57 research outputs found
Exact cosmological solutions with nonminimal derivative coupling
We consider a gravitational theory of a scalar field with nonminimal
derivative coupling to curvature. The coupling terms have the form and where
and are coupling parameters with dimensions of
length-squared. In general, field equations of the theory contain third
derivatives of and . However, in the case
the derivative coupling term reads and the order of corresponding field equations
is reduced up to second one. Assuming , we study the
spatially-flat Friedman-Robertson-Walker model with a scale factor and
find new exact cosmological solutions. It is shown that properties of the model
at early stages crucially depends on the sign of . For negative
the model has an initial cosmological singularity, i.e. in the limit ; and for positive the universe
at early stages has the quasi-de Sitter behavior, i.e. in the
limit , where . The corresponding scalar
field is exponentially growing at , i.e. . At late stages the universe evolution does not depend on
at all; namely, for any one has at
. Summarizing, we conclude that a cosmological model with
nonminimal derivative coupling of the form is able to explain in a unique manner both a
quasi-de Sitter phase and an exit from it without any fine-tuned potential.Comment: 7 pages, 2 figures. Accepted to PR
Black Hole in Thermal Equilibrium with a Spin-2 Quantum Field
An approximate form for the vacuum averaged stress-energy tensor of a
conformal spin-2 quantum field on a black hole background is employed as a
source term in the semiclassical Einstein equations. Analytic corrections to
the Schwarzschild metric are obtained to first order in , where denotes the mass of the black hole. The approximate
tensor possesses the exact trace anomaly and the proper asymptotic behavior at
spatial infinity, is conserved with respect to the background metric and is
uniquely defined up to a free parameter , which relates to the
average quantum fluctuation of the field at the horizon. We are able to
determine and calculate an explicit upper bound on by requiring that
the entropy due to the back-reaction be a positive increasing function in .
A lower bound for can be established by requiring that the metric
perturbations be uniformly small throughout the region , where
is the radius of perturbative validity of the modified metric. Additional
insight into the nature of the perturbed spacetime outside the black hole is
provided by studying the effective potential for test particles in the vicinity
of the horizon.Comment: 21 pages in plain LaTex. Three figures available upon request from
the first autho
Cosmology with nonminimal kinetic coupling and a Higgs-like potential
We consider cosmological dynamics in the theory of gravity with the scalar
field possessing the nonminimal kinetic coupling to curvature given as , and the Higgs-like potential
. Using the dynamical system
method, we analyze stationary points, their stability, and all possible
asymptotical regimes of the model under consideration. We show that the Higgs
field with the kinetic coupling provides an existence of accelerated regimes of
the Universe evolution. There are three possible cosmological scenarios with
acceleration: (i) {\em The late-time inflation} when the Hubble parameter tends
to the constant value,
as , while the scalar field tends to zero, , so that
the Higgs potential reaches its local maximum .
(ii) {\em The Big Rip} when and
as . (iii) {\em The Little Rip}
when and as
. Also, we derive modified slow-roll conditions for the Higgs field
and demonstrate that they lead to the Little Rip scenario.Comment: 29 pages, 11 figures, discussions and references added, to be
published on JCA
Giant wormholes in ghost-free bigravity theory
We study Lorentzian wormholes in the ghost-free bigravity theory described by
two metrics, g and f. Wormholes can exist if only the null energy condition is
violated, which happens naturally in the bigravity theory since the graviton
energy-momentum tensors do not apriori fulfill any energy conditions. As a
result, the field equations admit solutions describing wormholes whose throat
size is typically of the order of the inverse graviton mass. Hence, they are as
large as the universe, so that in principle we might all live in a giant
wormhole. The wormholes can be of two different types that we call W1 and W2.
The W1 wormholes interpolate between the AdS spaces and have Killing horizons
shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes
imaginary in the AdS zone, hence the gravitons behave as tachyons, but since
the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon
instability. For the W2 wormholes the g-geometry is globally regular and in the
far field zone it becomes the AdS up to subleading terms, its throat can be
traversed by timelike geodesics, while the f-geometry has a completely
different structure and is not geodesically complete. There is no evidence of
tachyons for these solutions, although a detailed stability analysis remains an
open issue. It is possible that the solutions may admit a holographic
interpretation.Comment: 26 pages, 6 figures, section 8.2 describing the W1b wormhole geometry
is considerably modifie
Composite vacuum Brans-Dicke wormholes
We construct a new static spherically symmetric configuration composed of
interior and exterior Brans-Dicke vacua matched at a thin matter shell. Both
vacua correspond to the same Brans-Dicke coupling parameter , however
they are described by the Brans class I solution with different sets of
parameters of integration. In particular, the exterior vacuum solution has
. In this case the Brans class I solution for any
reduces to the Schwarzschild one being consistent with restrictions on
the post-Newtonian parameters following from recent Cassini data. The interior
region possesses a strong gravitational field, and so the interior vacuum
solution has . In this case the Brans class I
solution describes a wormhole spacetime provided lies in the narrow
interval . The interior and exterior regions
are matched at a thin shell made from an ordinary perfect fluid with positive
energy density and pressure obeying the barotropic equation of state
with . The resulting configuration represents a
composite wormhole, i.e. the thin matter shell with the Schwarzschild-like
exterior region and the interior region containing the wormhole throat.Comment: 14 pages, 3 figure
Scalar multi-wormholes
In 1921 Bach and Weyl derived the method of superposition to construct new
axially symmetric vacuum solutions of General Relativity. In this paper we
extend the Bach-Weyl approach to non-vacuum configurations with massless scalar
fields. Considering a phantom scalar field with the negative kinetic energy, we
construct a multi-wormhole solution describing an axially symmetric
superposition of wormholes. The solution found is static, everywhere
regular and has no event horizons. These features drastically tell the
multi-wormhole configuration from other axially symmetric vacuum solutions
which inevitably contain gravitationally inert singular structures, such as
`struts' and `membranes', that keep the two bodies apart making a stable
configuration. However, the multi-wormholes are static without any singular
struts. Instead, the stationarity of the multi-wormhole configuration is
provided by the phantom scalar field with the negative kinetic energy. Anther
unusual property is that the multi-wormhole spacetime has a complicated
topological structure. Namely, in the spacetime there exist
asymptotically flat regions connected by throats.Comment: 11 pages, 13 figure
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