Greybody factors for rotating black holes in four dimensions

TL;DR

<3-5 sentences high-level summary> The paper derives and analyzes the greybody factors for scalar fields in the background of a general four-dimensional rotating black hole with four U(1) charges. It develops a detailed analytic approach by solving the angular and radial parts of the Klein-Gordon equation, and matching near-horizon and asymptotic solutions to obtain the absorption cross-sections across multiple regimes, including higher partial waves. The results reveal a Coulomb enhancement in four dimensions and connect the emission spectrum to an effective string theory with left/right moving sectors, providing a microscopic interpretation in terms of two-body and, for higher partial waves, multi-body processes. The work extends the 5D results to 4D, clarifying the conditions under which a two-body description applies and offering insights into the horizon's universal SL(2,R)×SL(2,R) structure and its implications for black hole thermodynamics and radiation.</paper_summary>

Abstract

We present the wave equation for a minimally coupled scalar field in the background of a rotating four-dimensional black hole that is parametrized by its mass, angular momentum, and four independent U(1) charges. The near horizon structure is identical to the five-dimensional case, and suggestive of an underlying description in string theory that is valid in the general non-extremal case. We calculate the greybody factors for the Hawking radiation. For sufficiently large partial wave number the emission spectrum can be calculated for general non-extremal black holes and any particle energy. We interpret this spectrum in terms of a multi-body process in an effective string theory.