We derive the effective equations of the membranes dual to black holes in a particular theory of ... more We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in 1/D upto linear order in the Gauss-Bonnet (GB) parameter β. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in 1/D but non-perturbatively in β for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes.
We write down the most general membrane equations dual to black holes for a general class of grav... more We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in 1/D in large D limit. We derive a “minimal” entropy current which satisfies a local form of second law from these membrane equations. We find that consistency with second law requires the membrane equations to satisfy certain constraints. We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes. Finally we observe a tension between second law and matching with Wald entropy for dual stationary black hole configurations, for the minimal entropy current. We propose a simple modification of the membrane entropy current so that it satisfies second law and also the stationary membrane entropy matches the Wald entropy.
We construct dynamical black hole solutions to Einstein Equations in presence of matter in the la... more We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large D limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of $$ \mathcal{O} $$ O (D0). Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in 1/D. We also obtain the equations governing the dual membranes up to the first sub-leading order in 1/D.
It has recently been argued that, classically, massless higher spin theories in AdS 3 have an enl... more It has recently been argued that, classically, massless higher spin theories in AdS 3 have an enlarged [FORMULA]-symmetry as the algebra of asymptotic isometries. In this note we provide evidence that this symmetry is realised (perturbatively) in the quantum theory. We perform a one loop computation of the fluctuations for a massless spin s field around a thermal AdS 3 background. The resulting determinants are evaluated using the heat kernel techniques of arXiv:0911.5085. The answer factorises holomorphically, and the contributions from the various spin s fields organise themselves into vacuum characters of the [FORMULA] symmetry. For the case of the hs(1, 1) theory consisting of an infinite tower of massless higher spin particles, the resulting answer can be simply expressed in terms of (two copies of) the MacMahon function.
We find the membrane equations which describe the leading order in 1/D dynamics of black holes in... more We find the membrane equations which describe the leading order in 1/D dynamics of black holes in the D → ∞ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor for the membrane whose conservation gives the membrane equations. We apply the membrane equations to predict the light quasi-normal mode spectrum of black holes and black branes in the theory of gravity under consideration.
We derive the effective equations of the membranes dual to black holes in a particular theory of ... more We derive the effective equations of the membranes dual to black holes in a particular theory of higher derivative gravity namely Einstein-Gauss-Bonnet (EGB) gravity at sub-leading order in 1/D upto linear order in the Gauss-Bonnet (GB) parameter β. We find an expression for an entropy current which satisfies a local version of second law onshell in this regime. We also derive the membrane equations upto leading order in 1/D but non-perturbatively in β for EGB gravity. In this regime we write down an expression for a world-volume stress tensor of the membrane and also work out the effective membrane equation for stationary black holes.
We write down the most general membrane equations dual to black holes for a general class of grav... more We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in 1/D in large D limit. We derive a “minimal” entropy current which satisfies a local form of second law from these membrane equations. We find that consistency with second law requires the membrane equations to satisfy certain constraints. We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes. Finally we observe a tension between second law and matching with Wald entropy for dual stationary black hole configurations, for the minimal entropy current. We propose a simple modification of the membrane entropy current so that it satisfies second law and also the stationary membrane entropy matches the Wald entropy.
We construct dynamical black hole solutions to Einstein Equations in presence of matter in the la... more We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large D limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of $$ \mathcal{O} $$ O (D0). Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in 1/D. We also obtain the equations governing the dual membranes up to the first sub-leading order in 1/D.
It has recently been argued that, classically, massless higher spin theories in AdS 3 have an enl... more It has recently been argued that, classically, massless higher spin theories in AdS 3 have an enlarged [FORMULA]-symmetry as the algebra of asymptotic isometries. In this note we provide evidence that this symmetry is realised (perturbatively) in the quantum theory. We perform a one loop computation of the fluctuations for a massless spin s field around a thermal AdS 3 background. The resulting determinants are evaluated using the heat kernel techniques of arXiv:0911.5085. The answer factorises holomorphically, and the contributions from the various spin s fields organise themselves into vacuum characters of the [FORMULA] symmetry. For the case of the hs(1, 1) theory consisting of an infinite tower of massless higher spin particles, the resulting answer can be simply expressed in terms of (two copies of) the MacMahon function.
We find the membrane equations which describe the leading order in 1/D dynamics of black holes in... more We find the membrane equations which describe the leading order in 1/D dynamics of black holes in the D → ∞ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor for the membrane whose conservation gives the membrane equations. We apply the membrane equations to predict the light quasi-normal mode spectrum of black holes and black branes in the theory of gravity under consideration.
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Papers by Arunabha Saha