Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-06-12
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Scientific paper
We investigate the time evolution of the temperature and entropy of a gravitationally collapsing de Sitter Schwarzschild domain wall as seen by an asymptotic observer. Recent work has completed this analysis for Schwarzschild and 3+1 BTZ domain walls. There were some striking qualitative differences between the two. Specifically, the BTZ domain wall exhibited a decrease in entropy over time. However, it contained both a cosmological constant and a different topology from the Schwarzschild domain wall, and we wish to isolate which of these is responsible for the qualitative differences. Hence, we will study the de Sitter Schwarzschild domain wall, as it has identical topology to the Schwarzschild domain wall yet also contains a cosmological constant. We utilize a wavefunctional approach where we couple a scalar field to the background of the collapsing domain wall and determine the spectrum of the radiation as a function of time. The fact that the distribution is thermal allows for the determination of the temperature as a function of time. Since the collapsing domain wall forms a black hole, we compare the final temperature to the Hawking temperature and find very good agreement. The temperature also exhibits the proper scaling with the mass of the domain wall. Using the thermodynamic definition of entropy and the temperature-mass relation, we find the entropy as a function of time. The entropy exhibits an interesting feature in that there is a very small decrease in entropy before it starts to increase and eventually approach a constant. This feature goes away for smaller values of the cosmological constant. This suggests that 1) gravitational collapse is prevented in a certain parameter space, and 2) the probable cause of the qualitative differences in the domain wall collapse of the Schwarzschild versus BTZ domain walls is the cosmological constant and not the topology.
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