PHYSICS SEMINAR
Extremal black holes and classical gravitational entropy
Dr. Ariel Edery
Physics Department
Bishop's University
Friday, October 22, 2010
1:30-2:30 pm
Nicolls 315
We show that extremal black holes have zero entropy by pointing out a simple fact: they are time-independent throughout the spacetime and therefore correspond to a single or unique metric field configuration. Though extremal black holes have an event horizon their corresponding maximally extended spacetime does not possess a bifurcate Killing horizon. We then show that non-extremal black holes, including the Schwarzschild black hole, contain a region hidden behind the event horizon where all their Killing vectors are spacelike. This region is nonstationary and the time t acts as a label for a continuous set of classical microstates, the phase space [hab (t), Pab (t)], where hab is the three-metric induced on a spacelike hypersurface ? and Pab is its momentum conjugate. We determine explicitly the phase space in the interior of the Schwarzschild black hole. The entropy is a measure of our ignorance of the interior configuration hidden behind the event horizon of the black hole. We provide numerical evidence from recent simulations of gravitational collapse in isotropic coordinates that the entropy of the Schwarzschild black hole stems from the region inside and near the event horizon where the metric fields are nonstationary. The rest of the spacetime, which is static, makes no contribution.
