing two robust waveform families, hierarchical population modeling, and both model-dependent and template-independent methods, the study places stringent constraints on potential deviations from GR in strong-field gravity. Across 24 high-significance BBH events, the results show no evidence for beyond-GR physics, tighten bounds on dispersion and graviton mass, and find Kerr-consistent remnant properties with no postmerger echoes. The findings strengthen GR’s validity in the dynamical, strong-field regime and demonstrate the power of joint analyses over multiple events in constraining new physics, while remaining aware of calibration and waveform-systematics that will improve with future data.

Abstract

Gravitational waves enable tests of general relativity in the highly dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1 October 2019, we evaluate the consistency of the data with predictions from the theory. We first establish that residuals from the best-fit waveform are consistent with detector noise, and that the low- and high-frequency parts of the signals are in agreement. We then consider parametrized modifications to the waveform by varying post-Newtonian and phenomenological coefficients, improving past constraints by factors of ${\sim}2$; we also find consistency with Kerr black holes when we specifically target signatures of the spin-induced quadrupole moment. Looking for gravitational-wave dispersion, we tighten constraints on Lorentz-violating coefficients by a factor of ${\sim}2.6$ and bound the mass of the graviton to $m_g \leq 3.09 \times 10^{-23} \mathrm{eV}/c^2$ with 90% credibility. We also analyze the properties of the merger remnants by measuring ringdown frequencies and damping times, constraining fractional deviations away from the Kerr frequency to $δ\hat{f}_{220} = 0.03^{+0.38}_{-0.35}$ for the fundamental quadrupolar mode, and $δ\hat{f}_{221} = 0.02^{+0.29}_{-0.33}$ for the first overtone; additionally, we find no evidence for postmerger echoes. Finally, we determine that our data are consistent with tensorial polarizations through a template-independent method. When possible, we assess the validity of general relativity based on collections of events analyzed jointly. We find no evidence for new physics beyond general relativity, for black hole mimickers, or for any unaccounted systematics.

Tests of General Relativity with Binary Black Holes from the second LIGO-Virgo Gravitational-Wave Transient Catalog

TL;DR

This work conducts a comprehensive suite of general relativity tests using binary black hole mergers from GWTC-2, combining residual, IMR-consistency, generation- and propagation-focused tests, remnant-ringdown analyses, echo searches, and polarization content. By employing two robust waveform families, hierarchical population modeling, and both model-dependent and template-independent methods, the study places stringent constraints on potential deviations from GR in strong-field gravity. Across 24 high-significance BBH events, the results show no evidence for beyond-GR physics, tighten bounds on dispersion and graviton mass, and find Kerr-consistent remnant properties with no postmerger echoes. The findings strengthen GR’s validity in the dynamical, strong-field regime and demonstrate the power of joint analyses over multiple events in constraining new physics, while remaining aware of calibration and waveform-systematics that will improve with future data.

Abstract

Gravitational waves enable tests of general relativity in the highly dynamical and strong-field regime. Using events detected by LIGO-Virgo up to 1 October 2019, we evaluate the consistency of the data with predictions from the theory. We first establish that residuals from the best-fit waveform are consistent with detector noise, and that the low- and high-frequency parts of the signals are in agreement. We then consider parametrized modifications to the waveform by varying post-Newtonian and phenomenological coefficients, improving past constraints by factors of ; we also find consistency with Kerr black holes when we specifically target signatures of the spin-induced quadrupole moment. Looking for gravitational-wave dispersion, we tighten constraints on Lorentz-violating coefficients by a factor of and bound the mass of the graviton to with 90% credibility. We also analyze the properties of the merger remnants by measuring ringdown frequencies and damping times, constraining fractional deviations away from the Kerr frequency to for the fundamental quadrupolar mode, and for the first overtone; additionally, we find no evidence for postmerger echoes. Finally, we determine that our data are consistent with tensorial polarizations through a template-independent method. When possible, we assess the validity of general relativity based on collections of events analyzed jointly. We find no evidence for new physics beyond general relativity, for black hole mimickers, or for any unaccounted systematics.

