Donald M. Witt

The metal-surface selection rule for infrared spectra of molecules adsorbed on small metal particles

Abstract The metal-surface selection rule predicts that some infrared absorption bands should be absent from the spectra of molecules adsorbed on metal particles. It predicts that those bands corresponding to molecular vibrations with an oscillating dipole moment parallel to the surface should be suppressed. We calculate that this selection rule should apply to adsorption on metal particles larger than about 20 A in diameter; for smaller particles the rule is weakened.

Phase transitions for flat anti-de Sitter black holes.

We reexamine the thermodynamics of anti-de Sitter (adS) black holes with Ricci flat horizons using the adS soliton as the thermal background. We find that there is a phase transition which is dependent not only on the temperature but also on the black hole area, which is an independent parameter. As in the spherical adS black hole, this phase transition is related via the adS/conformal-field-theory correspondence to a confinement-deconfinement transition in the large- N gauge theory on the conformal boundary at infinity.

Phase Transitions for Flat Anti{endash}de Sitter Black Holes

We reexamine the thermodynamics of anti-de Sitter (adS) black holes with Ricci flat horizons using the adS soliton as the thermal background. We find that there is a phase transition which is dependent not only on the temperature but also on the black hole area, which is an independent parameter. As in the spherical adS black hole, this phase transition is related via the adS/conformal-field-theory correspondence to a confinement-deconfinement transition in the large- N gauge theory on the conformal boundary at infinity.

Topological Censorship[Phys. Rev. Lett. 71, 1486 (1993)]

Classically, all topologies are allowed as solutions to the Einstein equations. However, one does not observe any topological structures on medium range distance scales, that is scales that are smaller than the size of the observed universe but larger than the microscopic scales for which quantum gravity becomes important. Recently, Friedman, Schleich and Witt have proven that there is topological censorship on these medium range distance scales: the Einstein equations, locally positive energy, and local predictability of physics imply that any medium distance scale topological structures cannot be seen. More precisely, we show that the topology of physically reasonable isolated systems is shrouded from distant observers, or in other words there is a topological censorship principle.

Symmetry groups of state vectors in canonical quantum gravity

In canonical quantum gravity, the diffeomorphisms of an asymptotically flat hypersurface S, not connected to the identity, but trivial at infinity, can act nontrivially on the quantum state space. Because state vectors are invariant under diffeomorphisms that are connected to the identity, the group of inequivalent diffeomorphisms is a symmetry group of states associated with S. This group is the zeroth homotopy group of the group of diffeomorphisms fixing a frame of infinity on S. It is calculated for all hypersurfaces of the form S=S3/G‐point, where the removed point is thought of as infinity on S and the symmetry group S is the zeroth homotopy group of the group of diffeomorphisms of S3/G fixing a point and frame, denoted π0u2009DiffF(S3/G). Before calculating π0u2009DiffF (S3/G), it is necessary to find π0 of the group of diffeomorphisms. Once π0u2009Diff(S3/G) is known, π0u2009Diffx0(S3/G) is calculated using a fiber bundle involving Diff(S3/G), Diffx0(S3/G), and S3/G. Finally, a fiber bundle involving DiffF(S3/G), ...

Homotopy is not isotopy for homeomorphisms of 3-manifolds

existence of a homeomorphism that is homotopic but not isotopic to the identity has remained an open question for closed 3-manifolds [I, 23. We consider here homeotopy groups:: of spherical spaces, finding as a by-product of our work an example of such a homeomorphism for a closed 3-manifold whose prime factors include certain spherical spaces. The homeotopy groups of a composite 3-manifold have as subgroups the disk-fixing or point-fixing homeotopy groups of each prime factor [3,4]. In the work reported here our primary aim has been to calculate, for spherical spaces the corresponding 0th homeotopy groups, the groups of path connected components of the spaces of disk-fixing and point- fixing homeomorphisms. Homeomorphism groups of spherical spaces have been considered recently by Rubinstein et al. [S-7]. Asano [8], Bonahon [9] and Ivanov [lo]. Their results are consistent with Hatcher’s conjecture [ 1 l] that for each spherical space the group of homeomorphisms has the same homotopy type as the group of isometries. Homotopy classes of the groups HO and XX of homeomorphisms that fix respectively a disk and a point do not generally have this character (for spherical spaces): in particular, nonzero elements of ~,,(&‘a) and rr,, (XX) are commonly not represented by isometries. For several spherical spaces of the form

On squashed black holes in Godel universes

We investigate five-dimensional rotating and charged black holes with squashed horizons in Goedel universes. The general solution was recently derived by applying a squashing transformation on the general nonextremal charged and rotating black hole in the Goedel universe found by Wu. We give a discussion of the squashed geometry and also consider its lift to ten dimensions and discuss the T-dual geometry. Finally, using the counterterms method we compute its conserved charges and explore its thermodynamics.

Internal symmetry groups of quantum geons

Abstract In canonical quantum gravity asymptotically trivial diffeomorphisms not deformable to the identity can act nontrivially on the quantum state space. We show that for many 3-manifolds, the inequivalent diffeomorphisms comprise coverings in SU(2) of crystallographic groups. When the diffeomorphism R 2π associated with 2π-rotation is nontrivial, state vectors can have half-integral angular momentum; we list all 3-manifolds with R 2π trivial.

The Generalized Hartle-Hawking initial state: Quantum field theory on Einstein conifolds

Recent arguments have indicated that the sum over histories formulation of quantum amplitudes for gravity should include sums over conifolds, a set of histories with more general topology than that of manifolds. This paper addresses the consequences of conifold histories in gravitational functional integrals that also include scalar fields. This study will be carried out explicitly for the generalized Hartle-Hawking initial state, that is the Hartle-Hawking initial state generalized to a sum over conifolds. In the perturbative limit of the semiclassical approximation to the generalized Hartle-Hawking state, one finds that quantum field theory on Einstein conifolds is recovered. In particular, the quantum field theory of a scalar field on de Sitter spacetime with

Thermodynamics of non-extremal Kaluza-Klein multi-black holes in five dimensions

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