SÉMINAIRE DU GRECO
"Two short talks: Dark matter distributions around massive black holes: A general relativistic analysis & The Schwarzschild metric: It's the coordinates, stupid!" 

Cliff Will 

Two Short Talks: (1) Dark matter distributions around massive black holes: A general relativistic analysis The cold dark matter at the center of a galaxy will be redistributed by the presence of a massive black hole. The redistribution may be determined using an approach pioneered by Gondolo and Silk: begin with a model distribution function for the dark matter, and ``grow" the black hole adiabatically, holding the adiabatic invariants of the motion constant. We have recently completed a fully relativistic calculation using the exact Schwarzschild geometry of the black hole (arXiv:1305.2619). We compare and contrast the result with that of Gondolo and Silk, and discuss the implications of the dark matter distribution for the motions of stars orbiting close to the black hole that might be candidates for testing the black hole nohair theorems. (2) The Schwarzschild metric: It's the coordinates, stupid! Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation that is simple and one that is a mess. We give a concrete illustration of the maxim that ``coordinates matter" using the exact Schwarzschild solution for a vacuum, static spherical spacetime. We review the standard textbook derivation, Schwarzschild's original 1916 derivation, and a derivation using the LandauLifshitz formulation of the Einstein field equations. The last derivation is much more complicated, has one aspect for which we have been unable to find a solution, and gives an explicit illustration of the fact that the Schwarzschild geometry can be described in infinitely many coordinate systems (arXiv:1308.0394)


lundi 28 octobre 2013  11:00 Salle des séminaires Évry Schatzman, Institut d'Astrophysique de Paris 
