Dynamical black holes with prescribed masses in spherical symmetry

TL;DR

This paper constructs spherically symmetric black hole solutions with prescribed initial and final Bondi masses, using Einstein-scalar field equations, and extends previous methods to handle large data and mass transitions.

Contribution

It introduces a method to produce global solutions with specified mass properties, advancing understanding of black hole formation and mass dynamics in spherical symmetry.

Findings

Existence of solutions with prescribed initial and final Bondi masses

Extension of Christodoulou's short pulse method to large data regimes

Approximate control of mass transition within an error margin

Abstract

We review our recent work on a construction of spherically symmetric global solutions to the Einstein--scalar field system with large bounded variation norms and large Bondi masses. We show that similar ideas, together with Christodoulou's short pulse method, allow us to prove the following result: Given $M_i \geq M_f>0$ and $\epsilon>0$, there exists a spherically symmetric (black hole) solution to the Einstein--scalar field system such that up to an error of size $\epsilon$, the initial Bondi mass is $M_i$ and the final Bondi mass is $M_f$. Moreover, if one assumes a continuity property of the final Bondi mass (which in principle follows from known techniques in the literature), then for $M_i>M_f>0$, the above result holds without an $\epsilon$-error.