Regular Poisson structures on massive non-rotating BTZ black holes

TL;DR

This paper explores the geometric and Poisson structures of non-rotating massive BTZ black holes, revealing intrinsic symplectic structures and providing a global metric expression for their dynamical evolution.

Contribution

It introduces a novel application of symmetric space techniques to characterize Poisson structures on BTZ black holes and derives a global metric expression for their dynamics.

Findings

Every non-rotating massive BTZ black hole space has an intrinsic regular Poisson structure.

The symplectic leaves of these structures are para-hermitian symmetric surfaces.

A global metric expression describes the black hole's evolution from initial to final singularity.

Abstract

We revisit the non-rotating massive BTZ black hole within a pseudo-Riemannian symmetric space context. Using classical symmetric space techniques we find that every such space intrinsically carries a regular Poisson structure whose symplectic leaves are para-hermitian symmetric surfaces. We also obtain a global expression of the metric yielding a dynamical description of the black hole from its initial to its final singularity.