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Can the Near-Horizon Black Hole Memory be detected through Binary Inspirals?

Sajad A. Bhat, Srijit Bhattacharjee, Shasvath J. Kapadia

TL;DR

The paper addresses whether near-horizon memory associated with BMS-like supertranslations could be inferred from gravitational-wave observations. It develops two detection scenarios in which an IMBBH near a supermassive black hole experiences a memory-induced change in its orbital separation, imprinting a discrete frequency shift on its GW signal; this imprint is analyzed using a Newtonian to 3.5PN framework and a discrete time shift model. Bayesian parameter estimation and model selection are employed to quantify the detectability, showing large Bayes factors (up to ~10^5) for plausible parameter choices, with enhanced prospects near extremal Kerr horizons. The work highlights a principled, though idealized, path to probing horizon symmetries with space-based GW detectors like LISA and points to future extensions involving EMRIs and more realistic environmental modeling.

Abstract

The memory effect, in the context of gravitational-waves (GWs), manifests itself in the permanent relative displacement of test masses when they encounter the GWs. A number of works have explored the possibility of detecting the memory when the source and detector are separated by large distances. A special type of memory, arising from BMS symmetries, called ``black-hole memory'', has been recently proposed. The black hole memory only manifests itself in the vicinity of its event horizon. Therefore, formally observing it requires placing a GW detector at the horizon of the BH, which prima-facie seems unfeasible. In this work, we describe a toy model that suggests a possible way the black hole memory may be observed, without requiring a human-made detector near the event horizon. The model considers a binary black hole (BBH), emanating GWs observable at cosmological distances, as a proxy for an idealized detector in the vicinity of a supermassive Schwarzschild black hole that is endowed with a supertranslation hair by sending a shock-wave to it. This sudden change affects the geometry near the horizon of the supertranslated black hole and it induces a change in the inspiraling orbital separation (and hence, orbital frequency) of the binary, which in turn imprints itself on the GWs. Using basic GW data analysis tools, we demonstrate that the black hole memory should be observable by a LISA-like space-based detector.

Can the Near-Horizon Black Hole Memory be detected through Binary Inspirals?

TL;DR

The paper addresses whether near-horizon memory associated with BMS-like supertranslations could be inferred from gravitational-wave observations. It develops two detection scenarios in which an IMBBH near a supermassive black hole experiences a memory-induced change in its orbital separation, imprinting a discrete frequency shift on its GW signal; this imprint is analyzed using a Newtonian to 3.5PN framework and a discrete time shift model. Bayesian parameter estimation and model selection are employed to quantify the detectability, showing large Bayes factors (up to ~10^5) for plausible parameter choices, with enhanced prospects near extremal Kerr horizons. The work highlights a principled, though idealized, path to probing horizon symmetries with space-based GW detectors like LISA and points to future extensions involving EMRIs and more realistic environmental modeling.

Abstract

The memory effect, in the context of gravitational-waves (GWs), manifests itself in the permanent relative displacement of test masses when they encounter the GWs. A number of works have explored the possibility of detecting the memory when the source and detector are separated by large distances. A special type of memory, arising from BMS symmetries, called ``black-hole memory'', has been recently proposed. The black hole memory only manifests itself in the vicinity of its event horizon. Therefore, formally observing it requires placing a GW detector at the horizon of the BH, which prima-facie seems unfeasible. In this work, we describe a toy model that suggests a possible way the black hole memory may be observed, without requiring a human-made detector near the event horizon. The model considers a binary black hole (BBH), emanating GWs observable at cosmological distances, as a proxy for an idealized detector in the vicinity of a supermassive Schwarzschild black hole that is endowed with a supertranslation hair by sending a shock-wave to it. This sudden change affects the geometry near the horizon of the supertranslated black hole and it induces a change in the inspiraling orbital separation (and hence, orbital frequency) of the binary, which in turn imprints itself on the GWs. Using basic GW data analysis tools, we demonstrate that the black hole memory should be observable by a LISA-like space-based detector.
Paper Structure (10 sections, 38 equations, 5 figures)

This paper contains 10 sections, 38 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Implantation of memory and its detection
  3. Memory for a non-rotating Black Hole
  4. A toy detection model
  5. A more realistic model
  6. Frequency modulation of the binary
  7. Bayesian Parameter Inference
  8. Model selection
  9. Results
  10. Conclusion

Figures (5)

  • Figure 1: Schematic representation of inspiralling IMBBH source emitting GWs in the vicinity of the horizon of a bald SMBH (on the left). Once the supertranslation (ST) 'hair' is attached to the bald SMBH due to some astrophysical shock wave, the proper distance between the components of the IMBBH is changed. The magnitude of the change in separation (ST memory) denoted by $\Delta L$ is given by Eqs. ( \ref{['memory-sch']},\ref{['memory-kerr']}). As the IMBBH separation increases (decreases), the binary will start emitting GWs at a lower (higher) frequency in comparison to the initial configuration (on the left).
  • Figure 2: The evolution of the characteristic (dimensionless) strain Moore:2014lga (inclination-averaged) of three representative IMBBH sources with equal-mass components (solid lines) shown in comparison to the characteristic (dimensionless) strain corresponding to the noise PSD of LISA (dashed curve). Luminosity distance of the IMBBH sources is fixed at $3$ Gpc. The red markers denote the GW strain and GW frequency of the IMBBH sources at the corresponding ISCO. The blue markers at $f_{\rm ref} = 4\, {\rm mHz}$ denote the time till ISCO. The black markers represent the characteristic strain, and GW frequency, $T_{\rm obs} = 4$ years before ISCO.
  • Figure 3: The Log-Bayes-Factor$({\rm ln \mathcal{B}}^{\rm b}_{\rm a})$ to determine whether the model of GWs with (b)/without (a) imprints of black hole memory for Schwarzschild black hole is preferred, is shown in the color scale. These Bayes factors are evaluated on a grid of total binary mass ($M_{\rm bin}$) and mass of supermassive black hole ($M$). GW frequency corresponding to the time when supertranslation hair is imparted to SMBH is fixed at $f_{\rm ref}=3\, {\rm mHz}$ (top row) or $f_{\rm ref}=8\, {\rm mHz}$ (bottom row). Dimensionless supertranslation charge $q_0$ is varied from left ($q_0= 10^{-8}$) to right ($q_0= 10^{-5}$) panels as shown. This figure corresponds to the case when ST memory leads to an increase (corresponding to $\cos(2\theta)= -1$ in Eq. \ref{['memory-sch']}) in binary separation.
  • Figure 4: Same as Figure \ref{['BF-positive-fref-fixed-sch']} but for extremal Kerr black hole (redshift $z_g=-0.4$) and this Figure corresponds to the case when ST memory leads to an increase (corresponding to $\cos(2\theta)= 0$ and $\cos(\phi)= 1$ in Eq. \ref{['memory-kerr']} ) in binary separation.
  • Figure 5: Same as Figure \ref{['BF-positive-fref-fixed-sch']} but for extremal Kerr black hole (redshift $z_g=0.7$) and this Figure corresponds to the case when ST memory leads to an increase (corresponding to $\cos(2\theta)= 0$ and $\cos(\phi)= 1$ in Eq. \ref{['memory-kerr']} ) in binary separation.