Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity

T. Padmanabhan, Int.Jour.Mod.Phys. D18

Original

2009

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D. Kothawala, T. Padmanabhan, Response of Unruh-DeWitt detector with time-dependent acceleration

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Padmanabhan T., A Physical Interpretation of Gravitational Field Equations

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The situation becomes more complex — and interesting — if an observer has a ‘normal’ thermodynamical system, say, a box of gas at some temperature, and accelerates through the inertial vacuum carrying it. Then the thermal behaviour attributed to the gas by the observer will be a convolution of ‘normal’ thermal behaviour and those arising from the acceleration temperature of spacetime, as perceived by the observer. Therefore even the ‘normal’ thermodynamics now acquires [ 14 ] a new level of observer dependence in non-inertial frames. This is not often emphasised but a little thought shows that it is inevitable

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In fact, the reason for choosing ∂ 𝒱 \partial\mathcal{V} to be a N = N= constant surface is to ensure a constant redshift factor between the temperatures attributed to different area elements. Also note that N ​ | 𝒂 | N|\boldsymbol{a}| tends to a finite, constant, surface gravity κ \kappa on a black hole horizon

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M.K. Parikh, S. Sarkar, arXiv:0903.1176

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