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.
Highlights
In the presence of extra massless fields, the stress-energy tensor will be modified at 1 post Minkowskian (PM)
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
Summary
The one-particle effective action aims to give an effective description of the gravitational or electromagnetic coupling for a compact source. Just as the Kerr-metric, the vector potential for Kerr-Newman can be written as an differential operator acting on the vector potential of a point source in flat space. As the latter corresponds to a point charge on the world-line minimally coupled to the Maxwell field, euμAμ, one can straightforwardly obtain the Kerr-Newman world-line action. We compute the three-point amplitude from this action and demonstrate that it matches with minimal coupling of spinning particles This is analogous to the situation for Kerr BHs [5, 20]. The expression will be later matched to a corresponding computation using QFT techniques
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