Generalized Painlev\'e-Gullstrand metrics

TL;DR

This paper introduces generalized Painleve-Gullstrand metrics that avoid horizon obstructions and can be derived via Lorentz boosts, improving the understanding of black hole horizon regularity and Hawking radiation calculations.

Contribution

It presents new generalized PG metrics that are regular at horizons and derived from standard metrics through Lorentz boosts, addressing previous obstructions.

Findings

Obstruction to spatially flat PG slicings demonstrated.

Generalized PG metrics introduced that remain regular at horizons.

These metrics help avoid problematic contributions in Hawking radiation derivations.

Abstract

An obstruction to the implementation of spatially flat Painleve-Gullstrand(PG) slicings is demonstrated, and explicitly discussed for Reissner-Nordstrom and Schwarzschild-anti-deSitter spacetimes. Generalizations of PG slicings which are not spatially flat but which remain regular at the horizons are introduced. These metrics can be obtained from standard spherically symmetric metrics by physical Lorentz boosts. With these generalized PG metrics, problematic contributions to the imaginary part of the action in the Parikh-Wilczek derivation of Hawking radiation due to the obstruction can be avoided.