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

Black holes and neutron stars in the generalized tensor-vector-scalar theory

Bekenstein's Tensor-Vector-Scalar (TeVeS) theory has had considerable success as a relativistic theory of Modified Newtonian Dynamics (MoND). However, recent work suggests that the dynamics of the theory are fundamentally flawed and numerous authors have subsequently begun to consider a generalization of TeVeS where the vector field is given by an Einstein-Aether action. Herein, I develop strong-field solutions of the generalized TeVeS theory, in particular exploring neutron stars as well as neutral and charged black holes. I find that the solutions are identical to the neutron star and black hole solutions of the original TeVeS theory, given a mapping between the parameters of the two theories, and hence provide constraints on these values of the coupling constants. I discuss the consequences of these results in detail including the stability of such spacetimes as well as generalizations to more complicated geometries.Comment: Accepted for publication in Physical Review

Threshold effects and Planck scale Lorentz violation: combined constraints from high energy astrophysics

Recent work has shown that dispersion relations with Planck scale Lorentz violation can produce observable effects at energies many orders of magnitude below the Planck energy M. This opens a window on physics that may reveal quantum gravity phenomena. It has already constrained the possibility of Planck scale Lorentz violation, which is suggested by some approaches to quantum gravity. In this work we carry out a systematic analysis of reaction thresholds, allowing unequal deformation parameters for different particle dispersion relations. The thresholds are found to have some unusual properties compared with standard ones, such as asymmetric momenta for pair creation and upper thresholds. The results are used together with high energy observational data to determine combined constraints. We focus on the case of photons and electrons, using vacuum Cerenkov, photon decay, and photon annihilation processes to determine order unity constraints on the parameters controlling O(E/M) Lorentz violation. Interesting constraints for protons (with photons or pions) are obtained even at O((E/M)^2), using the absence of vacuum Cerenkov and the observed GZK cutoff for ultra high energy cosmic rays. A strong Cerenkov limit using atmospheric PeV neutrinos is possible for O(E/M) deformations provided the rate is high enough. If detected, ultra high energy cosmological neutrinos might yield limits at or even beyond O((E/M)^2).Comment: 35 pages, 13 Figures, RevTex4. Version published in PRD. Expanded introduction, updated discussion of possible constraint if GZK cutoff is confirmed. Corrected typos. Added and updated reference

Primordial black hole evolution in tensor-scalar cosmology

A perturbative analysis shows that black holes do not remember the value of the scalar field $\phi$ at the time they formed if $\phi$ changes in tensor-scalar cosmology. Moreover, even when the black hole mass in the Einstein frame is approximately unaffected by the changing of $\phi$, in the Jordan-Fierz frame the mass increases. This mass increase requires a reanalysis of the evaporation of primordial black holes in tensor-scalar cosmology. It also implies that there could have been a significant magnification of the (Jordan-Fierz frame) mass of primordial black holes.Comment: 4 pages, revte

High energy constraints on Lorentz symmetry violations

Lorentz violation at high energies might lead to non linear dispersion relations for the fundamental particles. We analyze observational constraints on these without assuming any a priori equality between the coefficients determining the amount of Lorentz violation for different particle species. We focus on constraints from three high energy processes involving photons and electrons: photon decay, photo-production of electron-positron pairs, and vacuum Cerenkov radiation. We find that cubic momentum terms in the dispersion relations are strongly constrained.Comment: 7 pages, 1 figure, Talk presented at CPT01; the Second Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, 15-18 Aug. 2001. Minor numerical error corrected, gamma-decay constraint update

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

Signaling, Entanglement, and Quantum Evolution Beyond Cauchy Horizons

Consider a bipartite entangled system half of which falls through the event horizon of an evaporating black hole, while the other half remains coherently accessible to experiments in the exterior region. Beyond complete evaporation, the evolution of the quantum state past the Cauchy horizon cannot remain unitary, raising the questions: How can this evolution be described as a quantum map, and how is causality preserved? What are the possible effects of such nonstandard quantum evolution maps on the behavior of the entangled laboratory partner? More generally, the laws of quantum evolution under extreme conditions in remote regions (not just in evaporating black-hole interiors, but possibly near other naked singularities and regions of extreme spacetime structure) remain untested by observation, and might conceivably be non-unitary or even nonlinear, raising the same questions about the evolution of entangled states. The answers to these questions are subtle, and are linked in unexpected ways to the fundamental laws of quantum mechanics. We show that terrestrial experiments can be designed to probe and constrain exactly how the laws of quantum evolution might be altered, either by black-hole evaporation, or by other extreme processes in remote regions possibly governed by unknown physics.Comment: Combined, revised, and expanded version of quant-ph/0312160 and hep-th/0402060; 13 pages, RevTeX, 2 eps figure

Origin of the Thermal Radiation in a Solid-State Analog of a Black-Hole

An effective black-hole-like horizon occurs, for electromagnetic waves in matter, at a surface of singular electric and magnetic permeabilities. In a physical dispersive medium this horizon disappears for wave numbers with $k>k_c$. Nevertheless, it is shown that Hawking radiation is still emitted if free field modes with $k>k_c$ are in their ground state.Comment: 13 Pages, 3 figures, Revtex with epsf macro

Lorentz violating kinematics: Threshold theorems

Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably complicates detailed calculations in any such scenario, is that once one violates Lorentz invariance the analysis of thresholds in both scattering and decay processes becomes extremely subtle, with many new and naively unexpected effects. In the current article we develop several extremely general threshold theorems that depend only on the existence of some energy momentum relation E(p), eschewing even assumptions of isotropy or monotonicity. We shall argue that there are physically interesting situations where such a level of generality is called for, and that existing (partial) results in the literature make unnecessary technical assumptions. Even in this most general of settings, we show that at threshold all final state particles move with the same 3-velocity, while initial state particles must have 3-velocities parallel/anti-parallel to the final state particles. In contrast the various 3-momenta can behave in a complicated and counter-intuitive manner.Comment: V1: 32 pages, 6 figures, 3 tables. V2: 5 references adde