Aspects of Unitarity in Black Hole physics

Das, Arpit (2018) Aspects of Unitarity in Black Hole physics. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

We have investigated issues concerned with unitarity in some spherically symmetric (1+3) dimensional inhomogeneous models. To be specific, we focused on the dynamics of a spherical collapsing infinitesimally thin shell whose exterior in the neutral case is described by the Schwarzschild metric and in the charged case, by the Reissner-Nordström metric. We adopted the Wheeler-deWitt formalism for our study which gave rise to the "Functional Schrödinger method". To address the unitarity issues, we computed the density matrix for the "total" outgoing radiation in all the cases we investigated. We further computed the probability density plus the probability current for the concerned wavefunctions and showed that they all satisfy the continuity equation which in the Schrödinger picture implies unitarity. The density matrix approach was previously done in some detail regarding the Schwarzschild case and these models were shown to obey unitary evolution. However, the authors therein had to resort to some numerical simulations for their end results and plots. On the contrary, probability conservation which we demonstrate in this work is purely analytic in nature. Furthermore, we improve upon the previous works of and show that there density matrix approach can also be done analytically. Additionally, checking unitarity by probability conservation is a novelty of our work.

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