Paper Structure

This paper contains 25 sections, 12 equations, 19 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Data, events, and significance
  3. Parameter inference
  4. Individual events
  5. Sets of measurements
  6. Consistency tests
  7. Residuals test
  8. Residuals test
  9. Inspiral--merger--ringdown consistency test
  10. Tests of gravitational wave generation
  11. Generic modifications
  12. Spin-induced quadrupole moment
  13. Tests of gravitational wave propagation
  14. Remnant properties
  15. Ringdown
  16. ...and 10 more sections

Figures (19)

  • Figure 1: Upper limit on the residual network SNR ($\mathrm{SNR}_{90}$) for each event, as a function of SNR recovered by the maximum-likelihood template ($\mathrm{SNR}_\mathrm{GR}$), with the corresponding $p$-value shown in color (see Table \ref{['tab:residuals']}). Solid (empty) markers indicate events detected in O3a (O1 or O2). Diamonds highlight the O3a events yielding the highest (NAMENAMEGW190727AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856FF900.92N193.0SNR904.88SNRGR11.62p_SNR900.97runO3aEventsGW190727AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856) and lowest (NAMENAMEGW190421AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856FF900.81N193.0SNR907.52SNRGR10.47p_SNR900.07runO3aEventsGW190421AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856) $p$-values, $p=\IfEqCase{p_SNR90}{{NAME}{\IfEqCase{GW190727A}{{GW190413A}{GW190413\_052954}{GW190719A}{GW190719\_215514}{GW190620A}{GW190620\_030421}{GW190514A}{GW190514\_065416}{GW190731A}{GW190731\_140936}{GW190503A}{GW190503\_185404}{GW190602A}{GW190602\_175927}{GW190929A}{GW190929\_012149}{GW190517A}{GW190517\_055101}{GW190915A}{GW190915\_235702}{GW190425A}{GW190425}{GW190512A}{GW190512\_180714}{GW190630A}{GW190630\_185205}{GW190521A}{GW190521}{GW190413B}{GW190413\_134308}{GW190924A}{GW190924\_021846}{GW190930A}{GW190930\_133541}{GW190706A}{GW190706\_222641}{GW190408A}{GW190408\_181802}{GW190909A}{GW190909\_114149}{GW190728A}{GW190728\_064510}{GW190426A}{GW190426\_152155}{GW190412A}{GW190412}{GW190720A}{GW190720\_000836}{GW190521B}{GW190521\_074359}{GW190910A}{GW190910\_112807}{GW190803A}{GW190803\_022701}{GW190519A}{GW190519\_153544}{GW190708A}{GW190708\_232457}{GW190527A}{GW190527\_092055}{GW190513A}{GW190513\_205428}{GW190424A}{GW190424\_180648}{GW190727A}{GW190727\_060333}{GW190814A}{GW190814}{GW190707A}{GW190707\_093326}{GW190828A}{GW190828\_063405}{GW190828B}{GW190828\_065509}{GW190701A}{GW190701\_203306}{GW190421A}{GW190421\_213856}}}{FF90}{0.92}{N}{193.0}{SNR90}{4.88}{SNRGR}{11.62}{p_SNR90}{0.97}{run}{O3a}{Events}{\IfEqCase{GW190727A}{{GW190413A}{GW190413\_052954}{GW190719A}{GW190719\_215514}{GW190620A}{GW190620\_030421}{GW190514A}{GW190514\_065416}{GW190731A}{GW190731\_140936}{GW190503A}{GW190503\_185404}{GW190602A}{GW190602\_175927}{GW190929A}{GW190929\_012149}{GW190517A}{GW190517\_055101}{GW190915A}{GW190915\_235702}{GW190425A}{GW190425}{GW190512A}{GW190512\_180714}{GW190630A}{GW190630\_185205}{GW190521A}{GW190521}{GW190413B}{GW190413\_134308}{GW190924A}{GW190924\_021846}{GW190930A}{GW190930\_133541}{GW190706A}{GW190706\_222641}{GW190408A}{GW190408\_181802}{GW190909A}{GW190909\_114149}{GW190728A}{GW190728\_064510}{GW190426A}{GW190426\_152155}{GW190412A}{GW190412}{GW190720A}{GW190720\_000836}{GW190521B}{GW190521\_074359}{GW190910A}{GW190910\_112807}{GW190803A}{GW190803\_022701}{GW190519A}{GW190519\_153544}{GW190708A}{GW190708\_232457}{GW190527A}{GW190527\_092055}{GW190513A}{GW190513\_205428}{GW190424A}{GW190424\_180648}{GW190727A}{GW190727\_060333}{GW190814A}{GW190814}{GW190707A}{GW190707\_093326}{GW190828A}{GW190828\_063405}{GW190828B}{GW190828\_065509}{GW190701A}{GW190701\_203306}{GW190421A}{GW190421\_213856}}}}$ and $p=\IfEqCase{p_SNR90}{{NAME}{\IfEqCase{GW190421A}{{GW190413A}{GW190413\_052954}{GW190719A}{GW190719\_215514}{GW190620A}{GW190620\_030421}{GW190514A}{GW190514\_065416}{GW190731A}{GW190731\_140936}{GW190503A}{GW190503\_185404}{GW190602A}{GW190602\_175927}{GW190929A}{GW190929\_012149}{GW190517A}{GW190517\_055101}{GW190915A}{GW190915\_235702}{GW190425A}{GW190425}{GW190512A}{GW190512\_180714}{GW190630A}{GW190630\_185205}{GW190521A}{GW190521}{GW190413B}{GW190413\_134308}{GW190924A}{GW190924\_021846}{GW190930A}{GW190930\_133541}{GW190706A}{GW190706\_222641}{GW190408A}{GW190408\_181802}{GW190909A}{GW190909\_114149}{GW190728A}{GW190728\_064510}{GW190426A}{GW190426\_152155}{GW190412A}{GW190412}{GW190720A}{GW190720\_000836}{GW190521B}{GW190521\_074359}{GW190910A}{GW190910\_112807}{GW190803A}{GW190803\_022701}{GW190519A}{GW190519\_153544}{GW190708A}{GW190708\_232457}{GW190527A}{GW190527\_092055}{GW190513A}{GW190513\_205428}{GW190424A}{GW190424\_180648}{GW190727A}{GW190727\_060333}{GW190814A}{GW190814}{GW190707A}{GW190707\_093326}{GW190828A}{GW190828\_063405}{GW190828B}{GW190828\_065509}{GW190701A}{GW190701\_203306}{GW190421A}{GW190421\_213856}}}{FF90}{0.81}{N}{193.0}{SNR90}{7.52}{SNRGR}{10.47}{p_SNR90}{0.07}{run}{O3a}{Events}{\IfEqCase{GW190421A}{{GW190413A}{GW190413\_052954}{GW190719A}{GW190719\_215514}{GW190620A}{GW190620\_030421}{GW190514A}{GW190514\_065416}{GW190731A}{GW190731\_140936}{GW190503A}{GW190503\_185404}{GW190602A}{GW190602\_175927}{GW190929A}{GW190929\_012149}{GW190517A}{GW190517\_055101}{GW190915A}{GW190915\_235702}{GW190425A}{GW190425}{GW190512A}{GW190512\_180714}{GW190630A}{GW190630\_185205}{GW190521A}{GW190521}{GW190413B}{GW190413\_134308}{GW190924A}{GW190924\_021846}{GW190930A}{GW190930\_133541}{GW190706A}{GW190706\_222641}{GW190408A}{GW190408\_181802}{GW190909A}{GW190909\_114149}{GW190728A}{GW190728\_064510}{GW190426A}{GW190426\_152155}{GW190412A}{GW190412}{GW190720A}{GW190720\_000836}{GW190521B}{GW190521\_074359}{GW190910A}{GW190910\_112807}{GW190803A}{GW190803\_022701}{GW190519A}{GW190519\_153544}{GW190708A}{GW190708\_232457}{GW190527A}{GW190527\_092055}{GW190513A}{GW190513\_205428}{GW190424A}{GW190424\_180648}{GW190727A}{GW190727\_060333}{GW190814A}{GW190814}{GW190707A}{GW190707\_093326}{GW190828A}{GW190828\_063405}{GW190828B}{GW190828\_065509}{GW190701A}{GW190701\_203306}{GW190421A}{GW190421\_213856}}}}$ respectively.
  • Figure 2: Fraction of events yielding a residuals-test $p$-value less than or equal to the abscissa. The light-blue band marks the 90%-credible region for our measurement, factoring in the uncertainty due to a finite number of both events and background instantiations (Appendix \ref{['app:res']}). The meta $p$-value for a uniform distribution is 0.39.
