The black hole information paradox: from Hawking radiation to holographic correspondence

Abstract

In this thesis, we explore the correlation between the thermal entropy of the Hawking radiation and its entanglement entropy. We begin by presenting the particle creation phenomenon due to the spacetime curvature of a black hole using Hawking’s “semiclassical” approach. This calculation also suggests that black holes possess a thermal entropy proportional to its event horizon area, S ∼ R2, in (3+1) dimensions. This prompts us to find the correlation between a bulk volume and its boundary area, which can be described by the AdS/CFT correspondence. Using the Ryu-Takayanagi formula, at zero and finite temperature cases, the regulated geodesic length in AdS3 was then found to be directly proportional to the entanglement entropy of a finite CFT2 interval, whose endpoints coincide with that of the AdS3 geodesic. As an original contribution, this thesis shows that the finite-temperature entanglement entropy reduces to the zero-temperature entanglement entropy and thermal black hole entropy in the T → 0 and T → ∞ limits, respectively. Furthermore, the high-temperature entanglement entropy in (2+1)-dimensional black hole spacetime has the relation S ∼ R, analogous to the (3+1)-dimensional case. We thus postulate that the entanglement entropy is a generalisation of the thermal black hole entropy in any number of dimensions. The AdS/CFT correspondence is therefore an alternative way to compute the black hole entropy.