The paper by Ted Jacobson explores the thermodynamic interpretation of the Einstein equation, derived from the proportionality of entropy and horizon area, along with the fundamental relation \(\delta Q = TdS\). The key idea is to apply this relation to all local Rindler causal horizons through each spacetime point, where \(\delta Q\) and \(T\) are interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This perspective suggests that the Einstein equation is an equation of state, born in the thermodynamic limit as a relation between thermodynamic variables. The validity of this equation depends on the existence of local equilibrium conditions.
Jacobson argues that the analogy between classical General Relativity and thermodynamics is not just a coincidence but an identity, particularly in the context of black hole mechanics. He derives the Einstein equation from the proportionality of entropy and horizon area, showing that the equation of state arises naturally from the thermodynamic principles. The paper also discusses the role of gravitational lensing and the nature of heat flow across causal horizons, emphasizing the importance of local equilibrium conditions.
The author concludes that the Einstein equation, viewed in this thermodynamic context, may not be suitable for canonical quantization, similar to how the wave equation for sound in air is not canonically quantized. The paper suggests that understanding non-equilibrium spacetime may require a deeper exploration of these principles.The paper by Ted Jacobson explores the thermodynamic interpretation of the Einstein equation, derived from the proportionality of entropy and horizon area, along with the fundamental relation \(\delta Q = TdS\). The key idea is to apply this relation to all local Rindler causal horizons through each spacetime point, where \(\delta Q\) and \(T\) are interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This perspective suggests that the Einstein equation is an equation of state, born in the thermodynamic limit as a relation between thermodynamic variables. The validity of this equation depends on the existence of local equilibrium conditions.
Jacobson argues that the analogy between classical General Relativity and thermodynamics is not just a coincidence but an identity, particularly in the context of black hole mechanics. He derives the Einstein equation from the proportionality of entropy and horizon area, showing that the equation of state arises naturally from the thermodynamic principles. The paper also discusses the role of gravitational lensing and the nature of heat flow across causal horizons, emphasizing the importance of local equilibrium conditions.
The author concludes that the Einstein equation, viewed in this thermodynamic context, may not be suitable for canonical quantization, similar to how the wave equation for sound in air is not canonically quantized. The paper suggests that understanding non-equilibrium spacetime may require a deeper exploration of these principles.