Lorentz violation and black-hole thermodynamics

TL;DR

This paper investigates how Lorentz-violating modifications to Maxwell theory affect photon propagation near black holes, showing that some such theories do not alter the event horizon or violate thermodynamics.

Contribution

It demonstrates that certain Lorentz-violating photon theories with multiple maximal velocities do not necessarily modify black hole horizons or violate thermodynamic laws.

Findings

Modified photons follow null geodesics in an effective metric.

Not all Lorentz violations alter the event horizon.

Some Lorentz-violating theories are consistent with thermodynamics.

Abstract

We consider nonstandard photons from nonbirefringent modified Maxwell theory and discuss their propagation in a fixed Schwarzschild spacetime background. This particular modification of Maxwell theory is Lorentz-violating and allows for maximal photon velocities differing from the causal speed c of the asymptotic background spacetime. In the limit of geometrical optics, light rays from modified Maxwell theory are found to propagate along null geodesics in an effective metric. We observe that not every Lorentz-violating theory with multiple maximal velocities different from the causal speed c modifies the notion of the event horizon, contrary to naive expectations. This result implies that not every Lorentz-violating theory with multiple maximal velocities necessarily leads to a contradiction with the generalized second law of thermodynamics.