Holographic gravity and the surface term in the Einstein-Hilbert action

Padmanabhan, Τ.

doi:10.1590/s0103-97332005000200023

Cited by 83 publications

(130 citation statements)

References 18 publications

(28 reference statements)

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“…It is easy to verify, for example [20], that What is more, one can show that the surface term leads to the Wald entropy in spacetimes with horizon [4,21]. Since Lanczos-Lovelock Lagrangians have this structure, it is quite understandable that the semiclassical equations of motion have a thermodynamic interpretation.…”

Section: Discussionmentioning

confidence: 99%

Thermodynamic route to field equations in Lanczos-Lovelock gravity

2006

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Spacetimes with horizons show a resemblance to thermodynamic systems and one can associate the notions of temperature and entropy with them. In the case of Einstein-Hilbert gravity, it is possible to interpret Einstein's equations as the thermodynamic identity T dS = dE + P dV for a spherically symmetric spacetime and thus provide a thermodynamic route to understand the dynamics of gravity. We study this approach further and show that the field equations for LanczosLovelock action in a spherically symmetric spacetime can also be expressed as T dS = dE +P dV with S and E being given by expressions previously derived in the literature by other approaches. The Lanczos-Lovelock Lagrangians are of the form L = Q bcd a R a bcd with ∇ b Q bcd a = 0. In such models, the expansion of Q bcd a in terms of the derivatives of the metric tensor determines the structure of the theory and higher order terms can be interpreted quantum corrections to Einstein gravity. Our result indicates a deep connection between the thermodynamics of horizons and the allowed quantum corrections to standard Einstein gravity, and shows that the relation T dS = dE + P dV has a greater domain of validity that Einstein's field equations.

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Section: Discussionmentioning

confidence: 99%

Thermodynamic route to field equations in Lanczos-Lovelock gravity

2006

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“…One specific implementation of this idea considers the field equations of the theory to be 'emergent' in a well-defined sense, rather than use that term in a more speculative vein like e.g., considering the space and time themselves to be emergent etc. The evidence for such a specific interpretation comes from different facts like the possibility of interpreting the field equation in a wide class of theories as thermodynamic relations [5], the nature of action functional in gravitational theories and their thermodynamic interpretation [6], the possibility of obtaining the field equations from a thermodynamic extremum principle [7], application of equipartition ideas to obtain the density of microscopic degrees of freedom [8], the equivalence of Einstein's field equations to the NavierStokes equations near a null surface [9] etc. The important fact in the emergent paradigm is that one does not need to know about the details of the microscopic description of the theory.…”

Section: Introductionmentioning

confidence: 99%

Phase transition and scaling behavior of topological charged black holes in Hořava–Lifshitz gravity

Majhi

Roychowdhury

2012

Class. Quantum Grav.

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Gravity can be thought as an emergent phenomenon and it has a nice "thermodynamic" structure. In this context, it is then possible to study the thermodynamics without knowing the details of the underlying microscopic degrees of freedom. Here, based on the ordinary thermodynamics, we investigate the phase transition of the static, spherically symmetric charged black hole solution with arbitrary scalar curvature 2k in Hořava-Lifshitz gravity at the Lifshitz point z = 3. The analysis is done using the canonical ensemble frame work; i.e. the charge is kept fixed. We find (a) for both k = 0 and k = 1, there is no phase transition, (b) while k = −1 case exhibits the second order phase transition within the physical region of the black hole. The critical point of second order phase transition is obtained by the divergence of the heat capacity at constant charge. Near the critical point, we find the various critical exponents. It is also observed that they sati sfy the usual thermodynamic scaling laws.

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“…There have been several approaches which have attempted to do this with different levels of success [4,6,8].…”

Section: Introductionmentioning

confidence: 99%

Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

2007

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There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity, as well as for a wider class of Lanczos-Lovelock theories of gravity, it is possible to interpret the field equations near any spherically symmetric horizon as a thermodynamic identity T dS = dE + P dV . We study this approach further and generalize the results to two more generic cases within the context of general relativity: (i) stationary axis-symmetric horizons and (ii) time dependent evolving horizons . In both the cases, the near horizon structure of Einstein equations can be expressed as a thermodynamic identity under the virtual displacement of the horizon. This result demonstrates the fact that the thermodynamic interpretation of gravitational dynamics is not restricted to spherically symmetric or static horizons but is quite generic in nature and indicates a deeper connection between gravity and thermodynamics.

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Holographic gravity and the surface term in the Einstein-Hilbert action

Cited by 83 publications

References 18 publications

Thermodynamic route to field equations in Lanczos-Lovelock gravity

Thermodynamic route to field equations in Lanczos-Lovelock gravity

Phase transition and scaling behavior of topological charged black holes in Hořava–Lifshitz gravity

Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

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