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Public viva-voce Notification Date: Tuesday, 19 August 2025 Time: 2:00 PM Venue: Seminar Hall (Hybrid mode) The black hole information paradox for small Schwarzschild de Sitter black holes; and no-boundary extremal surfaces in slow roll inflation and other cosmologies Kaberi Goswami Chennai Mathematical Institute. 19-08-25 Abstract In the first part of the talk, we will focus on a ‘Small’ Schwarzschild de Sitter black hole in an effective 2-dimensional dilaton gravity theory and study the resolution of the black hole information paradox with respect to an observer considered to be in the static diamond of the background geometry. The small mass black hole undergoes Hawking evaporation in a frozen de Sitter background. Considering the purity of the matter state that formed the black hole, at later times of the evaporation, the entanglement entropy of Hawking radiation shows an unbounded growth with time, indicating the black hole information paradox in this background. Here we will show that a self-consistent island across the black hole horizon, semi-classically at later times of the evaporation, recovers expectations on the Page curve. One natural extension to this would be that the radiation eventually crosses the cosmological horizon and comes to the future boundary of the Schwarzschild de Sitter background. Next, we will study the resolution of the black hole information paradox for the same ‘Small’ mass Schwarzschild de Sitter black hole with respect to a (meta) observer, which collects the radiation closer to the future boundary. At later times of the evaporation, the evolution of the entanglement entropy shows unbounded growth with respect to the spatial coordinate, indicative of the information paradox. Here, we will also show that, considering appropriate self-consistent island regions around the horizons of black hole regions on both left and right cosmological horizons, the evolution of entanglement entropy of radiation recovers the Page curve. Further, we have also found that a Timelike separated quantum extremal surface for these radiation regions, and it gives a complex-valued on-shell generalized entropy of this radiation region. In the second part of the talk, we will study the no-boundary extremal surfaces in slow-roll inflation models, with perturbations to no-boundary global dS preserving the spatial isometry. While in pure de Sitter space of the Euclidean hemisphere gives a real area equalling half de Sitter entropy, the no-boundary extremal surface areas here have nontrivial real and imaginary pieces overall. We will show the evaluation of the area integrals in the complex time-plane, defining appropriate contours. For the 4-dim case, the real and imaginary finite corrections at leading order in the slow-roll parameter match those in the semiclassical expansion of the Wavefunction (or action), and corroborate the cosmic brane interpretation discussed previously. We also show no-boundary extremal surfaces in other cosmologies, including 3-dimensional inflation and Schwarzschild de Sitter spaces with small mass. All are invited to attend the viva-voce examination.
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