The information loss problem

Abstract

The paradox of information loss within black holes is a major problem in theoretical physics. Stephen Hawking showed that pure states evolve into mixed states and entanglement entropy for the Page curve increases monotonically. These two results violate the unitarity of quantum mechanics and imply that gravitational effects at the quantum scale is not well understood. This paradox has lead to the idea’s of holography and subsequently the AdS/CFT correspondence. Much progress towards the paradox relies on holography, which includes a formula for computing entanglement entropy for gravitational systems. This formula consists of two terms: 1) A quantum extremal surface and 2) Entropy for semi-classical gravity. We present the computation on how to locate quantum extremal surfaces using JT gravity in AdS2 and subsequently show the Island surface on a Penrose diagram. We carry out the saddle point approximation, showing where the semi-classical expansion comes from and how to compute higher order corrections using Feynman diagrams. We find that the formula for entanglement entropy in gravitational systems within the Island proposal does indeed produce a unitary Page curve. However, the Island proposal is inconsistent because it doesn’t address massive gravitons which are needed in dimensions higher than 2. It also fails to address that the stress-energy tensor Tμν is not conserved, because energy and momentum leaks into the non-gravitational bath.