Negative Komar Mass of Single Objects in Regular, Asymptotically Flat Spacetimes

TL;DR

This paper investigates axially symmetric, stationary, asymptotically flat spacetimes with black holes and rotating discs, revealing that both can have negative Komar mass despite satisfying energy conditions, and showing a transition between these objects.

Contribution

It demonstrates the existence of negative Komar mass in regular black hole and disc spacetimes, and explores the continuous transition between them.

Findings

Black holes and discs can have negative Komar mass.

Both spacetimes are regular and satisfy positive energy theorem.

Transition exists between discs and black holes with negative Komar mass.

Abstract

We study two types of axially symmetric, stationary and asymptotically flat spacetimes using highly accurate numerical methods. The one type contains a black hole surrounded by a perfect fluid ring and the other a rigidly rotating disc of dust surrounded by such a ring. Both types of spacetime are regular everywhere (outside of the horizon in the case of the black hole) and fulfil the requirements of the positive energy theorem. However, it is shown that both the black hole and the disc can have negative Komar mass. Furthermore, there exists a continuous transition from discs to black holes even when their Komar masses are negative.