Thermodynamics of spacetime: The Einstein equation of state.

  title={Thermodynamics of spacetime: The Einstein equation of state.},
  journal={Physical review letters},
  volume={75 7},
  • Jacobson
  • Published 4 April 1995
  • Physics
  • Physical review letters
The Einstein equation is derived from the form of black hole entropy together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler horizons through each spacetime point. Viewed in this way, the Einstein equation is an equation of state. It is born in the thermodynamic limit as a relation between thermodynamic variables, and its validity is seen to depend on the existence of local… 
Gravity from Spacetime Thermodynamics
The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by: (i) combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and (ii)
Beyond the Einstein Equation of State: Wald Entropy and Thermodynamical Gravity
We show that the classical equations of gravity follow from a thermodynamic relation, dQ = T dS, where S is taken to be the Wald entropy, applied to a local Rindler horizon at any point in spacetime.
Thermodynamics of spacetime in generally covariant theories of gravitation
It has been shown that the Einstein equation can be derived from the requirement that the First Law Q = TdS holds for all local Rindler causal horizons through each spacetime point. Here Q and T are
Einstein Equations for Generalized Theories of Gravity and the Thermodynamic Relation δQ=TδS are Equivalent
We show that the equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation deltaQ=TdeltaS. Our proof relies on extending previous arguments by using a more
Einstein equations for generalized theories of gravity and the thermodynamic relation deltaQ=TdeltaS are equivalent.
The equations of motion of generalized theories of gravity are equivalent to the thermodynamic relation deltaQ=TdeltaS and the implementation of Jacobson's proposal to express Einstein's equations as a thermodynamic equation of state is completed.
Thermodynamics in Modified Gravity Theories
We demonstrate that there exists an equilibrium description of thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the
Nonequilibrium thermodynamics of spacetime.
It is shown that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment.
Thermodynamics of Anomaly-Driven Cosmology
The Friedmann equations of general relativity can be derived from the first law of thermodynamics when the entropy of the apparent horizon of a spatially isotropic universe is given by the


Increase of black hole entropy in higher curvature gravity.
Within a class of higher curvature theories where the Lagrangian consists of a polynomial in the Ricci scalar, a conformally equivalent theory is used to establish that stationary black hole solutions with a Killing horizon satisfy the Zeroth Law, and that the Second Law holds in general for any dynamical process.
The world as a hologram
According to ’t Hooft the combination of quantum mechanics and gravity requires the three‐dimensional world to be an image of data that can be stored on a two‐dimensional projection much like a
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with ρ a function of the Ricci scalar, one finds that δQ = T dS implies (2π/hη)T ab = R ab −∇ a ∇ b ρ+f g ab for some function f
  • If the entropy density on the horizon takes the form e ρ dA
The World as a Hologram”, Stanford preprint SU- ITP-94-33
  • hep-th/9409089, to appear in J. Math. Phys.,
  • 1995
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