2016/04/13 by Kothawala, Dawood
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1604.03673
Assuming that an accelerated observer with four-velocity \bf u\rm R in a curved spacetime attributes the standard Bekenstein-Hawking entropy and Unruh temperature to his "local Rindler horizon", we show that the \rm \it change in horizon area under parametric displacements of the horizon has a very specific thermodynamic structure. Specifically, it entails information about the time-time component of the Einstein tensor: \bf G(\bf u\rm R, \bf u\rm R). Demanding that the result holds for all accelerated observers, this actually becomes a statement about the full Einstein tensor, \rm \bf G. We also present some perspectives on the free fall with four-velocity \bf u\rm ff across the horizon that leads to such a loss of entropy for an accelerated observer. Motivated by results for some simple quantum systems at finite temperature T, we conjecture that at high temperatures, there exists a universal, system-independent curvature correction to partition function and thermal entropy of \rm \it any freely falling system, characterised by the dimensional quantity Δ= \bf R(\bf u\rm ff, \bf u\rm ff) (ℏ c/kT )2.