טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentAdam Levi
SubjectSemiclassical Stress-Energy Tensor Computation and
Black Holes Evaporation
DepartmentDepartment of Physics
Supervisor Full Professor Ori Amos
Full Thesis textFull thesis text - English Version


Abstract

The subject of this Ph.D. thesis is semiclassical effects in black holes (BHs). A quantum field on a classical metric has a non-trivial stress-energy tensor. The naive computation of the stress tensor is divergent and one must renormalize it in order to obtain the renormalized stress-energy tensor (RSET). The RSET is the source term in the semiclassical Einstein equation, which determines the evolution of the metric. By solving the field equation coupled to the semiclassical Einstein equation one can study the evaporation of a black hole. Here we present our work on (1) The study of semiclassical correction to two-dimensional CGHS black holes using a static model. In two dimensions the evolution of the RSET is known analytically as a function of the metric (due to the trace-anomaly). We have analytically studied a static version of the CGHS model, and found the leading order corrections in large-mass for the Hawking temperature and outflux. (2) We present a new pragmatic mode-sum regularization (PMR) method to compute the renormalized expectation value of Φ2, which is often treated as a simplified case study for regularization methods before the RSET. We present the first variant of the method, aimed for stationary backgrounds, named the t-splitting variant. We show results computed in Schwarzschild for the Boulware vacuum state. (3) The angular-splitting variant of the PMR method is presented for the computation of Φ2. The angular variant is applicable to spherically-symmetric backgrounds. Results are given in Schwarzschild in all three vacuum states (Boulware, Hartle-Hawking and Unruh). (4) The PMR method is used for the first time for computing the RSET. We present the first results for the RSET in Schwarzschild for a minimally-coupled scalar field. The computations are done using three variants, the t-splitting, the angular splitting, and a newly presented variant, the φ-splitting, aimed for axially symmetric backgrounds. The results are then used to investigate the energy conditions. We find that the RSET violates all standard energy conditions (weak energy condition, null energy condition, averaged weak energy condition, and averaged null energy condition). (5) The computation of the RSET using the t-splitting variant is presented in detail. Results of the RSET in Schwarzschild are presented in all three vacuum states. (6) The PMR method is used to compute the RSET for a spinning BH (the Kerr metric), which was an open problem for over three decades. The results are computed using two different variants, the t-splitting and the φ-splitting, with good agreement between the two.