Equivalence of Noether charge and Hilbert action boundary term formulas for the black hole entropy in $F(R_{abcd})$ gravity theory
By working with the covariant phase space formalism, we have shown that not only can the Hamiltonian conjugate to a Killing vector field $ξ$ be expressed as the sum of the associated Noether charge and $ξ$ contracted with the Hilbert action boundary term for $F(R_{abcd})$ gravity, but also be written as its contraction with another $ξ$ independent tensor field. With this, we have proven the equivalence of Noether charge and Hilbert action boundary term formulae for the stationary black hole entropy in $F(R_{abcd})$ gravity, which is further substantiated by our explicit computation using both formulae.
hep-th↗