Thermodynamic Analysis of Gravitational Field Equations in Lyra Manifold

Abstract

The publication of this article was funded by SCOAP 3 .Considering the Einstein field equations in Lyra manifold and applying the unified first law of thermodynamics as well as the Clausius relation to the apparent horizon of FRW universe, we find the entropy of apparent horizon in Lyra manifold. In addition, the validity of second law of thermodynamics and its generalized form are also studied. Finally, we use the first law of thermodynamics in order to find the horizon entropy of static spherically symmetric spacetimes. Some results of considering (anti)de-Sitter and Schwarzschild metrics have also been addressed.

Accelerated cosmos in a nonextensive setup

“…In Einstein gravity, horizons may meet the Bekenstein-Hawking entropy-area law which is a non-extensive entropy [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. Moreover, it has recently been argued that a deep connection between dark energy and horizon entropy may exist in gravitational theories [47][48][49][50][51][52][53][54][55][56][57][58]. Indeed, although extensive statistical mechanics and its corresponding thermodynamics lead to interesting results about the universe expansion history [59], the mentioned points encourage physicists to use non-extensive statistical mechanics [60,61] in order to study the thermodynamic properties of spacetime and its related subjects [62][63][64][65][66][67][68][69][70][71][72][73][74][75].…”

Implications of Maximum Acceleration on Dynamics

“…The pioneering work on the direct connection between gravity and thermodynamics was done by Jacobson [10] who disclosed that the hyperbolic second order partial differential Einstein equation can be derived by applying the fundamental relation δQ = T dS together with proportionality of entropy to the horizon area of the black hole. This profound connection between the first law of thermodynamics and the gravitational field equations has been extensively observed in various gravity theories [11][12][13][14][15][16]. Applying the thermodynamics laws to dynamics and static horizons, one may obtain the gravitational field equations and the Friedmann equations in a wide range of gravity theory [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

“…This profound connection between the first law of thermodynamics and the gravitational field equations has been extensively observed in various gravity theories [11][12][13][14][15][16]. Applying the thermodynamics laws to dynamics and static horizons, one may obtain the gravitational field equations and the Friedmann equations in a wide range of gravity theory [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The deep connection between horizon thermodynamics and gravitational dynamics, help to understand why the field equations should encode information about horizon thermodynamics.…”

Generalized Misner–Sharp energy in generalized Rastall theory

“…The profound connection between thermodynamics and gravitational theories [20][21][22][23][24][25][26][27][28][29][30][31] motivates physicists to look for the Misner-Sharp mass in the various gravitational theories for studying the thermodynamic aspects of the theories [32][33][34][35][36][37][38][39]. The same analysis has been done in the Rastall framework [40] indicating that only when this theory reduces to the Einstein theory, the Bekenstein entropy is recovered in the static spherically symmetric spacetimes [40], a result in agreement with those of the dynamic studies [41,42].…”