Ijaz Durrani
In this paper, we investigate the geometry of black hole solutions within the framework of Lorentz-violating gravity theories, where local Lorentz invariance is not preserved at high energies or in the ultraviolet regime. Motivated by attempts to reconcile gravity with quantum theory and address the hierarchy problem, we explore black hole metrics arising in EinsteinÆther theory and Ho�?ava-Lifshitz gravity. The resulting spacetimes exhibit modified horizons, causal structures, and thermodynamics. The geometry is deeply influenced by preferred-frame effects and higher-derivative operators, challenging the classical picture of event horizons and singularities. We also discuss the potential observational signatures of such deviations, particularly in the context of gravitational wave echoes and modified shadow profiles.