Explorations in 2+1 AdS Pure Gravity: Path Integral Formulation and Partition Function Analyses in BTZ Mini-Superspace

TL;DR

This paper develops a Hamiltonian path integral approach for 2+1 AdS gravity, analyzing geometries including black holes and naked singularities, and derives entropy corrections without relying on conformal field theory.

Contribution

It introduces a novel path integral measure based on mini-superspace and computes entropy corrections for BTZ black holes and naked singularities without conformal field theory.

Findings

Derived temperature and angular potential for naked singularities.

Computed logarithmic entropy corrections for BTZ black holes.

Analyzed the sum over geometries including naked singularities.

Abstract

In this work, we employ the Hamiltonian approach to analyze the Lorentzian path integral in 2+1 AdS gravity, with an aim to sum over all possible geometries, including naked singularities and BTZ black holes, between fixed initial and final surfaces. A novel path integral measure, grounded on the metric over mini-superspace, is proposed for executing the path integral. Shifting to Euclidean geometries, we derive the temperature and angular potential of Euclidean naked singularities within the partition function. Significantly, without utilizing conformal field theory, we extract logarithmic corrections to the entropy of BTZ black holes and compute the entropy of naked singularities, along with their log corrections.