Page Curves of Black Holes in Higher Derivative Theories of Gravity and Cosmological Islands

My talk is based on arXiv:2204.11882, 2207.04048 and 2210.00331. In this talk, I will discuss how we obtain the Page curves of black holes in higher derivative theories of gravity. First, I will discuss one example (Reissner-Nordström black hole) based on Island proposal and then I will discuss the doubly holographic setup in M theory with inclusion of higher derivative terms. Using this setup we obtained the Page curve of eternal neutral black holes. In this process and in the context of the latter, we will show a hierarchy in the entanglement entropies of the Hartman-Maldacena(HM)-like and Island surfaces(IS) with respect to an exponential-in-N suppression factor at the leading order and with the inclusion of higher derivative corrections. After showing the existence of massless graviton eigenmode of the Laplace-Beltrami differential operator acting on the internal coordinates, we will show that due to an identical exponential-in-N suppression at the leading order in the entanglement entropies of, both, the HM-like and Island surfaces (and larger suppressions of the higher derivatives’ contributions), one is able to obtain the Page curve. Finally, I will discuss the application of the Island proposal for Schwarzschild de-Sitter black holes where we introduce cosmological islands to resolve the information problem in a de-Sitter patch.