Universal exponents of black hole phase transition at zero-temperature limit

While universal exponents for phase transitions are well-established at the critical point, the zero-temperature limit remains largely unexplored. The phase transition between small and large black holes in AdS space, analogous to that of a van der Waals fluid, provides an ideal approach for studying the first-order phase transitions near zero temperature, a regime where semi-classical black hole thermodynamics remains exact and can provide a benchmark for quantum gravity. By applying the Maxwell equal-area law to the coexistence curve, we analytically derive a set of universal exponents for the zero-temperature regime: α = 1 , β = 2 , and γ = d − 3 , with d being the spacetime dimension. Moreover, we demonstrate that these exponents are robust, holding irrespective of the black hole’s charge and spin. Our study establish novel universal behavior in the semi-classical level in the low-temperature regime of black hole thermodynamics, and the resulting exponents serve as a necessary benchmark that any complete theory of quantum gravity must reproduce in its semi-classical limit.