Merger Transitions in Brane--Black-Hole Systems: Criticality, Scaling, and Self-Similarity

TL;DR

This paper introduces a toy model to study phase transitions in brane-black-hole systems, revealing critical behavior and self-similarity akin to known gravitational phenomena like Choptuik collapse.

Contribution

It presents a simplified model capturing the critical merger transition in brane-black-hole systems, highlighting similarities with other gravitational phase transitions.

Findings

Existence of a critical solution at the merger threshold

Demonstration of self-similarity in the transition

Analogies with Choptuik critical collapse and black-string transitions

Abstract

We propose a toy model for study merger transitions in a curved spaceime with an arbitrary number of dimensions. This model includes a bulk N-dimensional static spherically symmetric black hole and a test D-dimensional brane interacting with the black hole. The brane is asymptotically flat and allows O(D-1) group of symmetry. Such a brane--black-hole (BBH) system has two different phases. The first one is formed by solutions describing a brane crossing the horizon of the bulk black hole. In this case the internal induced geometry of the brane describes D-dimensional black hole. The other phase consists of solutions for branes which do not intersect the horizon and the induced geometry does not have a horizon. We study a critical solution at the threshold of the brane-black-hole formation, and the solutions which are close to it. In particular, we demonstrate, that there exists a striking similarity of the merger transition, during which the phase of the BBH-system is changed, both with the Choptuik critical collapse and with the merger transitions in the higher dimensional caged black-hole--black-string system.