Black hole Near Horizons through the Looking Glass

TL;DR

This paper introduces a novel Carrollian (String-Carroll) geometric framework to describe the near-horizon regions of various non-extremal black holes, providing explicit mappings and analyzing probe dynamics.

Contribution

It establishes the concept of SC geometries as a universal near-horizon structure for non-extremal black holes, with detailed mappings for multiple black hole types.

Findings

SC geometry describes near-horizon structure of non-extremal black holes

Explicit mappings for Schwarzschild, Kerr, BTZ, and Lifshitz black holes

Probe analysis confirms the geometric approach's validity

Abstract

We show that the near horizon of a generic non-extremal black hole (BH) can be understood in terms of a Carrollian geometry with two null directions, also called a String-Carroll (SC) geometry. The base space of this fibre-bundle structure is a sphere (or a plane for a black brane) and the fibre is the two-dimensional Rindler spacetime. We launch a detailed study of probes in this geometry. We study particle geodesics and scalar fields. The first part of the paper constructs geodesics and probe scalar fields directly in the SC geometry. We then look at a wide class of examples, including the Schwarzschild BH and the Kerr BH in asymptotically flat spacetimes, the BTZ BH and the black brane in AdS spacetimes, as well as Lifshitz black holes and construct the explicit maps to the SC geometry to obtain results specific to each case. These results are reproduced by considering the probe particles and fields in the original BH background and taking the near-horizon limit of the solutions. Our encyclopedia of examples establishes the notion of SC geometries as near-horizon geometries of non-extremal black objects, paving the way for a detailed, intricate future analysis of the quantum aspects of this geometry.