A. J. M. Medved

Ratio of shear viscosity to entropy density in generalized theories of gravity

Near the horizon of a black brane solution in anti-de Sitter space, the long-wavelength fluctuations of the metric exhibit hydrodynamic behavior. For Einsteins theory, the ratio of the shear viscosity of near-horizon metric fluctuations {eta} to the entropy per unit of transverse volume s is {eta}/s=1/4{pi}. We propose that, in generalized theories of gravity, this ratio is given by the ratio of two effective gravitational couplings and can be different than 1/4{pi}. Our proposal confirms that {eta}/s is equal to 1/4{pi} for any theory that can be transformed into Einsteins theory, such as F(R) gravity. Our proposal also implies that matter interactions--except those including explicit or implicit factors of the Riemann tensor--will not modify {eta}/s. The proposed formula reproduces, in a very simple manner, some recently found results for Gauss-Bonnet gravity. We also make a prediction for {eta}/s in Lovelock theories of any order or dimensionality.

When black holes collide: Probing the interior composition by the spectrum of ringdown modes and emitted gravitational waves

The merger of colliding black holes (BHs) should lead to the production of ringdown or quasinormal modes (QNMs), which may very well be sensitive to the state of the interior. We put this idea to the test with a recent proposal that the interior of a BH consists of a bound state of highly excited, long, closed, interacting strings; figuratively, a collapsed polymer. We show, using scalar perturbations for simplicity, that such BHs do indeed have a distinct signature in their QNM spectrum: A new class of modes whose frequencies are parametrically lower than the lowest-frequency mode of a classical BH and whose damping times are parametrically longer. The reason for the appearance of the new modes is that our model contains another scale, the string length, which is parametrically larger than the Planck length. This distinction between the collapsed-polymer model and general-relativistic BHs could be made with gravitational-wave observations and offers a means for potentially measuring the strength of the coupling in string theory. For example, GW150914 already allows us to probe the strength of the string coupling near the regime which is predicted by the unification of the gravitational and gauge-theory couplings. We also derive bounds on the amplitude of the collapsed-polymer QNMs that can be placed by current and future gravitational-wave observations.

Proof of a universal lower bound on the shear viscosity to entropy density ratio

Abstract It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1 / 4 π in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.

Discovering the interior of black holes

The detection of gravitational waves (GWs) from black hole (BH) mergers provides an inroad toward probing the interior of astrophysical BHs. The general-relativistic description of the BH interior is that of empty spacetime with a (possibly) singular core. Recently, however, the hypothesis that the BH interior does not exist has been gaining traction, as it provides a means for resolving the BH information-loss problem. Here, we propose a simple method for answering the following question: Does the BH interior exist and, if so, does it contain some distribution of matter or is it mostly empty? Our proposal is premised on the idea that, similar to the case of relativistic, ultra-compact stars, any BH-like object whose interior has some matter distribution should support fluid modes in addition to the conventional spacetime modes. In particular, the Coriolis-induced Rossby (r-) modes, whose spectrum is mostly insensitive to the composition of the interior matter, should be a universal feature of such BH-like objects. In fact, the frequency and damping time of these modes are determined by only the objects mass and speed of rotation. The r-modes oscillate at a lower frequency, decay at a slower rate and produce weaker GWs than do modes of the spacetime class. Hence, they imprint a model-insensitive signature of a non-empty interior in the GW spectrum resulting from a BH merger. We find that future GW detectors, such as Advanced LIGO with its design sensitivity, have the potential of detecting such r-modes if the amount of GWs leaking out quantum mechanically from the interior of a BH-like object is sufficiently large.

Graviton n-point functions for UV-complete theories in Anti-de Sitter space

We calculate graviton n-point functions in an anti-de Sitter black brane background for effective gravity theories whose linearized equations of motion have at most two time derivatives. We compare the n-point functions in Einstein gravity to those in theories whose leading correction is quadratic in the Riemann tensor. The comparison is made for any number of gravitons and for all physical graviton modes in a kinematic region for which the leading correction can significantly modify the Einstein result. We find that the n-point functions of Einstein gravity depend on at most a single angle, whereas those of the corrected theories may depend on two angles. For the four-point functions, Einstein gravity exhibits linear dependence on the Mandelstam variable s versus a quadratic dependence on s for the corrected theory.

Evaluating the Wald Entropy from two-derivative terms in quadratic actions

We evaluate the Wald Noether charge entropy for a black hole in generalized theories of gravity. Expanding the Lagrangian to second order in gravitational perturbations, we show that contributions to the entropy density originate only from the coefficients of two-derivative terms. The same considerations are extended to include matter fields and to show that arbitrary powers of matter fields and their symmetrized covariant derivatives cannot contribute to the entropy density. We also explain how to use the linearized gravitational field equation rather than quadratic actions to obtain the same results. Several explicit examples are presented that allow us to clarify subtle points in the derivation and application of our method.

How black holes burn: Entanglement entropy evolution for an evaporating black hole

We present a calculation of the rate of information release from a Schwarzschild BH. We have recently extended Hawkings theory of black hole (BH) evaporation to account for quantum fluctuations of the background geometry, as well as for back-reaction and time-dependence effects. Our main result has been a two-point function matrix for the radiation that consists of Hawkings thermal matrix plus off-diagonal corrections that are initially small and become more important as the evaporation proceeds. Here, we show that, if the phases and amplitudes of the radiation matrix are recorded over the lifetime of the BH, then the radiation purifies in a continuous way. We conjecture that our results establish the maximal rate at which information can be released from a semiclassical BH, to be contrasted with the minimal rate that was predicted by Page on the basis of generic unitarity arguments. When the phases of the radiation matrix are not tracked, we show that it purifies only parametrically close to the end of the BH evaporation and does so extremely fast. Our main technical tool in the quantitative treatment of this purification is the purity of the radiation matrix and, its inverse, the participation ratio. These can be related to the Renyi entropy of the density matrix of the emitted radiation.

Graviton multipoint functions at the AdS boundary

The gauge-gravity duality can be used to relate connected multi-point graviton functions to connected multi-point correlation functions of the stress tensor of a strongly coupled fluid. Here, we show how to construct the connected graviton functions for a particular kinematic regime that is ideal for discriminating between different gravitational theories; in particular, between Einstein theory and its leading-order string theory correction. Our analysis begins with the one-particle irreducible graviton amplitudes in an anti-de Sitter black brane background. We show how these can be used to calculate the connected graviton functions and demonstrate that the two types of amplitudes agree in some cases. It is then asserted on physical grounds that this agreement persists in all cases for both Einstein gravity and its leading-order correction. This outcome implies that the corresponding field-theory correlation functions can be read directly off from the bulk Lagrangian, just as can be done for the ratio of the shear viscosity to the entropy density.

Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity

We discuss corrections to the ratio of shear viscosity to entropy density

Lovelock gravity is equivalent to Einstein gravity coupled to form fields

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