Counting a black hole in Lorentzian product triangulations

Details Counting a black hole in Lorentzian product triangulations Counting a black hole in Lorentzian product triangulations

2005-06-06

arxiv.org/abs/gr-qc/0506035v1

Class.Quant.Grav. 23 (2006) 3849-3878

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

42 pages, 11 figures

Scientific paper

10.1088/0264-9381/23/11/012

We take a step toward a nonperturbative gravitational path integral for black-hole geometries by deriving an expression for the expansion rate of null geodesic congruences in the approach of causal dynamical triangulations. We propose to use the integrated expansion rate in building a quantum horizon finder in the sum over spacetime geometries. It takes the form of a counting formula for various types of discrete building blocks which differ in how they focus and defocus light rays. In the course of the derivation, we introduce the concept of a Lorentzian dynamical triangulation of product type, whose applicability goes beyond that of describing black-hole configurations.

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