Ph.D Student | Adam Levi |
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Subject | Semiclassical Stress-Energy Tensor Computation and Black Holes Evaporation |

Department | Department of Physics |

Supervisor | Full Professor Ori Amos |

Full Thesis text |

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 Φ^{2}, 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 Φ^{2}. 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.