Can we consider anti-de Sitter spacetime an isolated system?

• Grant number: 22/04727-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2022
• End date: December 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: João Paulo Pitelli Manoel
• Grantee: Felipe Gomes Rodrigues da Cunha
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this undergraduate research project, the concept of non-globally hyperbolic space-times will be introduced to the student through the study of wave propagation in an asymptotically anti-de Sitter background. The study will be guided by the advisor's and his collaborators' article published recently in the periodic "Journal of Mathematical Physics" [1]. The main goal of this article, and therefore of this research program, is to understand how the boundary conditions imposed on the conformal infinity affect the information exchanges between the infinity and the bulk. We will show that only Dirichlet's and Neumann's conditions are compatible with the concept of "isolated space-time". All others (called "mixed" or "Robin's" conditions) would imply an exchange of energy/momentum between the boundary and the bulk. This implication goes against some articles that can be found in the literature, in which it's affirmed that the anti-de Sitter space-time would be isolated when tested by waves satisfying Robin's conditions.(AU)