Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity
arXiv:1505.05297 · doi:10.1007/JHEP10(2015)097
Abstract
Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity TdS=dE+PdV (where the variations are interpreted as changes due to virtual displacement along the affine parameter) in the near-horizon limit in static spacetimes. Here we generalize this result to any arbitrary null surface in an arbitrary spacetime and show that certain components of the Einstein's equations can be expressed in the form of the above thermodynamic identity. We also obtain an explicit expression for the thermodynamic energy associated with the null surface. Under appropriate limits, our expressions reduce to those previously derived in the literature. The components of the field equations used in obtaining the current result are orthogonal to the components used previously to obtain another related result, viz. that some components of the field equations reduce to a Navier-Stokes equation on any null surface, in any spacetime. We also describe the structure of Einstein's equations near a null surface in terms of three well-defined projections and show how the different results complement each other.
v2, 25 pages, no figures, to appear in JHEP
References in corpus (26)
- Thermodynamic Behavior of Friedmann Equation at Apparent Horizon of FRW Universe
- Unified First Law and Thermodynamics of Apparent Horizon in FRW Universe
- Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
- Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
- Dark Energy and Gravity
- Hawking Radiation of Apparent Horizon in a FRW Universe
- Thermodynamical Properties of Apparent Horizon in Warped DGP Braneworld
- Corrected Entropy-Area Relation and Modified Friedmann Equations
- Friedmann Equations and Thermodynamics of Apparent Horizons
- Deep Connection Between Thermodynamics and Gravity in Gauss-Bonnet Braneworld
- Thermodynamics of Apparent Horizon in Brane World Scenario
- Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
- Generalized Vaidya Spacetime in Lovelock Gravity and Thermodynamics on Apparent Horizon
- Holography of Gravitational Action Functionals
- The generalized second law of thermodynamics in generalized gravity theories
- Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
- Thermodynamics of Apparent Horizon in Brane World Scenarios
- Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
- Thermodynamics on the apparent horizon in generalized gravity theories
- Lanczos-Lovelock gravity from a thermodynamic perspective
- First law of thermodynamics and Friedmann-like equations in braneworld cosmology
- Evolution of Spacetime arises due to the departure from Holographic Equipartition in all Lanczos-Lovelock Theories of Gravity
- Holography in Action
- Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole
- The thermodynamic structure of Einstein tensor
- Thermodynamic structure of field equations near apparent horizon for radiating black holes
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- Diffeomorphism symmetries near a timelike surface in black hole spacetime
- BMS Goldstone modes near the horizon of a Kerr black hole are thermal
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- Emergent Gravity from an Augmented Variational Principle
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