The paper derives a multivariate Goon-Penco thermodynamic relation for Einstein-Bel-Robinson black holes, but the relation is just a rearrangement of the first law.
(2.12), it can be demonstrated that, under the condition that β and S remain constant, and when M → M0, both the black hole horizon position r+ and P are functions of η
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Universality on thermodynamic relation with corrections in Einstein-Bel-Robinson gravity Black hole
The paper derives a multivariate Goon-Penco thermodynamic relation for Einstein-Bel-Robinson black holes, but the relation is just a rearrangement of the first law.