Exact Collapse Solutions in D=4, N=4 Gauged Supergravity and Their Generalizations

TL;DR

This paper presents exact time-dependent solutions in four-dimensional N=4 gauged supergravity describing black hole formation and decay, including generalizations with scalar potentials, revealing instabilities in scalar-gravity systems.

Contribution

The authors construct new exact dynamical solutions in N=4 gauged supergravity, extend them with additional scalar potential terms, and analyze their higher-dimensional origins and stability.

Findings

Solutions describe decaying white holes settling into charged black holes

Extended solutions include scalar potential modifications and generalize Roberts solutions

Scalar fields can be unstable even with fixed-point potentials

Abstract

We construct an exact time-dependent solution in $D=4$, ${\cal N}=4$ gauged supergravity, where the gauge fields of the $U(1)\times U(1)$ subgroup of the $SO(4)$ carry independent conserved charges. The solution describes a decaying white hole that settles down to the final state as a static charged black hole. We analyze the global structure and lift the solution back to $D=11$ supergravity. We further extend the theory by adding an extra term in the scalar potential and obtain a more general class of collapse solutions. The result constitutes a charged generalization of the Roberts solution and the dynamical scalar-hairy black hole solutions that have been very recently found by us. The generalized Roberts solutions demonstrate that a scalar coupled to gravity can be unstable even when it is confined by a scalar potential with a fixed point.