2,832 research outputs found
Friedmann branes with variable tension
We introduce brane-worlds with non-constant tension, strenghtening the
analogy with fluid membranes, which exhibit a temperature-dependence according
to the empirical law established by E\"otv\"os. This new degree of freedom
allows for evolving gravitational and cosmological constants, the latter being
a natural candidate for dark energy. We establish the covariant dynamics on a
brane with variable tension in full generality, by considering asymmetrically
embedded branes and allowing for non-standard model fields in the 5-dimensional
space-time. Then we apply the formalism for a perfect fluid on a Friedmann
brane, which is embedded in a 5-dimensional charged Vaidya-Anti de Sitter
space-time.Comment: 12 pages, to appear in Phys. Rev.
On the validity of the 5-dimensional Birkhoff theorem: The tale of an exceptional case
The 5-dimensional (5d) Birkhoff theorem gives the class of 5d vacuum
space-times containing spatial hypersurfaces with cosmological symmetries. This
theorem is violated by the 5d vacuum Gergely-Maartens (GM) space-time, which is
not a representant of the above class, but contains the static Einstein brane
as embedded hypersurface. We prove that the 5d Birkhoff theorem is still
satisfied in a weaker sense: the GM space-time is related to the degenerated
horizon metric of certain black-hole space-times of the allowed class. This
result resembles the connection between the Bertotti-Robinson space-time and
the horizon region of the extremal Reissner-Nordstrom space-time in general
relativity.Comment: 13 pages; v2: title amended, to be published in Classical and Quantum
Gravit
Gravitational radiation reaction in compact binary systems: Contribution of the quadrupole-monopole interaction
The radiation reaction in compact spinning binaries on eccentric orbits due
to the quadrupole-monopole interaction is studied. This contribution is of
second post-Newtonian order. As result of the precession of spins the magnitude
of the orbital angular momentum is not conserved. Therefore a proper
characterization of the perturbed radial motion is provided by the energy
and angular average . As powerful computing tools, the generalized
true and eccentric anomaly parametrizations are introduced. Then the secular
losses in energy and magnitude of orbital angular momentum together with the
secular evolution of the relative orientations of the orbital angular momentum
and spins are found for eccentric orbits by use of the residue theorem. The
circular orbit limit of the energy loss agrees with Poisson's earlier result.Comment: accepted for publication in Phys. Rev.
Asymmetric Swiss-cheese brane-worlds
We study a brane-world cosmological scenario with local inhomogeneities
represented by black holes. The brane is asymmetrically embedded into the bulk.
The black strings/cigars penetrating the Friedmann brane generate a
Swiss-cheese type structure. This universe forever expands and decelerates, as
its general relativistic analogue. The evolution of the cosmological fluid
however can proceed along four branches, two allowed to have positive energy
density, one of them having the symmetric embedding limit. On this branch a
future pressure singularity can arise for either (a) a difference in the
cosmological constants of the cosmological and black hole brane regions (b) a
difference in the left and right bulk cosmological constants. While the
behaviour (a) can be avoided by a redefinition of the fluid variables, (b)
establishes a critical value of the asymmetry over which the pressure
singularity occurs. We introduce the pressure singularity censorship which
bounds the degree of asymmetry in the bulk cosmological constant. We also show
as a model independent generic feature that the asymmetry source term due to
the bulk cosmological constant increases in the early universe. In order to
obey the nucleosynthesis constraints, the brane tension should be constrained
therefore both from below and from above. With the maximal degree of asymmetry
obeying the pressure singularity censorship, the higher limit is 10 times the
lower limit. The degree of asymmetry allowed by present cosmological
observations is however much less, pushing the upper limit to infinity.Comment: v2: considerably expanded, 19 pages, 8 figures, many new references.
