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Kerr-Newman stress-tensor from minimal coupling

Ming-Zhi Chung, Yu-tin Huang, Jung-Wook Kim

Abstract

In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the "minimal coupling" for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

Kerr-Newman stress-tensor from minimal coupling

Abstract

In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the "minimal coupling" for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

Paper Structure

This paper contains 20 sections, 82 equations, 2 figures.

Table of Contents

  1. Introduction and conclusion
  2. EM minimal coupling and the Kerr-Newman one-particle EFT
  3. The one-particle EFT for Kerr-Newman
  4. Stress tensor of Kerr-Newman solution
  5. Matching with the metric
  6. Matching $\mathcal{O}(GQ^2)$ impulse
  7. Impulse from geodesic equation
  8. Impulse from amplitude
  9. Kerr-Newman stress tensor from form factors
  10. Kinematical set-up
  11. Evaluating the integrand
  12. Comparison with classical computations
  13. Computing $\Delta_{\mu\nu} P^\mu P^\nu$
  14. Computing $\Delta_{\mu\nu} P^\mu E^\nu$
  15. Computing $\Delta_{\mu\nu} E^\mu E^\nu$
  16. ...and 5 more sections

Figures (2)

  • Figure 1: Contributions to the 1 PM stress tensor form factor. The purely gravitational contribution is given by the tree-level gravitational minimal coupling, while the photon couplings contribute through one-loop effects. Since the charge appears as $Q^2G$, the one-loop diagram is still 1 PM.
  • Figure 2: (a) The scattering plane. The Kerr-Newman black hole of mass $M$, charge $Q$ and spin $a$ is centered at the origin. The scalar test particle of mass $m$ and charge $q$ is moving with initial proper velocity $u_1$ and the impact parameter is aliged with the $x$ axis. (b) The Feynman diagram needed to compute the impulse via amplitude method.