טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentLiora Dori
SubjectEvaporation of 2-Dimensional Black Holes
DepartmentDepartment of Physics
Supervisor Full Professor Ori Amos


Abstract

The idea that nature allows the existence of spacetime regions that let nothing escape their gravitational attraction is probably one of the most intriguing predictions of classical general relativity. Ironically, discovering that due to quantum effects radiation does escape this fatal attraction, did not resolve the mystery. Rather, it intensified it.

As Hawking first discovered in 1974, black holes emit thermal radiation ("Hawking radiation") at a steady rate, which eventually may lead to their complete evaporation. The evaporation process, arising from quantum mechanical effects in a gravitational field, should obviously be investigated within a quantum-gravity theory. However, the latter hasn't been formulated yet. Nevertheless, assuming the black hole is macroscopic, one can carry out the investigations within a semiclassical framework, in which the metric is treated classically but the matter fields are treated quantum-mechanically.

The semiclassical field equations are governed by the generalized (namely, semiclassical) Einstein equation. Naturally, one is interested in solving the 4-dimensional generalized Einstein equation, hoping to relate its solution to astrophysical black holes. Unfortunately, only in 2 dimensions we can write this equation in a consistent form, i.e., as a closed system of hyperbolic, partial differential equations.

Such a semiclassical model of 2-dimensional black hole was first presented by Callan, Giddings, Harvey and Strominger (CGHS). The CGHS model exhibits the main features of an evaporating black-hole and in particular, the 2-dimensional analog of Hawking radiation. Therefore it can serve as a toy-model for the corresponding 4-dimensional evaporating black hole. The analytical solution of the CGHS model is yet unknown, however solutions can be obtained by numerical integration of the field equations.

In this work, we investigate numerically the evaporation process of a two-dimensional, CGHS black hole. We solve the CGHS equations numerically, and verify the validity of the numerical solution by comparing it to several recent works which analyzed the CGHS model by several analytic approximations. The numerical code we have developed, allows us to obtain the solution over a considerable part of the semiclassical spacetime, thus to explore some of the most interesting phenomena involved in the evaporation process of a black hole, especially, the Hawking radiation.