  • Figure 3: Results of the IMR consistency test for the selected BBH events with median $(1+z) M < 100 M_{\odot}$ (see Table \ref{['tab:imr_test_params']}). The main panel shows the 90% credible regions of the posteriors for $(\Delta M_{\rm f} / \bar{M}_{\rm f}, \Delta \chi_{\rm f} / \bar{\chi}_{\rm f})$ assuming a uniform prior, with the cross marking the expected value for GR. The side panels show the marginalized posterior for $\Delta M_{\rm f} / \bar{M}_{\rm f}$ and $\Delta \chi_{\rm f} / \bar{\chi}_{\rm f}$. The gray distribution correspond to the product of all the individual posteriors. O3a (pre-O3a) events are plotted with solid (dot--dashed) traces. Color encodes the redshifted total mass in solar masses, with a turnover between blue and red around the median of the $(1+z) M/ M_{\odot}$ distribution for the plotted events. The results for GW190412AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856 and GW190814AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856 are identified by dotted and dashed contours, respectively. The two events with contours that do not enclose the origin are GW170823 (dot--dashed) and GW190814AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856 (dashed). GW190408AGW190413AGW190413_052954GW190719AGW190719_215514GW190620AGW190620_030421GW190514AGW190514_065416GW190731AGW190731_140936GW190503AGW190503_185404GW190602AGW190602_175927GW190929AGW190929_012149GW190517AGW190517_055101GW190915AGW190915_235702GW190425AGW190425GW190512AGW190512_180714GW190630AGW190630_185205GW190521AGW190521GW190413BGW190413_134308GW190924AGW190924_021846GW190930AGW190930_133541GW190706AGW190706_222641GW190408AGW190408_181802GW190909AGW190909_114149GW190728AGW190728_064510GW190426AGW190426_152155GW190412AGW190412GW190720AGW190720_000836GW190521BGW190521_074359GW190910AGW190910_112807GW190803AGW190803_022701GW190519AGW190519_153544GW190708AGW190708_232457GW190527AGW190527_092055GW190513AGW190513_205428GW190424AGW190424_180648GW190727AGW190727_060333GW190814AGW190814GW190707AGW190707_093326GW190828AGW190828_063405GW190828BGW190828_065509GW190701AGW190701_203306GW190421AGW190421_213856 has a multimodal posterior that results in the small contour (blue) away from zero.
  • Figure 4: Distributions for the remnant mass (blue) and spin (red) fractional deviations, as obtained by hierarchically combining the results in Fig. \ref{['fig:imr_test_posteriors']} (solid trace). For comparison, we also show the result obtained using only GWTC-1 events (dot dashed trace). The probability densities summarize our expectation for the fraction of observed events with a given value of $\Delta M_{\rm f} / \bar{M}_{\rm f}$ and $\Delta \chi_{\rm f} / \bar{\chi}_{\rm f}$, as defined in Eq. \ref{['eq:inf:hier_dist']}. GR predicts no deviation on either parameter (vertical dashed line). Triangles mark the GWTC-2 medians, and vertical bars the symmetric 90%-credible intervals.
  • Figure 5: $90\%$ upper bounds on the absolute magnitude of the GR violating parameters $\delta \hat{p}_i$. The left and middle panels show the $-1$PN through $3.5$PN inspiral coefficients, while the right panel shows the postinspiral coefficients $\{\delta\hat{\beta}_i,\, \delta\hat{\alpha}_i\}$. Constraints obtained from individual events with IMRPhenomPv2 are represented by horizontal stripes, colored by the median redshifted chirp mass $(1+z)\mathcal{M}$, inferred assuming GR. Gray triangles (black wedges) mark the constraints obtained with IMRPhenomPv2 (SEOBNRv4_ROM) when all GWTC-2 events are combined assuming a shared deviation from GR. For reference, we show the equivalent results for GWTC-1 (IMRPhenomPv2) and the individual constraints from GW170817 (IMRPhenomPv2_NRTidal), as red and blue circles respectively.
  • ...and 14 more figures