Dissertação de Mestrado #683 – Lucas de Souza Menicucci – 19/08/2022

Investigations towards the microscopic origin of the entropy of black holes revealed a interesting property of the amount of the entanglement between two complementary spatial regions for the vacuum state of a real free scalar field \cite{bombelli_quantum_1986}, its proportionality with the area separating the regions. From that point, entropy of entanglement has enlarged its range of applicability as an important tool for exploring the internal structure of quantum field theories. Although the area law proved to be a specific case, new studies have unveiled the dependency of this quantity on geometric features of spacetime by the presence of universal coefficients. In this dissertation, a numerical study of the entanglement entropy of a real scalar field on a curved background is presented. Two universal coefficients are estimated with good agreement with its predicted values. A description of the used techniques as well as a brief revision of the necessary theories are also included.