Equivalence Found in Black Hole Entropy Formulations

Recent research has established a significant equivalence in the realm of black hole thermodynamics, specifically relating to the Noether charge and the Hilbert action boundary term formulae for black hole entropy within the framework of F(R_{abcd}) gravity theory. The authors, Wei Guo, Xiyao Guo, Mingfeng Li, Zili Mou, and Hongbao Zhang, have utilized the covariant phase space formalism to demonstrate that the Hamiltonian associated with a Killing vector field can be expressed as a combination of the Noether charge and a term derived from the Hilbert action boundary. This finding not only reinforces existing theories regarding black hole entropy but also introduces a new tensor field that is independent of the Killing vector, further enriching the theoretical landscape of gravitational physics.

The implications of this research are profound, as it provides a clearer understanding of how different formulations of gravity can yield consistent results regarding black hole entropy. This equivalence could pave the way for new insights into the nature of black holes and their thermodynamic properties, potentially influencing future studies in quantum gravity and cosmology. The paper, titled "On the equivalence of Noether charge and Hilbert action boundary term formulae for the black hole entropy in F(R_{abcd}) gravity theory," is available on arXiv and can be accessed through the following link: arXiv:2406.15138.