Poincare recurrences of Schwarzschild black holes

TL;DR

This paper explores how quantum effects near a Schwarzschild black hole horizon induce Poincare recurrences in Green functions, suggesting modifications in near-horizon geometry consistent across various models.

Contribution

It demonstrates that quantum-induced modifications to the effective potential near the horizon lead to Poincare recurrences, independent of specific potential modifications.

Findings

Quantum effects alter the effective potential near the horizon.

Poincare recurrences emerge in Green functions due to these modifications.

Results are consistent across different near-horizon models.

Abstract

We discuss massive scalar perturbations of a Schwarzschild black hole. We argue that quantum effects alter the effective potential near the horizon resulting in Poincare recurrences in Green functions. Results at the semi-classical level are independent of the details of the modification of the potential provided its minimum near the horizon is inversely proportional to the square of the Poincare time. This modification may be viewed as a change in the near-horizon geometry. We consider explicitly the examples of a brick wall, a smooth cutoff and a wormhole-like modification showing that they all lead to the same results at leading order.