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