Hidden symmetries and decay for fields outside a Kerr black hole

Wednesday, August 25, 2010 -
2:00pm to 4:00pm
The Kerr solutions to Einstein's equations describe rotating black holes. For the wave equation in flat-space and outside the non-rotating, Schwarzschild black holes, one method for proving decay is the vector-field method, which uses the energy-momentum tensor and vector-fields. Outside the Schwarzschild black hole, a key intermediate step in proving decay involved proving a Morawetz estimate using a vector-field which pointed away from the photon sphere, where null geodesics orbit the black hole. Outside the Kerr black hole, the photon orbits have a more complicated structure. By using the hidden symmetry of Kerr, we can replace the Morawetz vector-field by a fifth-order operator which, in an appropriate sense, points away from the photon orbits. This allows us to prove the necessary Morawetz estimate, also called a local energy decay estimate, which is a key step in proving pointwise decay estimates.This is joint work with Lars Andersson.At the end, I also hope to speak about current work on Maxwell's equations.
Pieter Blue
University of Edinburgh
Event Location: 
Fine Hall 314