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. Lorentz symmetry breaking can emerge spontaneously when tensor fields acquire nonzero vacuum expectation values. When frozen in these vacuum states, the dynamics of Lorentz-violating tensor fields may reduce to geometric constraints, potentially ruling out 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 preferred spacetime directions emerging from 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.

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• Alternative gravity theories
• Gravitation