Lorentz violation and Hawking radiation

Since the event horizon of a black hole is a surface of infinite redshift, it might be thought that Hawking radiation would be highly sensitive to Lorentz violation at high energies. In fact, the opposite is true for subluminal dispersion. For superluminal dispersion, however, the outgoing black hole modes emanate from the singularity in a state determined by unknown quantum gravity processes.Comment: 5 pages, Talk presented at CPT01; the Second Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, 15-18 Aug. 200

Einstein-Aether Waves

Local Lorentz invariance violation can be realized by introducing extra tensor fields in the action that couple to matter. If the Lorentz violation is rotationally invariant in some frame, then it is characterized by an ``aether'', i.e. a unit timelike vector field. General covariance requires that the aether field be dynamical. In this paper we study the linearized theory of such an aether coupled to gravity and find the speeds and polarizations of all the wave modes in terms of the four constants appearing in the most general action at second order in derivatives. We find that in addition to the usual two transverse traceless metric modes, there are three coupled aether-metric modes.Comment: 5 pages; v2: Remarks added concerning gauge invariance of the waves and hyperbolicity of the equations. Essentially the version published in PR

Destroying black holes with test bodies

If a black hole can accrete a body whose spin or charge would send the black hole parameters over the extremal limit, then a naked singularity would presumably form, in violation of the cosmic censorship conjecture. We review some previous results on testing cosmic censorship in this way using the test body approximation, focusing mostly on the case of neutral black holes. Under certain conditions a black hole can indeed be over-spun or over-charged in this approximation, hence radiative and self-force effects must be taken into account to further test cosmic censorship.Comment: Contribution to the proceedings of the First Mediterranean Conference on Classical and Quantum Gravity (talk given by T. P. S.). Summarizes the results of Phys. Rev. Lett. 103, 141101 (2009), arXiv:0907.4146 [gr-qc] and considers further example

Degenerate Metric Phase Boundaries

The structure of boundaries between degenerate and nondegenerate solutions of Ashtekar's canonical reformulation of Einstein's equations is studied. Several examples are given of such "phase boundaries" in which the metric is degenerate on one side of a null hypersurface and non-degenerate on the other side. These include portions of flat space, Schwarzschild, and plane wave solutions joined to degenerate regions. In the last case, the wave collides with a planar phase boundary and continues on with the same curvature but degenerate triad, while the phase boundary continues in the opposite direction. We conjecture that degenerate phase boundaries are always null.Comment: 16 pages, 2 figures; erratum included in separate file: errors in section 4, degenerate phase boundary is null without imposing field equation

Construction of N = 2 Chiral Supergravity Compatible with the Reality Condition

We construct N = 2 chiral supergravity (SUGRA) which leads to Ashtekar's canonical formulation. The supersymmetry (SUSY) transformation parameters are not constrained at all and auxiliary fields are not required in contrast with the method of the two-form gravity. We also show that our formulation is compatible with the reality condition, and that its real section is reduced to the usual N = 2 SUGRA up to an imaginary boundary term.Comment: 16 pages, late

Mechanics of universal horizons

Modified gravity models such as Ho\v{r}ava-Lifshitz gravity or Einstein-{\ae}ther theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" - hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-{\ae}ther theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-{\ae}ther Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.Comment: Minor clarifications. References update

A positive energy theorem for Einstein-aether and Ho\v{r}ava gravity

Energy positivity is established for a class of solutions to Einstein-aether theory and the IR limit of Ho\v{r}ava gravity within a certain range of coupling parameters. The class consists of solutions where the aether 4-vector is divergence free on a spacelike surface to which it is orthogonal (which implies that the surface is maximal). In particular, this result holds for spherically symmetric solutions at a moment of time symmetry.Comment: 4 page