Christopher Eling

Nonequilibrium thermodynamics of spacetime.

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.

Lorentz violation and perpetual motion

We show that any Lorentz-violating theory with two or more propagation speeds is in conflict with the generalized second law of black hole thermodynamics. We do this by identifying a classical energy-extraction method, analogous to the Penrose process, which would decrease the black hole entropy. Although the usual definitions of black hole entropy are ambiguous in this context, we require only very mild assumptions about its dependence on the mass. This extends the result found by Dubovsky and Sibiryakov, which uses the Hawking effect and applies only if the fields with different propagation speeds interact just through gravity. We also point out instabilities that could interfere with their black hole perpetuum mobile, but argue that these can be neglected if the black hole mass is sufficiently large.

Static post-Newtonian equivalence of general relativity and gravity with a dynamical preferred frame

Department of Physics, University of MarylandCollege Park, MD 20742-4111 USAA generally covariant extension of general relativity (GR) in which a dynamical unit timelike vec-tor field is coupled to the metric is studied in the asymptotic weak field limit of spherically symmetricstatic solutions. The two post-Newtonian parameters known as the Eddington-Robertson-Schiff pa-rameters are found to be identical to those in the case of pure GR, except for some non-genericvalues of the coefficients in the Lagrangian.I. INTRODUCTION

Numerical simulations of gravitational collapse in Einstein-aether theory

We study gravitational collapse of a spherically symmetric scalar field in Einstein-aether theory (general relativity coupled to a dynamical unit timelike vector field). The initial value formulation is developed, and numerical simulations are performed. The collapse produces regular, stationary black holes, as long as the aether coupling constants are not too large. For larger couplings a finite area singularity occurs. These results are shown to be consistent with the stationary solutions found previously.

Holographic Screens and Transport Coefficients in the Fluid/Gravity Correspondence

We consider in the framework of the fluid-gravity correspondence the dynamics of hypersurfaces located in the holographic radial direction at r = r(0). We prove that these hypersurfaces evolve, to all orders in the derivative expansion and including all higher curvature corrections, according to the same hydrodynamics equations with identical transport coefficients. The analysis is carried out for normal fluids as well as for superfluids. Consequently, this proves the exactness of the bulk viscosity formula derived by us [J. High Energy Phys. 06 (2011) 007] via the null horizon dynamics.

Reversible and Irreversible Spacetime Thermodynamics for General Brans-Dicke Theories

We derive the equations of motion for Palatini F(R) gravity by applying an entropy balance law TdS={delta}Q+{delta}N to the local Rindler wedge that can be constructed at each point of spacetime. Unlike previous results for metric F(R), there is no bulk viscosity term in the irreversible flux {delta}N. Both theories are equivalent to particular cases of Brans-Dicke scalar-tensor gravity. We show that the thermodynamical approach can be used ab initio also for this class of gravitational theories and it is able to provide both the metric and scalar equations of motion. In this case, the presence of an additional scalar degree of freedom and the requirement for it to be dynamical naturally imply a separate contribution from the scalar field to the heat flux {delta}Q. Therefore, the gravitational flux previously associated to a bulk viscosity term in metric F(R) turns out to be actually part of the reversible thermodynamics. Hence we conjecture that only the shear viscosity associated with Hartle-Hawking dissipation should be associated with irreversible thermodynamics.

Hydrodynamics and viscosity in the Rindler spacetime

In the past year it has been shown that one can construct an approximate (d + 2) dimensional solution of the vacuum Einstein equations dual to a (d + 1) dimensional fluid satisfying the Navier-Stokes equations. The construction proceeds by perturbing the flat Rindler metric, subject to the boundary conditions of a non-singular causal horizon in the interior and a fixed induced metric on a given timelike surface r = rc in the bulk. We review this fluid-Rindler correspondence and show that the shear viscosity to entropy density ratio of the fluid on r = rc takes the universal value 1/4π both in Einstein gravity and in a wide class of higher curvature generalizations. Since the precise holographic duality for this spacetime is unknown, we propose a microscopic explanation for this viscosity based on the peculiar properties of quantum entanglement. Using a novel holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk, we calculate a shear viscosity and find ...