Corrected entropy of Friedmann-Robertson-Walker universe in tunneling method

Abstract

In this paper, we study the thermodynamic quantities of Friedmann-Robertson-Walker (FRW) universe by using the tunneling formalism beyond semiclassical approximation developed by Banerjee and Majhi [25]. For this we first calculate the corrected Hawking-like temperature on apparent horizon by considering both scalar particle and fermion tunneling. With this corrected Hawking-like temperature, the explicit expressions of the corrected entropy of apparent horizon for various gravity theories including Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, f (R) gravity and scalar-tensor gravity, are computed. Our results show that the corrected entropy formula for different gravity theories can be written into a general expression (4.39) of a same form. It is also shown that this expression is also valid for black holes. This might imply that the expression for the corrected entropy derived from tunneling method is independent of gravity theory, spacetime and dimension of the spacetime. Moreover, it is concluded that the basic thermodynamical property that the corrected entropy on apparent horizon is a state function is satisfied by the FRW universe.

Tunnelling of Massive/Massless Bosons from the Apparent Horizon of FRW Universe

“…Hence, we have successfully derived the same relation for the Hawking temperature as in the case of scalar and Dirac particles tunnelled from the apparent horizon of FRW universe [29][30][31][32]. We point out that this thermal flux of radiation with a temperature can be detected by Kodama observer which is inside the apparent horizon.…”

“…Recently the quantum tunnelling of scalar and Dirac particles from the apparent horizon in a FRW universe has been investigated in [29][30][31][32]. On the other hand, since the famous thermodynamical derivation of Einstein's field equation by Jacobson [33], thermodynamical aspects of the apparent horizon in for FRW universe have been widely studied in the context of different gravity theories [34].…”

Self-similarity, conservation of entropy/bits and the black hole information puzzle

“…ζ(s) = ∞ n=1 n −s . Other works [11][12][13] have investigated quantum corrections to the entropy beyond the classical level. These expressions, in general, involve logarithmic and higher order divergences as M → 0 as we also find to be the case for our generic expression in eq.…”

Logarithmic corrections to black hole and black ring entropy in tunneling approach

“…Our analysis can be easily extended to the cases of various black holes and FRW universe model [28,29,30,31,32,33], without assigning H as specific polynomials for each case :…”