Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-04-04
Phys.Rev.Lett.75:1260-1263,1995
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages, 1 figure. Revised version has core unchanged but paper rewritten and expanded to clarify the reasoning and to emphasi
Scientific paper
10.1103/PhysRevLett.75.1260
The Einstein equation is derived from the proportionality of entropy and horizon area 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 causal horizons through each spacetime point, with $\delta Q$ 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.
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