Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory

TL;DR

This paper investigates gravitational collapse in a minimally modified gravity theory, VCDM, revealing a black hole formation process with a static interior and a need for UV completion, while maintaining consistency with large-scale cosmology.

Contribution

It demonstrates how black hole formation occurs in VCDM, a minimally modified gravity theory, showing a specific collapse foliation and the implications for UV completion and cosmological consistency.

Findings

Collapse leads to a static interior with a vanishing lapse at a finite radius.

The endpoint of collapse occurs in infinite cosmological time.

VCDM can describe the universe's large-scale evolution despite the shadowy mode.

Abstract

We study the spherically symmetric collapse of a cloud of dust in VCDM, a class of gravitational theories with two local physical degrees of freedom. We find that the collapse corresponds to a particular foliation of the Oppenheimer-Snyder solution in general relativity (GR) which is endowed with a constant trace for the extrinsic curvature relative to the time $t$ constant foliation. For this solution, we find that the final state of the collapse leads to a static configuration with the lapse function vanishing at a radius inside the apparent horizon. Such a point is reached in an infinite time-$t$ interval, $t$ being the cosmological time, i.e. the time of an observer located far away from the collapsing cloud. The presence of this vanishing lapse endpoint implies the necessity of a UV completion to describe the physics inside the resulting black hole. On the other hand, since the corresponding cosmic time $t$ is infinite, VCDM can safely describe the whole history of the universe at large scales without knowledge of the unknown UV completion, despite the presence of the so-called shadowy mode.