Thermodynamics for Kodama observer in general spherically symmetric spacetimes

Abstract

By following the spirit of arXiv:1003.5665, we define a new Tolman temperature of Kodama observer directly related to its acceleration. We give a generalized integral form of thermodynamics relation on virtual sphere of constant r in non-static spherical symmetric spacetimes. This relation contains work term contributed by 'redshift work density', 'pressure density' and 'gravitational work density'. We illustrate it in RN black hole, Dilaton-Maxwell-Einstein black hole and Vaidya black hole. We argue that the co-moving observers are not physically related to Kodama observers in FRW universe unless in the vacuum case. We also find that a generalized differential form of first law is difficult to be well defined, and it would not give more information than the integral form.

Unruh–DeWitt Detectors in Spherically Symmetric Dynamical Space-Times

“…It should be noted that in literature, the dynamical temperature is usually given in the form T = H/2π (exceptions are the papers [29,30]) with…”

“…In particular, this gives naturally a positive temperature for de Sitter space-time, a long debated question years ago, usually resolved by changing the sign of the horizon's energy. It should be noted that in literature, the dynamical temperature is usually given in the form T = H 2π (exceptions are the papers [26,27]) with H 2 = Λ/3 ≡ H 2 0 . Of course this is the expected result for de Sitter space in inflationary coordinates, but it ceases to be correct in any other coordinate system since, for example, H = H 0 tanh H 0 t in global coordinate system with positive spatial curvature.…”

Proper time reparametrization in cosmology: Möbius symmetry and Kodama charges

“…These generators are canonical quantities associated to any spherically symmetric vacuum backgrounds. Having presented briefly the Kodama machinery, it is worth pointing that since its introduction, the Kodama vector has been used for different purposes: it provides in particular an efficient tool to capture the causal structure of a given spherically symmetric spacetime and its (possibly dynamical) apparent horizons [20], formulate the thermodynamics of time-dependent spacetimes [21][22][23], and it can also serve to select a preferred foliation where interesting simplifications occur [24][25][26]. Finally, we stress that while we should focus on the two standard generators (K + , K − ) in the following, more general conserved currents can be constructed out of the Kodama vector, as discussed in detail in [26].…”

Thermodynamics on the maximally symmetric holographic screen and entropy from conical singularities

“…At almost the same time, Padmanabhan reinterpreted the relation E = 2T S [7] between the Komar energy, temperature and entropy as the equipartition rule of energy [8]. Many research works have been done in this area (see [9][10][11][12][13][14][15][16]39] for an incomplete list of them).…”