Exact anisotropic black-brane solutions in arbitrary D satisfy the third law only for restricted warp factors and couplings; otherwise S(T) is multi-valued.
Third Law of Black-Hole Dynamics: A Formulation and Proof
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Lifshitz-like black branes in arbitrary dimensions and the third law of thermodynamics
Exact anisotropic black-brane solutions in arbitrary D satisfy the third law only for restricted warp factors and couplings; otherwise S(T) is multi-valued.