Lorentz Violation and Hawking Radiation

As evidenced by this meeting, there is a growing feeling that Lorentz invariance should be questioned and tested. Tentative results from from quantum gravity and string theory hint that the ground state may not be Lorentz invariant, and new techniques are allowing for experiments with unprecedented precision and astrophysical observations at unprecedented high energies. Moreover, due to the unboundedness of the boost parameter, exact Lorentz invariance, while mathematically elegant, is unverifiable and therefore suspect. Most work exploring possible Lorentz violation has focused on non gravitational physics—i.e. flat spacetime. Much less has been done to investigate Lorentz breaking in curved spacetime, or in gravitational phenomena themselves. The event horizon of a black hole, being a surface of infinite redshift, is a particularly good probe of the limits of boost invariance at high energies. Since Hawking radiation emerges from the vicinity of the horizon, it is therefore interesting to investigate the impact of Lorentz violation on Hawking radiation. To pursue this question, however, one must first address another question: if Lorentz violation exists, what becomes of general relativity? In flat spacetime, Lorentz breaking is described by couplings to constant symmetry breaking tensors Va, Wab, ... . To formulate Lorentz breaking in a curved spacetime without destroying general covariance such tensors must become dynamical tensor fields fields that satisfy (effective) field equations. An implementation of this, with a unit timelike vector u(x) as the Lorentz breaking field, is the subject of another contribution to these proceedings . Such a field preserves rotation invariance and, since it is a unit vector, contains no information other than the determination of a preferred rest frame at each point of spacetime. For the present purposes let us just imagine that some such implementation exists.