By Lotze T.
This degree thesis is anxious with the quantum box theoretical commentary that Black Holes should not solely black yet as a substitute radiate debris with a thermal strength distribution.This phenomenon has been recognized because the mid-seventies and is called, after its discoverer, the Hawking impression
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Extra resources for Two-dimensional models of black hole radiation (diplomarbeit)
Sample text
3) . 3) the regularization parameter µ occurs; this notation is, however, only symbolic. Later in this chapter, we will see explicitly how the regularization is done. 4) indicate points in spacetime where the d’Alembertian in question acts. The derivation of the corrections S(2) and S(3) in [8] already fixes the boundary conditions: They describe the spherically symmetric collapse of a cloud of dust in the distant past. ‘Distant’ means that we have approximately stationary radiation at the time when we evaluate the energy momentum tensor.
2 1 µν − g ( φ) ln φ 2 µ2 ,(µ 1 − φ φ,ν) − g µν ln φ 2 µ2 1 2 m − 1 m2 − ,(µ φ ,ε φ m2 1 − φ ,ε φ,ε + ln − µ2 φ φ ,ν) φ ,ε + m2 1 − φ m2 1 − φ . 13) easier to handle. 2) simplify the diagonal stress tensor components considerably: only terms without g µν survive. uu . The other one has the same Of the (u, u) and (v, v) components, we consider T(2) form, only with v in place of u. 13), ∞ − 1 1 1 2 ln φ φ,u − dm φ φ . T(2) uu = 4π µ2 m2 − ,u ,u m2 − ,u 0 By eqn. 3), this can be written as T(2) uu ∞ 1 = 4π dm2 m2 0 1 − φ,u φ,u − m2 1 − φ ,u m2 1 − φ ,u .
The action S describing a relativistic field theory consists of two parts: the gravitational action Sg , and the matter action Sm : S = S g + Sm . 1) from the action S. In order to do this, we have to decide on an explicit expression for Sg . In four dimensions we choose 1 Sg(4) = d4 x −g (4) R(4) . 3) 16π This action is known as the Einstein-Hilbert action [1]. Its variation with respect to the metric yields the left-hand side of eqn. 1). The matter part The right-hand side is not further specified in eqn.