Collapse to Black Holes in Brans-Dicke Theory: II. Comparison with General Relativity

TL;DR

This paper compares black hole formation in Brans-Dicke theory with general relativity, revealing differences in dynamical evolution and horizon behavior, including horizon crossing and area decrease, due to violations of classical energy conditions.

Contribution

It demonstrates that dynamical black holes in Brans-Dicke theory can differ significantly from those in general relativity, especially during collapse, due to violations of energy conditions.

Findings

Black holes in Brans-Dicke theory match GR in final state

During collapse, apparent horizons can pass outside event horizons

Event horizon area can decrease over time in Brans-Dicke spacetimes

Abstract

We discuss a number of long-standing theoretical questions about collapse to black holes in the Brans-Dicke theory of gravitation. Using a new numerical code, we show that Oppenheimer-Snyder collapse in this theory produces black holes that are identical to those of general relativity in final equilibrium, but are quite different from those of general relativity during dynamical evolution. We find that there are epochs during which the apparent horizon of such a black hole passes {\it outside\/} the event horizon, and that the surface area of the event horizon {\it decreases\/} with time. This behavior is possible because theorems which prove otherwise assume $R_{ab}l^al^b \ge 0$ for all null vectors $l^a$. We show that dynamical spacetimes in Brans-Dicke theory can violate this inequality, even in vacuum, for any value of $\omega$.