Multiple Killing Horizons: the initial value formulation for $\Lambda$-vacuum

TL;DR

This paper studies the formation of Multiple Killing Horizons in vacuum spacetimes with a cosmological constant, using characteristic initial value problems and proposing a more general Near Horizon Geometry definition.

Contribution

It introduces a new framework for analyzing Multiple Killing Horizons via characteristic initial value problems and generalizes the Near Horizon Geometry concept to include fixed points.

Findings

Characterization of Multiple Killing Horizons in vacuum with cosmological constant

Development of initial value problem approach for horizon emergence

Generalized Near Horizon Geometry definition including fixed points

Abstract

In Class. Quantum Grav. 35 (2018) 155015 we have introduced the notion of "Multiple Killing Horizon" and analyzed some of its general properties. Multiple Killing Horizons are Killing horizons for two or more linearly independent Killing vectors simultaneously. In this paper we focus on the vacuum case, possibly with cosmological constant, and study the emergence of Multiple Killing Horizons in terms of characteristic initial value problems for two transversally intersecting null hypersurfaces. As a relevant outcome, a more general definition of Near Horizon Geometry is put forward. This new definition avoids the use of Gaussian null coordinates associated to the corresponding degenerate Killing vector and thereby allows for inclusion of its fixed points.