Abstract
We establish the link between the thermodynamics and the quantum theory of black hole horizons through the construction of the thermodynamic partition function, partly based on some physically plausible arguments, by beginning from the description of quantum states of the horizon, considering loop quantum gravity (LQG) as the underlying theory. Although the effective “thermalized” form of the partition function has been previously used in the literature to study the effect of thermal fluctuations of the black hole horizon, nonetheless the direct link to any existing quantum theory (which is here taken to be LQG), especially a derivation of the partition function from the quantum states of the horizon, appears to be hitherto absent. This work is an attempt to bridge this small, but essential, gap that appears to be present between the existing literature of quantum theory and thermodynamics of black holes. Furthermore, it may be emphasized that this work isonlyconcerned with themetric independentapproaches to black hole thermodynamics.
Highlights
The thermodynamic properties associated with spacetime geometry are intimately associated with the presence of a physical horizon
The fact that the entropy of spacetime geometry vanishes in the absence of a horizon [1] strongly motivates one to think of independent quantum degrees of freedom of the horizon giving rise to the thermodynamic properties uniquely associated with the horizon; and the derivation of the thermodynamic partition function right from the scratch, which has been presented in this work, satifactorily quenches the urge by establishing the all needed direct link between the quantum and thermodynamic aspects of the horizon
The major acquisition one can have by studying this work is the logical step by step derivation of the theromodynamic partition functions of the black hole horizon based on the underlying quantum geometric framework and a clear understanding about the role of quantum and thermal fluctuations in the corresponding thermodynamics
Summary
The thermodynamic properties associated with spacetime geometry are intimately associated with the presence of a physical horizon. This is the underlying physical essence of this particular statistical mechanical approach to horizon thermodynamics presented and investigated in [2, 3, 9,10,11,12,13,14] None of these works [2, 3, 9,10,11,12,13,14] presents a logical straightforward derivation of the partition function based on the fundamental quantum structure of black hole horizons, which would have made the link between the microscopic quantum theory of the horizon and the associated thermodynamics as had been urged by the works in [1, 4,5,6,7,8]. The structure of the paper can be debriefed as follows
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