Islands and Page curves in charged dilaton black holes

We study the Page curve for eternal Garfinkle–Horowitz–Strominger dilaton black holes in four dimensional asymptotically flat spacetime by using the island paradigm. The results demonstrate that without the island, the entanglement entropy of Hawking radiation is proportional to time and becomes divergent at late times. While taking account of the existence of the island outside the event horizon, the entanglement entropy stops growing at late times and eventually reaches a saturation value. This value is twice of the Bekenstein–Hawking entropy and consistent with the finiteness of the von Neumann entropy of eternal black holes. Moreover, we discuss the impact of the stringy coefficient n and charge Q on the Page time and the scrambling time respectively. For the non-extremal case, the influence of the coefficient n on them is small compared to the influence of the charge Q. However, for the extremal case, the Page time and the scrambling time become divergent or near vanishing. This implies the island paradigm needs further investigation.

Komar integral and Smarr formula for axion-dilaton black holes versus S duality

We construct the Komar integral for axion-dilaton gravity using Wald’s formalism and momentum maps and we use it to derive a Smarr relation for stationary axion-dilaton black holes. While the Wald-Noether 2-form charge is not invariant under SL(2, ℝ) electric-magnetic duality transformations because Wald’s formalism does not account for magnetic charges and potentials, the Komar integral constructed with it turns out to be invariant and, in more general theories, it will be fully symplectic invariant. We check the Smarr formula obtained with the most general family of static axion-dilaton black holes.

Overcharging dilaton black holes in (2 + 1) dimensions to extremality and beyond

We test whether static charged dilaton black holes in [Formula: see text] dimensions can be turned into naked singularities by sending in test particles from infinity. We derive that overcharging is possible and generic for both extremal and nearly extremal black holes. Our analysis also implies that nearly extremal charged dilaton black holes can be continuously driven to extremality and beyond, unlike nearly extremal Ban̆ados–Teitelboim–Zanelli, Kerr and Reissner–Nordström black holes which are overspun or overcharged by a discrete jump. Thus, the weak form of the cosmic censorship conjecture and the third law of black hole thermodynamics are both violated in the interaction of charged dilaton black holes in [Formula: see text] dimensions, with test particles. We also derive that there exist no points, where the heat capacity vanishes or diverges in the transition from black holes to naked singularities. The phase transitions that could potentially prevent the formation of naked singularities do not occur.