We show that the presence of spacetime torsion, unlike any other non-trivial modifications of the Einstein gravity, does \emph{not} affect black hole entropy. The theory being diffeomorphism invariant leads to a Noether current and hence to a Noether charge, which can be associated to the heat content of the spacetime. Furthermore, the evolution of the spacetime inheriting torsion can be encoded in the difference between suitably defined surface and bulk degrees of freedom. For static spacetimes the surface and bulk degrees of freedom coincides, leading to holographic equipartition. In doing so one can see that the surface degrees of freedom originate from horizon area and it is clear that spacetime torsion never contributes to the surface degrees of freedom and hence neither to the black hole entropy. We further show that the gravitational Hamiltonian in presence of torsion does not inherit any torsion dependence in the boundary term and hence the first law originating from the variation of the Hamiltonian, relates entropy to area. This reconfirms our claim that torsion does not modify the black hole entropy.


  • Introduction and MotivationBlack holes have a characteristic temperature and entropy associated with them and this leads to the formulation of the laws of black hole mechanics [1]

  • The correspondence between gravitational dynamics and spacetime thermodynamics transcends general relativity and holds good for a variety of alternative gravitational theories, including Lanczos-Lovelock models of gravity. In both general relativity and Lanczos-Lovelock models of gravity, the associated Noether current provides a bag full of thermodynamic relations, including an estimation of the black hole entropy in these theories

  • In this work we have explicitly demonstrated, that even though the presence of spacetime torsion modifies the gravitational Lagrangian and the field equations in a non-trivial manner, there is no effect of the same on the black hole entropy

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Introduction and Motivation

Black holes have a characteristic temperature and entropy associated with them and this leads to the formulation of the laws of black hole mechanics [1]. The string theory calculation works only for supersymmetric or near-extremal black holes [9,10,15,16,17,18], while loop quantum gravity has to assume some choice for the ill-understood immirzi parameter [11, 19,20,21,22,23] It was not at all clear if the above black hole entropy would remain the same by performing some non trivial modifications to general relativity, such as including higher derivative terms in the action or dropping the assumption about a symmetric connection by including torsion as an additional degree of freedom.

Noether Current in Presence of Spacetime Torsion
Holographic Equipartition and Spacetime Evolution in EinsteinCartan Theory
Hamiltonian Analysis in Presence of Torsion and The First Law
Concluding Remarks

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