This thesis explores two avenues into understanding the physics of black holes and horizons beyond general relativity, via analogue models and Lorentz violating theories. Analogue spacetimes have wildly different dynamics to general relativity; this means time-independent black hole solutions have fewer symmetries, allowing the possibility of non-Killing horizons in stationary solutions. Surface gravity is one of the most important quantities characterizing black holes, with many physically distinct definitions. In the case of non-Killing horizons these different definitions of surface gravity are truly different quantities. This also has application to modified theories of gravity, where there is no reason to expect all horizons to be Killing horizons. In Lorentz violating theories, the situation becomes even stranger, as Killing horizons are at best low energy barriers, but for superluminal dispersion relations a true causal barrier, the universal horizon, may be present. Universal horizons are extremely interesting as they seem to be linked to the thermodynamic consistency of Lorentz-violating theories. Hence, we investigate the nature of these universal horizons via a ray tracing study, and delve into what happens near both the universal and Killing horizons. From this study we determine the surface gravity of universal horizons by the peeling properties of rays near the horizon. As the surface gravity is strongly linked to the properties of Hawking radiation, we investigate whether, and at what temperature these horizons radiate. Finally, we combine our investigations of universal horizons and analogue spacetimes, and ask why we have not seen a universal horizon in studies of analogue gravity. We examine some possibilities to include an aether distinct from the velocity flow characterizing analogue spacetimes, laying the groundwork for an analogue universal horizon.
