Quantum information theory and the black hole information paradox

Abstract

This thesis discusses the information-theoretic concepts of Black Holes. Its primary focus is describing black hole dynamics with unitary operators within the perspective of quantum information theory and AdS/CFT arguments on why black hole evaporation is likely to be unitary. This thesis also provides mathematical backgrounds of classical black holes and quantum field theory in curved space. Then we introduced entanglement entropy and compared the shell of photons in a pure state to free harmonic oscillators. Afterward, we introduce an interaction term in the hamiltonian for t > 0, which we call a sudden quench. Finally, we have calculated the time evolved entanglement entropy for N-quenched oscillators and graphically demonstrated the entanglement entropy for various N. We want to model the time dependent entanglement entropy S1 between the internal and emitted radiation of a black hole. As for a future project, we want to regularize a quantum field to the Hamiltonian of N-quenched oscillators and compute the entanglement entropy S2 that results from tracing degrees of freedom inside an imaginary sphere. Hence, as S1 increases with time as the photons’ shell begins to collapse, we have a comparable situation, using the ideas about holography, with the time evolution of the S2.