A Better Quantum Extremal Surface and Island Interpretation that Explains the Associated Massive Gravity

Abstract

In a paper about multi-fold black holes, we describe the evolution of black holes, their evaporation and entropy. With a particle-based model, we recover the correct Page curve, and resolve the black hole information paradox. Doing so we encounter a quantum extremal surface, as proposed by others using the conventional approach of the island and replica trick. In a subsequent paper, we show that the definitions of the quantum extremal surfaces coincide, while our physical interpretation are rather radically different: an horizon for the multi-folds attached to virtual particles in the multi-fold universe, versus an island à la Wheeler’s bag of gold for the conventional replica trick. We dispute as a result a widely held view that Wheeler’s bag of gold could isolate most of their content from the parent universe. Others have questioned the replica trick with its use of JT gravity, and shown that it implies massive gravity, which might not correspond to a universe where General Relativity (GR) reigns. We show, in multi-fold scenarios, that the inability for multi-folds to escape the quantum extremal surface implies massive gravity effects, while remaining able to recover GR. Therefore, we can provide microscopic mechanisms to explain how massless gravity becomes massive. We also justify relying on JT gravity, by the 2D massless Higgs bosons dilaton random walks. On the other hand, in an asymptotic AdS universe, the replica trick requires the introduction of a reservoir for the evaporated particles, beyond the boundary of AdS, otherwise evaporation can’t take place. Letting gravitons enter the reservoir implies massive gravity, while preventing them from entering the reservoir leads to a different Page curve, and therefore, no resolution of the black hole information paradox. We provide new microscopic interpretations to these scenarios, explaining away these issues, and dealing with the encounter of quantum extremal surface outside the black hole in the presence of a thermal bath. Doing so, we confirms the better suitability of the multi-fold interpretation of the quantum extrema surface, and island, while supporting the replica trick and island formula approach, and resolving the black hole information paradox once and for all.Already knowing that multi-folds appear with GR at Planck scales, and with other hints, the multi-fold analysis applies to our real universe, and the paper provides a microscopic interpretation of quantum extremal surfaces, the correct page curve, the resolution of the black hole information paradox, and the apparition of massive gravity associated to quantum extremal surfaces.From the island formula and replica trick at low masses, we encounter hints of our past proposal for new life cycles of black holes (small extremal black holes splitting into another extremal black hole and an evaporating black hole), which invalidate the strict Weak Gravity Conjecture, and justify the Ultimate Unification (UU) proposal. It is quite a confirmation.