On problems in de Sitter spacetime physics: scalar field, black holes and instability

Master thesis
Research group: 
Quantum Gravity
Jelle Hartong

Various coordinate systems and the conformal structure of de Sitter and Schwarzschild-de Sitter spacetime are discussed. A de Sitter space is shown to have a horizon and no spatial infinity. The spacetime is essentially nonstationary.
Scalar particles are introduced on a fixed de Sitter background and quantized using the method of covariant quantization. First it is shown that there exists a two-parameter family of inequivalent vacua. Then it is argued that the only physically acceptable vacuum is the euclidean vacuum. The Green’s functions defined with respect to this vacuum are periodic in imaginary time and are thus thermal Green’s functions. The temperature being the same for all observers is an intrinsic property of the de Sitter spacetime. The appearance of this temperature is an example of the generality of the Hawking radiation experienced by a horizon. A geometric interpretation of the temperature of the black hole and cosmological event horizons appearing in the Schwarzschild-de Sitter space will be given in terms of the surface gravity of the horizon, euclidean sections and the removal of conical singularities that appear in static coordinate systems. An important result in this is that
the black hole horizon temperature is always higher than the temperature of the cosmological event horizon. Then it is shown that there exist scalar particles which have no Minkowskian analogue in the sense that their mass parameter cannot be related to the mass parameter of the Poincar´e group.
Finally, the question of the stability of de Sitter space is discussed. A de Sitter space is stable with respect to any classical perturbation. However, an instability occurs in the semi-classical regime. In a semi-classical approximation of the partition function a sum over the finite temperature gravitational instantons is obtained. One such instanton is S2 × S2. This has an unstable fluctuation which appears as an imaginary contribution to the partition function of de Sitter space. De Sitter space undergoes thermally induced topological changes in which the entire spacetime decays into a Schwarzschild-de Sitter spacetime. However, the black hole will evaporate and de Sitter spacetime is left behind.

Publication date: 
July, 2004