On the self-consistency of compact objects in Lorentz-violating gravity theories

TL;DR

This paper examines the conditions under which compact objects can exist consistently in Lorentz-violating gravity theories, revealing that many previously proposed solutions are physically invalid due to geometric constraints.

Contribution

It develops a framework to assess the physical consistency of compact objects in Lorentz-violating theories, identifying constraints that exclude certain solutions.

Findings

Many solutions in Lorentz-violating gravity are physically inadmissible.

Geometric constraints eliminate incompatible metric configurations.

The framework guides future studies of compact objects in these theories.

Abstract

Self-consistent solutions in Lorentz-violating gravity theories require the simultaneous satisfaction of: (i) the corresponding Einstein field equations, (ii) the matter field equations, and (iii) the Lorentz-violating field equations. In vacuum states, the dynamics of Lorentz-violating tensor fields may reduce to geometric constraints, potentially precluding entire classes of compact objects. These constraints are crucial for ensuring physical consistency in Lorentz-violating frameworks, as they eliminate metric families incompatible with the anisotropies induced by spontaneous Lorentz symmetry breaking. We investigate the criteria governing the emergence of these geometric constraints and analyze their consequences. Our analysis establishes a consistency framework for evaluating compact objects in these theories, demonstrating that several previously reported solutions in Lorentz-violating gravity models are physically inadmissible.