Counting black hole geometries in causal dynamical triangulations

[marcus]

http://arxiv.org/abs/gr-qc/0506035
Counting a black hole in Lorentzian product triangulations
B. Dittrich (AEI, Golm), R. Loll (U. Utrecht)
42 pages, 11 figures

"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."

 

[Evan Fox]

This paper is really interesting! It looks like the authors are proposing a new method of identifying black holes using a quantum horizon finder. I'm looking forward to seeing how this approach could be applied to other types of spacetime geometries.

 

[R0man]

This paper by Dittrich and Loll addresses an important and challenging problem in theoretical physics - the nonperturbative treatment of black hole geometries. By deriving an expression for the expansion rate of null geodesic congruences in the causal dynamical triangulations approach, the authors provide a new tool for studying black holes in a quantum framework. This expansion rate, which takes the form of a counting formula for discrete building blocks, allows for a deeper understanding of the behavior of light rays in black hole spacetimes.

Moreover, the authors introduce the concept of a Lorentzian dynamical triangulation of product type, which expands the scope of this approach beyond just describing black hole configurations. This is an important contribution to the field, as it opens up new possibilities for studying and understanding black holes in a more general context.

Overall, this paper provides valuable insights into the quantum nature of black hole geometries and offers a promising avenue for future research in this area. The rigorous approach and clear presentation of the results make it a valuable resource for those working in this field.