Do Singularity Theorems hold if we consider quantum effects?

Author(s)

Lissa de Souza Campos

• Document type: Master's Dissertation
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 2018-10-11

Examining board members

Joao Carlos Alves Barata; Andre Gustavo Scagliusi Landulfo; Daniel Augusto Turolla Vanzela

• Advisor: Joao Carlos Alves Barata

Abstract

There are two quantum loopholes in the Singularity Theorems of General Relativity: violations of the classical energy conditions and quantum fluctuations of the spacetime geometry. In this dissertation, we study the first loophole and approach Singularity Theorems through the energy condition. We review the algebraic approach of Quantum Field Theory for the Klein-Gordon field and, within it, we review the derivation of a quantum energy inequality for Hadamard states on globally hyperbolic spacetimes. However quantum energy inequalities cannot be directly applied to Singularity Theorems, we show that generalized Hawking and Penrose Theorems are proven considering weakened energy conditions inspired by them. Hence, Singularity Theorems do hold under subtle quantum effects. The question of whether interaction or backreaction effects could break them is still open; there are reasons to expect both answers. (AU)

• FAPESP's process: 16/11090-9 - Singularity theorems and energy inequalities in quantum field theories in curved space-times
• Grantee: Lissa de Souza Campos
• Support Opportunities: Scholarships in Brazil - Master