Electrodynamics on Cosmological Scales

Maxwell's equations cannot describe a homogeneous and isotropic universe with a uniformly distributed net charge, because the electromagnetic field tensor in such a universe must be vanishing everywhere. For a closed universe with a nonzero net charge, Maxwell's equations always fail regardless of the spacetime symmetry and the charge distribution. The two paradoxes indicate that Maxwell's equations need be modified to be applicable to the universe as a whole. We consider two types of modified Maxwell equations, both can address the paradoxes. One is the Proca-type equation which contains a photon mass term. This type of electromagnetic field equations can naturally arise from spontaneous symmetry breaking and the Higgs mechanism in quantum field theory, where photons acquire a mass by eating massless Goldstone bosons. However, photons loose their mass when symmetry is restored, and the paradoxes reappear. The other type of modified Maxwell equations, which are more attractive in our opinions, contain a term with the electromagnetic potential vector coupled to the spacetime curvature tensor. This type of electromagnetic field equations do not introduce a new dimensional parameter and return to Maxwell's equations in a flat or Ricci-flat spacetime. We show that the curvature-coupled term can naturally arise from the ambiguity in extending Maxwell's equations from a flat spacetime to a curved spacetime through the minimal substitution rule. Some consequences of the modified Maxwell equations are investigated. The results show that for reasonable parameters the modification does not affect existing experiments and observations. However, the field equations with a curvature-coupled term can be testable in astrophysical environments where mass density is high or the gravity of electromagnetic radiation plays a dominant role in dynamics, e.g., interior of neutron stars and the early universe.Comment: 23 pages, including 1 figure. Version matching publication in GR

Time Machines Constructed from Anti-de Sitter Space

In this paper time machines are constructed from anti-de Sitter space. One is constructed by identifying points related via boost transformations in the covering space of anti-de Sitter space and it is shown that this Misner-like anti-de Sitter space is just the Lorentzian section of the complex space constructed by Li, Xu, and Liu in 1993. The others are constructed by gluing an anti-de Sitter space to a de Sitter space, which could describe an anti-de Sitter phase bubble living in a de Sitter phase universe. Self-consistent vacua for a massless conformally coupled scalar field are found for these time machines, whose renormalized stress-energy tensors are finite and solve the semi-classical Einstein equations. The extensions to electromagnetic fields and massless neutrinos are discussed. It is argued that, in order to make the results consistent with Euclidean quantization, a new renormalization procedure for quantum fields in Misner-type spaces (Misner space, Misner-like de Sitter space, and Misner-like anti-de Sitter space) is required. Such a "self-consistent" renormalization procedure is proposed. With this renormalization procedure, self-consistent vacua exist for massless conformally coupling scalar fields, electromagnetic fields, and massless neutrinos in these Misner-type spaces.Comment: 17 pages (revtex), 6 figures (4 postscript, 2 gif

K-theory for ring C*-algebras attached to function fields with only one infinite place

We study the K-theory of ring C*-algebras associated to rings of integers in global function fields with only one single infinite place. First, we compute the torsion-free part of the K-groups of these ring C*-algebras. Secondly, we show that, under a certain primeness condition, the torsion part of K-theory determines the inertia degrees at infinity of our function fields.Comment: 27 page

Observational Signatures of the Magnetic Connection between a Black Hole and a Disk

In this Letter we use a simple model to demonstrate the observational signatures of the magnetic connection between a black hole and a disk: (1) With the magnetic connection more energy is dissipated in and radiated away from regions close to the center of the disk; (2) The magnetic connection can produce a very steep emissivity compared to the standard accretion; (3) The observational spectral signature of the magnetic connection can be robust. These signatures may be identified with the observations of Chandra and XMM-Newton. In fact, the steep emissivity index for the Seyfert 1 galaxy MCG--6-30-15 inferred from the recent XMM-Newton observation is very difficult to be explained with a standard accretion disk but can be easily explained with the magnetic connection between a black hole and a disk.Comment: 10 pages, 3 figure

A new approach to recent constructions of C*-algebras from modular index theory

We present a new approach to C*-algebras recently constructed in the context of modular index theory by Carey, Phillips, Putnam and Rennie. It turns out that their constructions can be identified with full corners of ideals in semigroup C*-algebras. This new point of view leads to a systematic analysis of these algebras and their canonical maximal abelian subalgebras.Comment: 22 page