Holographic entanglement entropy at finite temperature

The holographic correspondence AdS/CFT is a powerful duality that connects a theory of gravity in anti-de Sitter space with a (quantum) conformal field theory that lives on the boundary of the spacetime. In this context, the Ryu-Takayanagi formula allows to compute entanglement entropies of CFTs by computing the area of an extremal surface that extends from the boundary into the bulk of AdS. In this project we will use this formula and apply it to the case of black hole solutions, which represent thermal states. This will allow us to study the dependence of holographic entanglement entropy on the temperature. Furthermore, we will consider modifications of Einstein gravity in the bulk, which also lead to modifications of the Ryu-Takayanagi formula. Using this generalized formula, we will then study the expansion of the holographic entanglement entropy for small temperatures and investigate the possible universal character of the coefficients of this expansion. These results will also be interpreted in the context of the first law of entanglement entropy. The analysis could also be extended by studying the effect of a chemical potential on the entanglement entropy.