Dynamical apparent horizons in inhomogeneous Brans-Dicke universes

TL;DR

This paper investigates the behavior of apparent horizons in inhomogeneous Brans-Dicke universes, revealing multiple evolving horizons, their mergers, and the conditions under which naked singularities can form.

Contribution

It introduces and analyzes a family of spherically symmetric, time-dependent solutions in Brans-Dicke gravity with multiple evolving horizons and horizon mergers.

Findings

Presence of multiple evolving apparent horizons.

Horizon mergers can lead to naked singularities.

Explicit limits to general relativity and static solutions.

Abstract

The presence and evolution of apparent horizons in a two-parameter family of spherically symmetric, time-dependent solutions of Brans-Dicke gravity are analyzed. These solutions were introduced to model space- and time-varying gravitational couplings and are supposed to represent central objects embedded in a spatially flat universe. We find that the solutions possess multiple evolving apparent horizons, both black hole horizons covering a central singularity and cosmological ones. It is not uncommon for two of these horizons to merge, leaving behind a naked singularity covered only by a cosmological horizon. Two characteristic limits are also explicitly worked out: the limit where the theory reduces to general relativity and the limit where the solutions become static. The physical relevance of this family of solutions is discussed.