Thermodynamics of Spacetime: The Einstein Equation of State

1995/04/04 by Ted Jacobson · 3 voices · 12 citations
Physics and Astronomy · #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevlett.75.1260

arxiv published 1995/04/04 · arxiv updated 1995/06/06

Abstract

The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation δQ=TdS connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with δQ and T interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.

Cited by

• Why Geometry Should Not Be Quantized: A Causal-Medium Unification of Gravity and Quantum Mechanics
• Finite Entropy Implies Finite Dimension in Quantum Gravity
• Cosmological FLRW phase transitions under exponential corrected entropy
• Gravity from equilibrium thermodynamics of stretched light cones
• Semi-classical spacetime thermodynamics
• Modified Unruh Thermodynamics in Emergent Gravity: Finite Heat Capacity and Rényi Entropy
• Modified cosmology through generalized mass-to-horizon entropy: observational constraints from DESI DR2 BAO data
• Testing the Generalized Second Law in (2+1)-Dimensional Cosmology: Holographic Entropy Bounds and Observational Constraints
• Thermal aspects of the anomalous ω→ ∞ limit of Brans-Dicke gravity
• Quasi-Normal Modes and Nonlinear Electrodynamics in Black Hole Phase Transitions
• Why Emergence of Gravity in Matrix Theories is Entropic
• Ted Jacobson [wikipedia]

Discussions

• Ted's paper (arxiv.org/abs/gr-qc/95...) predated Verlinde (arxiv.org/abs/1001.0785) by at least 15 years [bsky, 3 points, 2 comments]
• when entropy increases some energy is released This isn't always true. You can have endotheormic reactions which absorb heat from the environment. and when energy is released changes in spacetime occu [stackexchange, 2 points]
• The Einstein Equation of State: https://arxiv.org/abs/gr-qc/9504004 Space from Hilbert Space: https://arxiv.org/abs/1606.08444 Einstein's Equation from Entanglement: https://arxiv.org/abs/1712.02803 [bsky, 0 points, 0 comments]

Related

• Thermodynamics of Spacetime and Unimodular Relativity
• Exploring the Nature of Gravity
• On relativistic thermodynamics
• Trivial Entropy of Matter in Gravitation
• Thermodynamics and Relativity, A Condensed Explanation of their Close Connection