Relativity Seminar
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Tue, 09/10/2007 12:00 |
Stefan Hollands |
Relativity Seminar  |
L3 |
| It has been known for some time that in more than 4 spacetime dimensions, there is a considerably larger variety of black "hole" solutions, having e.g. different horizon topology. In particular, they are no longer fully characterized by their asymptotic charges (mass, angular momenta) alone. We give a partial classification theorem for higher dimensions, for solutions with sufficiently many axial Killing fields. We show that higher dimensional black holes may be fully characterized by their asymptotic charges, together with certain "moduli" and "winding numbers" that are analogous to those of Seiffert fibrations. In particular, we find constraints on the possible horizon topologies. In 5 dimensions, they may be either a black "hole" (sphere), black "ring", or a black "lens". | |||
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Tue, 30/10/2007 11:00 |
Juan Valiente Kroon (Queen Mary College, London) |
Relativity Seminar |
L3 |
| I will discuss ongoing work to provide a proof for the following conjecture: if the development of a time symmetric, conformally flat initial data set admits a smooth null infinity, then the initial data is Schwarzschildean in a neighbourhood of infinity. The strategy to construct a proof consists in a detailed analysis of a certain type of expansions that can be obtained using H. Friedrich's "cylinder at infinity" formalism. I will also discuss a toy model for the analysis of the Maxwell field near the spatial infinity of the Schwarzschild spacetime | |||
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Tue, 13/11/2007 11:00 |
Helmut Friedrich (Max Planck Society) |
Relativity Seminar |
L3 |
| Static vacuum data and their conformal classes play an important role in the discussion of the smoothness of gravitational fields at null infinity. We study the question under which conditions such data admit non-trivial conformal rescalings which lead again to such data. Some of the restrictions implied by this requirement are discussed and it is shown that there exists a 3-parameter family of static vacuum data which are not conformally flat and which admit non-trivial rescalings. | |||
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Tue, 27/11/2007 11:00 |
Prof. James Vickers (University of Southampton) |
Relativity Seminar |
L3 |
| In this talk I will look at a definition of the energy-momentum for the dynamical horizon of a black hole. The talk will begin by examining the role of a special class of observers at null infinity determined by Bramson's concept of frame alignment. It is shown how this is given in terms of asymptotically constant spinor fields and how this framework may be used together with the Nester-Witten two form to give a definition of the Bondi mass at null infinity. After reviewing Ashtekar's concept of an isolated horizon we will look at the propagation of spinor fields and show how to introduce spinor fields for the horizon which play the role of the asymptotically constant spinor fields at null infinity, giving a concept of alignment of frames on the horizon. It turns out that the equations satisfied by these spinor fields give precisely the Dougan-Mason holomorphic condition on the cross sections of the horizon, together with a simple propagation equation along the generators. When combined with the Nester-Witten 2-form these equations give a quasi-local definition of the mass and momentum of the black hole, as well as a formula for the flux across the horizon. These ideas are then generalised to the case of a dynamical horizon and the results compared to those obtained by Ashtekar as well as to the known answers for a number of exact solutions. | |||
