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 black hole 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.

A worldsheet for Kerr

“…As an example, we compute the leading impulse on a probe particle with mass, spin and NUT charge moving in a Kerr-Taub-NUT background. The charged generalisation of the NJ complex map can similarly be connected to the behaviour of three-point amplitudes in the classical limit [98][99][100][101][102][103], and we will reproduce results recently derived from this perspective [102], furthermore calculating the leading angular impulse (i.e. the change in spin during scattering) for the first time.…”

Quadratic-in-spin Hamiltonian at $$ \mathcal{O} $$(G2) from scattering amplitudes

“…Refs. [92][93][94][95][96][97] applied the definition of minimal coupling of [84] to classical solutions. In this way they made contact with the classical double copy of ref.…”

Minimal spin deflection of Kerr-Newman and supersymmetric black hole

“…Note that when we count the powers of G, the eikonal phase up to linear order in G would require the computation of both tree and 1-loop amplitudes, because the GQ 2 dependent piece in the Kerr-Newman metric comes from a one-loop amplitude as shown JHEP10(2021)011 in [34]. However, we are near the extremal limit where Q i ∼ √ Gm i , so the tree level photon exachange amplitude scales as…”

“…It was shown in [34] that Kerr-Newman black holes minimal couples to both graviton and photon. Here we construct the O(G 1 ) eikonal phase of two KN black hole scattering with tunable charge to mass ratio defined as…”

“…For the former, the tunable parameter is the charge while for the latter is the central charge. For Kerr-Newman, it was shown in [29,34], that the 1 PM spin-multipoles are given by gravitational and electro-magentic minimal coupling. We analyze the corresponding eikonal phase in the near extremal limit.…”