Beyond Lorentz invariance: a journey from Analogue to Hořava Gravity

In this thesis, we explore a scenario in which local Lorentz invariance is broken at high energies. This approach is primarily motivated by the pursuit of a quantum gravity theory, specifically Hořava gravity, where Lorentz violation is introduced so to achieve power-counting renormalizability. In laboratory settings, Lorentz invariance violations intersect with gravity through analogue models, where the breakdown of Lorentz symmetry is a common feature of quantum perturbations within analogue black hole geometries. Analogue experiments have successfully measured Hawking radiation, which is anticipated and deserved to remain robust despite the breakdown of Lorentz symmetry. We begin by revisiting the analogue framework, demonstrating the resilience of the Hawking effect in the presence of Lorentz symmetry breaking. Subsequently, we apply these insights to Lorentz-violating gravity models, reexamining the concept of black holes and introducing the notion of the universal horizon, a Lorentz-breaking counterpart to the traditional Killing horizon. We investigate how the evaporation of a Ho\v{r}ava gravity black hole reflects an intriguing interplay between universal horizon and the relativistic Killing horizon, highlighting a deeper connection between thermodynamics and gravity that goes beyond Lorentz invariance. This relationship is further explored in flat spacetimes by investigating the Unruh effect, where we employ a novel construction of the Rindler wedge to demonstrate that the duality between acceleration and gravity remains intact. Finally, we focus on the ultraviolet aspects of Hořava gravity, assessing its potential as a viable quantum gravity candidate and reviewing the current status in essessing its perturbative renormalizability. The overall picture that emerges is coherent: on one hand, the proposed quantum gravity theory offers a compelling theoretical appeal due to its renormalizability. On the other, the resulting phenomenology provides intriguing insights into the enduring connection between thermality and gravity.