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

- Brustein, R, Gorbonos, D, Hadad, M, Medved, A J M

**Authors:**Brustein, R , Gorbonos, D , Hadad, M , Medved, A J M**Date:**2011**Language:**English**Type:**Article**Identifier:**vital:6816 , http://hdl.handle.net/10962/d1004326**Description:**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.**Full Text:****Date Issued:**2011

**Authors:**Brustein, R , Gorbonos, D , Hadad, M , Medved, A J M**Date:**2011**Language:**English**Type:**Article**Identifier:**vital:6816 , http://hdl.handle.net/10962/d1004326**Description:**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.**Full Text:****Date Issued:**2011

Gravitational entropy and thermodynamics away from the horizon

**Authors:**Brustein, R , Medved, A J M**Date:**2012**Language:**English**Type:**Article**Identifier:**vital:6818 , http://hdl.handle.net/10962/d1004328**Description:**We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state**Full Text:****Date Issued:**2012

**Authors:**Brustein, R , Medved, A J M**Date:**2012**Language:**English**Type:**Article**Identifier:**vital:6818 , http://hdl.handle.net/10962/d1004328**Description:**We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field theory thermodynamic relation TdS=dE+PdV supplemented by an equation of state**Full Text:****Date Issued:**2012

Graviton multipoint functions at the AdS boundary

**Authors:**Brustein, R , Medved, A J M**Date:**2013**Language:**English**Type:**text , Article**Identifier:**vital:6819 , http://hdl.handle.net/10962/d1004425**Description:**The gauge-gravity duality can be used to relate connected multipoint graviton functions to connected multipoint 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 off directly from the bulk Lagrangian, just as can be done for the ratio of the shear viscosity to the entropy density.**Full Text:****Date Issued:**2013

**Authors:**Brustein, R , Medved, A J M**Date:**2013**Language:**English**Type:**text , Article**Identifier:**vital:6819 , http://hdl.handle.net/10962/d1004425**Description:**The gauge-gravity duality can be used to relate connected multipoint graviton functions to connected multipoint 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 off directly from the bulk Lagrangian, just as can be done for the ratio of the shear viscosity to the entropy density.**Full Text:****Date Issued:**2013

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

**Authors:**Brustein, R , Medved, A J M**Date:**2012**Language:**English**Type:**text , Article**Identifier:**vital:6820 , http://hdl.handle.net/10962/d1004427**Description:**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.**Full Text:****Date Issued:**2012

**Authors:**Brustein, R , Medved, A J M**Date:**2012**Language:**English**Type:**text , Article**Identifier:**vital:6820 , http://hdl.handle.net/10962/d1004427**Description:**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.**Full Text:****Date Issued:**2012

Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in ultraviolet-complete theories with a gravity dual

**Authors:**Brustein, R , Medved, A J M**Date:**2011**Language:**English**Type:**text , Article**Identifier:**vital:6817 , http://hdl.handle.net/10962/d1004327**Description:**We reconsider, from a novel perspective, how unitarity constrains the corrections to the ratio of shear viscosity η to entropy density s. We start with higher-derivative extensions of Einstein gravity in asymptotically anti-de Sitter spacetimes. It is assumed that these theories are derived from string theory and thus have a unitary UV completion that is dual to a unitary, UV-complete boundary gauge theory. We then propose that the gravitational perturbations about a solution of the UV-complete theory are described by an effective theory whose linearized equations of motion have at most two time derivatives. Our proposal leads to a concrete prescription for the calculation of η/s for theories of gravity with arbitrary higher-derivative corrections. The resulting ratio can take on values above or below 1/4π and is consistent with all the previous calculations, even though our reasoning is substantially different. For the purpose of calculating η/s, our proposal also leads to only two possible candidates for the effective two-derivative theory: Einstein and Gauss-Bonnet gravity. The distinction between the two is that Einstein gravity satisfies the equivalence principle, and so its graviton correlation functions are polarization-independent, whereas the Gauss-Bonnet theory has polarization-dependent correlation functions. We discuss the graviton three-point functions in this context and explain how these can provide additional information on the value of η/s.**Full Text:****Date Issued:**2011

**Authors:**Brustein, R , Medved, A J M**Date:**2011**Language:**English**Type:**text , Article**Identifier:**vital:6817 , http://hdl.handle.net/10962/d1004327**Description:**We reconsider, from a novel perspective, how unitarity constrains the corrections to the ratio of shear viscosity η to entropy density s. We start with higher-derivative extensions of Einstein gravity in asymptotically anti-de Sitter spacetimes. It is assumed that these theories are derived from string theory and thus have a unitary UV completion that is dual to a unitary, UV-complete boundary gauge theory. We then propose that the gravitational perturbations about a solution of the UV-complete theory are described by an effective theory whose linearized equations of motion have at most two time derivatives. Our proposal leads to a concrete prescription for the calculation of η/s for theories of gravity with arbitrary higher-derivative corrections. The resulting ratio can take on values above or below 1/4π and is consistent with all the previous calculations, even though our reasoning is substantially different. For the purpose of calculating η/s, our proposal also leads to only two possible candidates for the effective two-derivative theory: Einstein and Gauss-Bonnet gravity. The distinction between the two is that Einstein gravity satisfies the equivalence principle, and so its graviton correlation functions are polarization-independent, whereas the Gauss-Bonnet theory has polarization-dependent correlation functions. We discuss the graviton three-point functions in this context and explain how these can provide additional information on the value of η/s.**Full Text:****Date Issued:**2011

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

**Authors:**Brustein, R , Medved, A J M**Date:**2011**Language:**English**Type:**text , Article**Identifier:**vital:6815 , http://hdl.handle.net/10962/d1004325**Description:**We discuss corrections to the ratio of shear viscosity to entropy density η/s in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio η/s remains at the Einstein-gravity value of 1/4π to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, η/s can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of η/s can decrease below 1/4π when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein gravity.**Full Text:****Date Issued:**2011

**Authors:**Brustein, R , Medved, A J M**Date:**2011**Language:**English**Type:**text , Article**Identifier:**vital:6815 , http://hdl.handle.net/10962/d1004325**Description:**We discuss corrections to the ratio of shear viscosity to entropy density η/s in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio η/s remains at the Einstein-gravity value of 1/4π to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, η/s can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of η/s can decrease below 1/4π when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein gravity.**Full Text:****Date Issued:**2011

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