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Binary dynamics from Einstein-Maxwell theory at second post-Newtonian order using effective field theory

Pawan Kumar Gupta

TL;DR

The paper addresses the problem of incorporating charges into the conservative two-body dynamics of binary black holes at second post-Newtonian order. It employs an effective field theory approach (NRGR) with a temporal Kaluza–Klein (NRG) decomposition to derive the 2PN Lagrangian for Einstein–Maxwell theory, using Feynman diagrams and dimensional regularization to handle loop integrals. The authors recover the Coulomb potential at leading order, reproduce the known 1PN charged-gravity results, and provide a comprehensive 2PN Lagrangian that includes q^2 v^4, G q^2 v^2, G q^4, and G^2 q^2 contributions, validated against known EM and GR limits. The work demonstrates the efficiency and consistency of the EFT/NRG framework for high-precision conservative binary dynamics with charge, with implications for constraining charges on astrophysical binaries from gravitational-wave observations.

Abstract

The detection of gravitational waves from binary black holes sources has opened the possibility to search for electric charges and "dark" charges on black holes, the latter being candidates for dark matter. This requires theoretical predictions about the effect of charges on the inspiral of binary black holes in order to place constraint on charges. The effects of these charges on the inspiral of binary black holes can be described using Einstein-Maxwell theory. They have previously been derived up to first post-Newtonian (1PN) order, and the results were recently used to place bounds on the charge-to-mass ratio on black holes. Here we use the effective field theory approach with a metric parameterization based on a temporal Kaluza-Klein decomposition with non-relativistic gravitational fields to arrive at the Lagrangian for binary motion under the influence of charges up to 2PN order.

Binary dynamics from Einstein-Maxwell theory at second post-Newtonian order using effective field theory

TL;DR

The paper addresses the problem of incorporating charges into the conservative two-body dynamics of binary black holes at second post-Newtonian order. It employs an effective field theory approach (NRGR) with a temporal Kaluza–Klein (NRG) decomposition to derive the 2PN Lagrangian for Einstein–Maxwell theory, using Feynman diagrams and dimensional regularization to handle loop integrals. The authors recover the Coulomb potential at leading order, reproduce the known 1PN charged-gravity results, and provide a comprehensive 2PN Lagrangian that includes q^2 v^4, G q^2 v^2, G q^4, and G^2 q^2 contributions, validated against known EM and GR limits. The work demonstrates the efficiency and consistency of the EFT/NRG framework for high-precision conservative binary dynamics with charge, with implications for constraining charges on astrophysical binaries from gravitational-wave observations.

Abstract

The detection of gravitational waves from binary black holes sources has opened the possibility to search for electric charges and "dark" charges on black holes, the latter being candidates for dark matter. This requires theoretical predictions about the effect of charges on the inspiral of binary black holes in order to place constraint on charges. The effects of these charges on the inspiral of binary black holes can be described using Einstein-Maxwell theory. They have previously been derived up to first post-Newtonian (1PN) order, and the results were recently used to place bounds on the charge-to-mass ratio on black holes. Here we use the effective field theory approach with a metric parameterization based on a temporal Kaluza-Klein decomposition with non-relativistic gravitational fields to arrive at the Lagrangian for binary motion under the influence of charges up to 2PN order.
Paper Structure (19 sections, 86 equations, 6 figures, 1 table)

This paper contains 19 sections, 86 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. EINSTEIN-MAXWELL THEORY
  3. Point Particle Action
  4. Charged Particle Action
  5. Einstein-Hilbert Action
  6. Electromagnetic action
  7. Power counting and Feynman diagrams
  8. Coulomb Potential
  9. 1 PN order Potential
  10. $q^2v^2$ order diagrams
  11. $Gq^2$ order diagrams
  12. 2PN order
  13. $q^2v^4$ order diagrams
  14. $Gq^2v^2$ order diagrams
  15. $Gq^4$ order diagrams
  16. ...and 4 more sections

Figures (6)

  • Figure 1: Diagram (a) shows the Coulomb interaction at $\mathcal{O}(q^2)$
  • Figure 2: Diagrams (b) and (c) are 1PN corrections at $\mathcal{O}(q^2v^2)$, and the rest of the diagrams are also 1PN corrections at $\mathcal{O}(Gq^2)$
  • Figure 3: Diagrams that have $\mathcal{O}(q^2v^4)$ and time derivatives.
  • Figure 4: Diagrams that have $\mathcal{O}(Gq^2v^2)$.
  • Figure 5: Diagrams that have $\mathcal{O}(Gq^4)$.
  • ...and 1 more figures