New theoretical work proposes a revision of the classical bound that prevents the formation of extremal Reissner-Nordström (eRN) black holes, based on quantum considerations. The formation of these black holes would violate the third law of thermodynamics. Previous research had shown that self-gravitating charged scalar fields could collapse to form eRNs in finite time, implying a violation of this fundamental law. However, a classical bound, known as Reall's bound, was established, stating that the formation of an eRN black hole was impossible if the field's mass-to-charge ratio exceeded unity (m/e ≥ 1).

The authors of this study suggest that Reall's bound is not entirely sharp. They argue that the electric field of a charged system can spontaneously polarize the vacuum under certain conditions, creating pairs of charged particles that would discharge the black hole. This quantum process would ensure the validity of the third law of thermodynamics in the regime where (eQ/ħ)² > (mQ/ħ)² + 1/4, where Q is the system's charge.

Motivated by the preservation of the third law of thermodynamics, the researchers conjecture that the classical Reall bound should be strengthened. They propose that classical considerations should dynamically prevent eRN black holes from forming in the regime m/e ≥ √(1 - (ħ / 2eQ)²). This new adjusted bound accounts for quantum polarization effects, which, beyond a certain point, cannot protect the third law of thermodynamics on their own. This proposal opens new avenues for understanding the interplay between gravity, quantum mechanics, and thermodynamics in extreme environments.