When Isolated Horizons met Near Horizon Geometries

TL;DR

This paper explores the connection between isolated horizons and near horizon geometries in general relativity, deriving NHG from IH and highlighting a previously underrecognized link between these frameworks.

Contribution

It provides a novel derivation of near horizon geometries from isolated horizons, clarifying their relationship and filling a gap in existing literature.

Findings

Derived NHG from IH by composing spacetimes with Killing horizons.

Identified a class of solutions with extremal horizons.

Highlighted the overlooked link between IH and NHG frameworks.

Abstract

There are two mathematical relativity frameworks generalizing the black hole theory: the theory of isolated horizons (IH) and the theory of near horizon geometries (NHG). We outline here and discuss the derivation of the NHG from the theory of IH by composing spacetimes from IH. The simplest but still quite general class of solutions to Einstein's equations of this type defines spacetimes foliated by Killing horizons emanating from extremal horizons. That derivation, clearly being a link between the two frameworks, seems to be unknown to the NHG researchers and is hardly acknowledged in reviews on the IH. This lecture was a contribution to the Mathematical Structures session of the 2nd LeCosPA International Symposium "Everything about Gravity" celebrating the centenary of Einstein's General Relativity on December 14-18, 2015 in Taipei.