MSc PHYSICS DISSERTATION
Numerical Study of Thermodynamics During Classical Gravitational Collapse in
3 + 1 and 4 + 1 Dimensions
Benjamin Constantineau
Thursday, January 27, 2011
2:00 pm
Hamilton 300
We track a thermodynamic function, the free energy F, during the classical gravitational collapse of a 4D (3+1) massless scalar field to a Schwarzschild black hole in isotropic coordinates. Standard black hole thermodynamics predicts that the free energy F = E TS for the 4D Schwarzschild black hole is E/2 where E is the black hole mass, T the Hawking temperature and S the entropy. Our numerical simulations show that at late stages of the collapse the free energy function approaches a value to within 3% to 5% of the expected E/2 result, the difference being partly due to the presence of an outgoing matter wave in the exterior region. As far as we know, these results represent the first numerical confirmation of 4D black hole thermodynamics from classical gravitational collapse. We also present numerical results for the thermodynamics during the classical gravitational collapse of a 5D massless scalar field. The free energy function in this case approaches E/3 as expected. We show that in both the 4D and 5D cases the black hole entropy stems from the region inside and near the event horizon where the metric fields are nonstationary.
