Kerr black holes as elementary particles
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Abstract
Long ago, Newman and Janis showed that a complex deformation <i>z → z</i> + <i>ia</i> of the Schwarzschild solution produces the Kerr solution. The underlying explanation for this relationship has remained obscure. The complex deformation has an electromagnetic counterpart: by shifting the Coloumb potential, we obtain the EM field of a certain rotating charge distribution which we term <span class="mathjax-tex">\\( \\sqrt{\\mathrm{Kerr}} \\)</span>. In this note, we identify the origin of this shift as arising from the exponentiation of spin operators for the recently defined “minimally coupled” three-particle amplitudes of spinning particles coupled to gravity, in the large- spin limit. We demonstrate this by studying the impulse imparted to a test particle in the background of the heavy spinning particle. We first consider the electromagnetic case, where the impulse due to <span class="mathjax-tex">\\( \\sqrt{\\mathrm{Kerr}} \\)</span> is reproduced by a charged spinning particle; the shift of the Coloumb potential is matched to the exponentiated spin-factor appearing in the amplitude. The known impulse due to the Kerr black hole is then trivially derived from the gravitationally coupled spinning particle via the double copy.