A Topological Origin of Black Hole Mass

TL;DR

This paper proposes that black hole mass can be understood as a topological charge derived from new vacuum solutions in gravity, linking the photon sphere to topological properties.

Contribution

It introduces bubble spacetimes in first order gravity, revealing a topological interpretation of the photon sphere and phase boundaries in black hole analogs.

Findings

The boundary surface of static bubbles has a universal topological number.

The photon sphere coincides with the topological boundary in these solutions.

Event horizon boundaries are shown to be topologically trivial.

Abstract

We show that the notion of a black hole mass could be superceded by that of a topological charge in a spacetime without matter and curvature singularity. This feature emerges through a set new spacetime solutions of first order gravity in vacuum, named as bubble spacetimes, constructed here by weaving together the degenerate and nondegenerate metric phases. For a static bubble, the boundary surface connecting the two phases is characterized by a universal topological number. Notably, this surface coincides with the photon sphere of the conventional black hole irrespective of the presence of the cosmological constant. In contrast, a phase boundary located at the event horizon is shown to be topologically trivial. Thus, along with the black hole mass, the photon sphere also acquires a topological interpretation.