Pressure singularity censorship introduced, strict limits on the possible
degree of asymmetry derived. v3: model independent analysis shows that the
asymmetry bounds the brane tension from above. Limits on the maximal tension
set. Version published in JCA
Non-uniform Braneworld Stars: an Exact Solution
The first exact interior solution to Einstein's field equations for a static
and non-uniform braneworld star with local and non-local bulk terms is
presented. It is shown that the bulk Weyl scalar is always
negative inside the stellar distribution, in consequence it reduces both the
effective density and the effective pressure. It is found that the anisotropy
generated by bulk gravity effect has an acceptable physical behaviour inside
the distribution. Using a Reissner-N\"{o}rdstrom-like exterior solution, the
effects of bulk gravity on pressure and density are found through matching
conditions.Comment: 22 pages, 3 figures, version to be published in International Journal
of Modern Physics D (IJMPD
Linear Einstein equations and Kerr-Schild maps
We prove that given a solution of the Einstein equations for the
matter field , an autoparallel null vector field and a solution
of the linearized Einstein equation on the
given background, the Kerr-Schild metric ( arbitrary constant) is an exact solution of the Einstein equation for the
energy-momentum tensor . The mixed form of the Einstein equation for
Kerr-Schild metrics with autoparallel null congruence is also linear. Some more
technical conditions hold when the null congruence is not autoparallel. These
results generalize previous theorems for vacuum due to Xanthopoulos and for
flat seed space-time due to G\"{u}rses and G\"{u}rsey.Comment: 9 pages, accepted by Class. Quant. Gra
Gravitational radiation reaction in compact binary systems: Contribution of the magnetic dipole-magnetic dipole interaction
We study the gravitational radiation reaction in compact binary systems
composed of neutron stars with spin and huge magnetic dipole moments
(magnetars). The magnetic dipole moments undergo a precessional motion about
the respective spins. At sufficiently high values of the magnetic dipole
moments, their interaction generates second post-Newtonian order contributions
both to the equations of motion and to the gravitational radiation escaping the
system. We parametrize the radial motion and average over a radial period in
order to find the secular contributions to the energy and magnitude of the
orbital angular momentum losses, in the generic case of \textit{eccentric}
orbits. Similarly as for the spin-orbit, spin-spin, quadrupole-monopole
interactions, here too we deduce the secular evolution of the relative
orientations of the orbital angular momentum and spins. These equations,
supplemented by the evolution equations for the angles characterizing the
orientation of the dipole moments form a first order differential system, which
is closed. The circular orbit limit of the energy loss agrees with Ioka and
Taniguchi's earlier result
Geometrodynamics in a spherically symmetric, static crossflow of null dust
The spherically symmetric, static spacetime generated by a crossflow of
non-interacting radiation streams, treated in the geometrical optics limit
(null dust) is equivalent to an anisotropic fluid forming a radiation
atmosphere of a star. This reference fluid provides a preferred / internal
time, which is employed as a canonical coordinate. Among the advantages we
encounter a new Hamiltonian constraint, which becomes linear in the momentum
conjugate to the internal time (therefore yielding a functional Schr\"{o}dinger
equation after quantization), and a strongly commuting algebra of the new
constraints.Comment: Section on boundary behavior and fall-off conditions of canonical
variables added. New references, 1 new figure, 12 pages. Version accepted in
Phys.Rev.
Gravitational dynamics in s+1+1 dimensions II. Hamiltonian theory
We develop a Hamiltonian formalism of brane-world gravity, which singles out
two preferred, mutually orthogonal directions. One is a unit twist-free field
of spatial vectors with integral lines intersecting perpendicularly the brane.
The other is a temporal vector field with respect to which we perform the
Arnowitt-Deser-Misner decomposition of the Einstein-Hilbert Lagrangian. The
gravitational variables arise from the projections of the spatial metric and
their canonically conjugated momenta as tensorial, vectorial and scalar
quantities defined on the family of hypersurfaces containing the brane. They
represent the gravitons, a gravi-photon and a gravi-scalar, respectively. From
the action we derive the canonical evolution equations and the constraints for
these gravitational degrees of freedom both on the brane and outside it. By
integrating across the brane, the dynamics also generates the tensorial and
scalar projection of the Lanczos equation. The vectorial projection of the
Lanczos equation arises in a similar way from the diffeomorphism constraint.
Both the graviton and the gravi-scalar are continuous across the brane, however
the momentum of the gravi-vector has a jump, related to the energy transport
(heat flow) on the brane.Comment: 13 page
The geometry of the Barbour-Bertotti theories II. The three body problem
We present a geometric approach to the three-body problem in the
non-relativistic context of the Barbour-Bertotti theories. The Riemannian
metric characterizing the dynamics is analyzed in detail in terms of the
relative separations. Consequences of a conformal symmetry are exploited and
the sectional curvatures of geometrically preferred surfaces are computed. The
geodesic motions are integrated. Line configurations, which lead to curvature
singularities for , are investigated. None of the independent scalars
formed from the metric and curvature tensor diverges there.Comment: 16 pages, 2 eps figures, to appear in Classical and Quantum Gravit
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