76,876 research outputs found

### 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

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