Entanglement entropy for spherically symmetric regular black holes

Abstract

The Bardeen and Hayward spacetimes are here considered as standard configurations of spherically symmetric regular black holes. Assuming the thermodynamics of such objects to be analogous to standard black holes, we compute the island formula in the regime of small topological charge and large vacuum energy, respectively for Bardeen and Hayward spacetimes. Late and early-time domains are separately discussed, with particular emphasis on the island formations. We single out conditions under which it is not possible to find out islands at early-times and how our findings depart from the standard Schwarzschild case. Motivated by the fact that those configurations extend Reissner-Nordstr\"{o}m and Schwarzschild-de Sitter metrics through the inclusion of regularity behavior at $r=0$, we show how the effect of regularity induces modifications on the overall entanglement entropy. Finally, the Page time is also computed, showing its asymptotic behavior. Specifically, the Page time exhibits slight departures with respect to the Schwarzschild case, more evident in the Hayward metric only. Conversely, our findings on Page time show that the Bardeen regular black hole is quite indistinguishable from the Schwarzschild case.