# Radiations From Geometries Using Painlev\'e-Gullstrand Coordinates

## TL;DR

This paper investigates quantum radiation phenomena in curved geometries using Painlevé-Gullstrand coordinates, revealing how different observer frames perceive radiation near black holes and their relation to flat spacetime scenarios.

## Contribution

It provides a covariant analysis of quantum effects in non-singular geometries and compares perceptions of radiation between stationary and freely-falling observers.

## Key findings

- Observer-dependent radiation detection consistent with flat spacetime analogs.
- Differences in descriptions depend only on local proper accelerations.
- Radiation perceptions vanish for distant observers away from the horizon.

## Abstract

The principle of equivalence is used to examine covariant descriptions of quantum phenomena within the global exterior of geometries described using Painlev\'e- Gullstrand coordinates, which are everywhere non-singular away from their center. The differences between the descriptions of observers stationary within the curvilinear geometry and those in a locally-flat freely-falling system that is momentarily at rest are found to depend only on local proper accelerations, becoming vanishingly small for increasingly distant observers. Away from the horizon, the local detections of outgoing massless radiations from the ground state of the freely-falling observers are found to be consistent with those of Rindler observers accelerating in flat space-time.