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

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

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

Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?

Because of the limit in the number of gamma-ray bursts (GRBs) with available redshifts and spectra, all current investigations on the correlation among GRB variables use burst samples with redshifts that span a very large range. The evolution and selection effects have thus been ignored, which might have important influence on the results. In this Letter, we divide the 48 long-duration GRBs in Amati (2006, 2007) into four groups with redshift from low to high, each group contains 12 GRBs. Then we fit each group with the Amati relation \log E_\iso = a + b \log E_\p, and check if the parameters $a$ and $b$ evolve with the GRB redshift. We find that $a$ and $b$ vary with the mean redshift of the GRBs in each group systematically and significantly. Monte-Carlo simulations show that there is only $\sim 4$ percent of chance that the variation is caused by the selection effect arising from the fluence limit. Hence, our results may indicate that GRBs evolve strongly with the cosmological redshift.Comment: 5 pages, including 5 figures. MNRAS Letters accepte

A New Unified Theory of Electromagnetic and Gravitational Interactions

In this paper we present a new unified theory of electromagnetic and gravitational interactions. By considering a four-dimensional spacetime as a hypersurface embedded in a five-dimensional bulk spacetime, we derive the complete set of field equations in the four-dimensional spacetime from the five-dimensional Einstein field equation. Besides the Einstein field equation in the four-dimensional spacetime, an electromagnetic field equation is derived: $\nabla_a F^{ab}-\xi R^b_{\;\,a}A^a=-4\pi J^b$ with $\xi=-2$, where $F^{ab}$ is the antisymmetric electromagnetic field tensor defined by the potential vector $A^a$, $R_{ab}$ is the Ricci curvature tensor of the hypersurface, and $J^a$ is the electric current density vector. The electromagnetic field equation differs from the Einstein-Maxwell equation by a curvature-coupled term $\xi R^b_{\;\,a}A^a$, whose presence addresses the problem of incompatibility of the Einstein-Maxwell equation with a universe containing a uniformly distributed net charge as discussed in a previous paper by the author [L.-X. Li, Gen. Relativ. Gravit. {\bf 48}, 28 (2016)]. Hence, the new unified theory is physically different from the Kaluza-Klein theory and its variants where the Einstein-Maxwell equation is derived. In the four-dimensional Einstein field equation derived in the new theory, the source term includes the stress-energy tensor of electromagnetic fields as well as the stress-energy tensor of other unidentified matter. Under some conditions the unidentified matter can be interpreted as a cosmological constant in the four-dimensional spacetime. We argue that, the electromagnetic field equation and hence the unified theory presented in this paper can be tested in an environment with a high mass density, e.g., inside a neutron star or a white dwarf, and in the early epoch of the universe.Comment: 41 pages, including 1 figure and 1 table. A new section is added to describe the relation to the Kaluza-Klein theory. Version accepted to Frontiers of Physic

Electromagnetic Force on a Brane

A fundamental assumption in the theory of brane world is that all matter and radiation are confined on the four-dimensional brane and only gravitons can propagate in the five-dimensional bulk spacetime. The brane world theory did not provide an explanation for the existence of electromagnetic fields and the origin of the electromagnetic field equation. In this paper, we propose a model for explaining the existence of electromagnetic fields on a brane and deriving the electromagnetic field equation. Similar to the case in Kaluza-Klein theory, we find that electromagnetic fields and the electromagnetic field equation can be derived from the five-dimensional Einstein field equation. However, the derived electromagnetic field equation differs from the Maxwell equation by containing a term with the electromagnetic potential vector coupled to the spacetime curvature tensor. So it can be considered as generalization of the Maxwell equation in a curved spacetime. The gravitational field equation on the brane is also derived with the stress-energy tensor for electromagnetic fields explicitly included and the Weyl tensor term explicitly expressed with matter fields and their derivatives in the direction of the extra-dimension. The model proposed in the paper can be regarded as unification of electromagnetic and gravitational interactions in the framework of brane world theory.Comment: 8 page