# Pulsation of black holes

## TL;DR

This paper investigates how quantum gravity effects can cause black holes to pulsate instead of forming singularities, potentially observable through gravitational waves in non-spherical cases.

## Contribution

It introduces a model of pulsating black holes using loop quantum cosmology and braneworld corrections, avoiding singularities and describing horizon dynamics.

## Key findings

- Black holes can pulsate between maximum and minimum sizes.
- Quantum effects replace singularities with oscillatory behavior.
- Gravitational waves may reveal black hole pulsations in non-spherical cases.

## Abstract

The Hawking-Penrose singularity theorem states that a singularity forms inside a black hole in general relativity. To remove this singularity one must resort to a more fundamental theory. Using a corrected dynamical equation arising in loop quantum cosmology and braneworld models, we study the gravitational collapse of a perfect fluid sphere with a rather general equation of state. In the frame of an observer comoving with this fluid, the sphere pulsates between a maximum and a minimum size, avoiding the singularity. The exterior geometry is also constructed. There are usually an outer and an inner apparent horizon, resembling the Reissner-Nordstr\"om situation. For a distant observer the {horizon} crossing occurs in an infinite time and the pulsations of the black hole quantum "beating heart" are completely unobservable. However, it may be observable if the black hole is not spherical symmetric and radiates gravitational wave due to the quadrupole moment, if any.