Bulletin of the American Physical Society
2007 APS April Meeting
Volume 52, Number 3
Saturday–Tuesday, April 14–17, 2007; Jacksonville, Florida
Session K7: Classical and Semi-classical Gravity |
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Sponsoring Units: GGR Chair: James Isenberg, University of Oregon Room: Hyatt Regency Jacksonville Riverfront Grand 8 |
Sunday, April 15, 2007 1:15PM - 1:51PM |
K7.00001: The present status of quantum field theory in curved spacetime Invited Speaker: Quantum field theory in curved spacetime is the theory of quantum fields propagating in a classical curved spacetime, as described by general relativity. This theory has been applied to describe such important and interesting phenomena as particle creation by black holes and perturbations in the early universe associated with inflation. On account of the absence of Poincare symmetry and the lack of a preferred ``vacuum state'' or natural notion of ``particles,'' some major conceptual issues arose as to how the theory is to be formulated. By the mid-1980's it was understood how to give a mathematically rigorous formulation of the theory of a free quantum field in curved spacetime by focusing attention on the algebraic relations satisfied by the field observables. However, only during the past decade has major progress been made in providing a mathematically satisfactory formulation of renormalization for interacting fields in curved spacetime. This talk will describe some of the recent developments and elucidate some of the insights that have thereby been attained regarding the nature of quantum field theory. [Preview Abstract] |
Sunday, April 15, 2007 1:51PM - 2:27PM |
K7.00002: Black Hole Rigidity Invited Speaker: We show that for arbitrary spacetime dimensions greater than or equal to 3+1, stationary black holes which are analytic solutions of the vacuum Einstein equations must have an extra symmetry (in addition to the assumed stationarity). [Preview Abstract] |
Sunday, April 15, 2007 2:27PM - 3:03PM |
K7.00003: On the topology of higher dimensional black holes Invited Speaker: Hawking's theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy condition are topologically 2-spheres. This conclusion extends to outer apparent horizons in spacetimes that are not necessarily stationary. Inspired by recent developments in the study of higher dimensional black holes, Rick Schoen and I have obtained a natural generalization of Hawking's results to higher dimensions by showing that cross sections of the event horizon (in the stationary case) and outer apparent horizons (in the general case) are of positive Yamabe type, i.e., admit metrics of positive scalar curvature. This implies many well-known restrictions on the topology, and is consistent with recent examples of five dimensional stationary black hole spacetimes with horizon topology $S^2 \times S^1$. In this talk we shall describe this joint work with Schoen, as well as more recent developments which address certain borderline cases arising in this work. [Preview Abstract] |
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