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Register a new userSolid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the Renyi Extended Phase Space Approach
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Added by
Ekapong Hirunsirisawat
Publication date
2021
fields
Physics
and research's language is
English
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Recently, it has been found that, with the Renyi statistics, the asymptotically flat Schwarzschild black hole can be in thermal equilibrium with infinite heat reservior at a fixed temperature when its event horizon radius is larger than the characteristic length scale $L_lambda=1/sqrt{pi lambda}$, where $lambda$ is the nonextensivity parameter. In the Renyi extended phase space with the $PdV$ work term, an off-shell free energy in the canonical ensemble with the thermodynamic volume as an order parameter is considered to identify a first-order Hawking-Page (HP) phase transition as a solid/liquid phase transition. It has the latent heat of fusion from solid (corresponding to thermal radiation) to liquid (corresponding to black hole) in the form of $sim 1/sqrt{lambda}$; this is evident of the absence of the HP phase transition in the case of asymptotically flat Schwarzschild black hole from the GB statistics ($lambda=0$). Moreover, we investigate the generalized second law of black hole thermodynamics (GSL) in Renyi statistics by considering the black hole as a working substance in heat engine. Interestingly, an efficiency $eta$ of the black hole in a Carnot cycle takes the form $eta_c=1-T_text{C}/T_text{H}$. This confirms the validity of the GSL in the Renyi extended phase space.
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The phase structure and critical phenomena of the 3+1 dimensional charged black holes in asymptotically flat spacetime are investigated in terms of thermodynamic properties within the Renyi statistics. With this approach as the non-extensive parameter above zero, we find that the charged black hole can be in thermodynamic equilibrium with surrounding thermal radiation, and have a Hawking-Page phase transition in the same way in the case of AdS charged black hole. This gives more evidence supporting the proposal that there exists an equivalence between the black hole thermodynamics in asymptotically flat spacetime via Renyi statistics and that in asymptotically AdS spacetime via Gibbs-Boltzmann statistics, proposed by Czinner et al. However, the present work also provides another aspect of supporting evidence through exploring the extended phase space within the Renyi statistics. Working on a modified version of Smarr formula, the thermodynamic pressure $P$ and volume $v$ of a charged black hole are found to be related to the non-extensive parameter. The resulting $P-v$ diagram indicates that the thermodynamics of charged black holes in asymptotically flat spacetime via Renyi statistics has the Van der Waals phase structure, equivalent to that in asymptotically AdS spacetime via Gibbs-Boltzmann statistics.
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