Black holes in Lorentz gauge theory

TL;DR

This paper investigates black hole solutions within the Lorentz gauge theory of gravity, revealing multiple phases with distinct properties and exploring their implications for black hole structure and singularities.

Contribution

It introduces new black hole solutions in Lorentz gauge theory across different phases, including general vacuum, charged, and symmetry-broken configurations.

Findings

In the SO(3) phase, vacuum solutions are characterized by two parameters, one related to mass.

The SO(1,2) phase yields Schwarzschild solutions with unique horizon properties.

Symmetry-broken phases are incompatible with black hole solutions.

Abstract

Black hole solutions are explored in the Lorentz gauge theory of gravity. The fields of the theory are the gauge potential in the adjoint and a scalar in the fundamental representation of the Lorentz group, a metric tensor then emerging as a composite field in a symmetry-broken phase. Three distinct such phases of the theory are considered. In an SO(3) phase, the fundamental field is identified with a generalised Painlev\'e-Gullstrand-Lema\^itre coordinate time. In the static spherically symmetric case it is a stealth scalar, and the general vacuum solution is then parameterised by two constants, one related to the black hole mass and the other to an observer. Also, formulations of pregeometric first order electromagnetism are considered in order to construct a consistent realisation of a charged black hole. In an SO(1,2) phase of the theory, the Schwarzschild solution is realised as a configuration wherein the fundamental field is real outside and imaginary inside the horizon. In this phase the field can be associated with an effective radial pressure resulting in additional singularities and asymptotic non-flatness. Finally, a symmetry-broken phase which would correspond to solutions in an alternative attempt at a Lorentz gauge theory is shown to be incompatible with black holes.