PHYSICS SEMINAR
THE GRAVITATIONAL COLLAPSE OF A 5D INSTANTON AND ITS FREE ENERGY
Benjamin Constantineau
Physics Department
Bishop's University
Friday, January 22, 2010
1:30-2:30 pm
Nicolls 1
We studied numerically the spherically symmetric gravitational collapse of a 5D (4+1)-dimensional Yang-Mills instanton coupled to gravity in an asymptotically flat spacetime and followed the time evolution of the matter field, the metric fields and their respective conjugate momenta. Besides the static initial conditions, we also investigate the non-static case where the conjugate momentum for the matter field is nonzero initially. By a perturbation scheme, we can obtain the initial state of all fields to arbitrary accuracy (one needs to go to higher orders of perturbation theory as the momentum increases). The numerical simulations reveal that at late stages of the collapse, when thermal equilibrium is reached, the spacetime outside the horizon does not settle exactly into the 5D Schwarzschild spacetime. We discuss the physical phenomenon that is responsible for this. We track a thermodynamic potential, the “free energy”, as a function of time and we show that at late stages it matches the expected value from black hole thermodynamics. The entropy is observed to accumulate along a thin slice near the horizon and it is shown to be gravitational in origin. An important result of our classical dynamical study is that entropy requires the fields to be non-static near the horizon. This may possibly resolve a long-standing paradox between the entropy of stationary black holes and the no-hair theorem which suggests zero entropy.
