21 research outputs found
A note on the Deser-Tekin charges
Perturbed equations for an arbitrary metric theory of gravity in
dimensions are constructed in the vacuum of this theory. The nonlinear part
together with matter fields are a source for the linear part and are treated as
a total energy-momentum tensor. A generalized family of conserved currents
expressed through divergences of anti-symmetrical tensor densities
(superpotentials) linear in perturbations is constructed. The new family
generalizes the Deser and Tekin currents and superpotentials in quadratic
curvature gravity theories generating Killing charges in dS and AdS vacua. As
an example, the mass of the -dimensional Schwarzschild black hole in an
effective AdS spacetime (a solution in the Einstein-Gauss-Bonnet theory) is
examined.Comment: LATEX, 7 pages, no figure
Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions
As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall
see here that they also simplify the Gauss-Bonnet tensor, which turns out to be
only quadratic in the arbitrary Kerr-Schild function f when the seed metric is
maximally symmetric. This property allows us to give a simple analytical
expression for its trace, when the seed metric is a five dimensional maximally
symmetric spacetime in spheroidal coordinates with arbitrary parameters a and
b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet
tensor (with a cosmological term) when the seed metric is flat and the
oblateness parameters are equal, a=b. Armed with these results we give in a
compact form the solution of the trace of the Einstein-Gauss-Bonnet field
equations with a cosmological term and a different than b. We then examine
whether this solution for the trace does solve the remaining field equations.
We find that it does not in general, unless the Gauss-Bonnet coupling is such
that the field equations have a unique maximally symmetric solution.Comment: 10 pages, no figures, references added. Last version for CQ
Non-topological gravitating defects in five-dimensional anti-de Sitter space
A class of five-dimensional warped solutions is presented. The geometry is
everywhere regular and tends to five-dimensional anti-de Sitter space for large
absolute values of the bulk coordinate. The physical features of the solutions
change depending on the value of an integer parameter. In particular, a set of
solutions describes generalized gravitating kinks where the scalar field
interpolates between two different minima of the potential. The other category
of solutions describes instead gravitating defects where the scalar profile is
always finite and reaches the same constant asymptote both for positive and
negative values of the bulk coordinate. In this sense the profiles are
non-topological. The physical features of the zero modes are discussed.Comment: 9 pages, 4 figure
New features of flat (4+1)-dimensional cosmological model with a perfect fluid in Gauss-Bonnet gravity
We investigated a flat multidimensional cosmological model in Gauss-Bonnet
gravity in presence of a matter in form of perfect fluid. We found analytically
new stationary regimes (these results are valid for arbitrary number of spatial
dimensions) and studied their stability by means of numerical recipes in
4+1-dimensional case. In the vicinity of the stationary regime we discovered
numerically another non-singular regime which appears to be periodical.
Finally, we demonstrated that the presence of matter in form of a perfect fluid
lifts some constraints on the dynamics of the 4+1-dimensional model which have
been found earlier.Comment: 14 pages, 5 figures, 1 table; v2 minor corrections, conclusions
unchange
Generalised Israel Junction Conditions for a Gauss-Bonnet Brane World
In spacetimes of dimension greater than four it is natural to consider higher
order (in R) corrections to the Einstein equations. In this letter generalized
Israel junction conditions for a membrane in such a theory are derived. This is
achieved by generalising the Gibbons-Hawking boundary term. The junction
conditions are applied to simple brane world models, and are compared to the
many contradictory results in the literature.Comment: 4 page
General Gauss-Bonnet brane cosmology
We consider 5-dimensional spacetimes of constant 3-dimensional spatial
curvature in the presence of a bulk cosmological constant. We find the general
solution of such a configuration in the presence of a Gauss-Bonnet term. Two
classes of non-trivial bulk solutions are found. The first class is valid only
under a fine tuning relation between the Gauss-Bonnet coupling constant and the
cosmological constant of the bulk spacetime. The second class of solutions are
static and are the extensions of the AdS-Schwarzchild black holes. Hence in the
absence of a cosmological constant or if the fine tuning relation is not true,
the generalised Birkhoff's staticity theorem holds even in the presence of
Gauss-Bonnet curvature terms. We examine the consequences in brane world
cosmology obtaining the generalised Friedmann equations for a perfect fluid
3-brane and discuss how this modifies the usual scenario.Comment: 20 pages, no figures, typos corrected, refs added, section IV changed
yielding novel result
Kaluza-Klein and Gauss-Bonnet cosmic strings
We make a systematic investigation of stationary cylindrically symmetric
solutions to the five-dimensional Einstein and Einstein-Gauss-Bonnet equations.
Apart from the five-dimensional neutral cosmic string metric, we find two new
exact solutions which qualify as cosmic strings, one corresponding to an
electrically charged cosmic string, the other to an extended superconducting
cosmic string surrounding a charged core. In both cases, test particles are
deflected away from the singular line source. We extend both kinds of solutions
to exact multi-cosmic string solutions.Comment: 26 pages, LaTex, no figure
Conserved Charges in Einstein Gauss-Bonnet theory
Using Noether's identities, we define a superpotential with respect to a
background for the Einstein Gauss-Bonnet theory of gravity. As an example, we
show that its associated conserved charge yields the mass-energy of a
D-dimensional Gauss-Bonnet black hole in an anti-de Sitter spacetime.Comment: 17 pages, LaTeX, references added, typos corrected, version to appear
in Class. Quant. Gra
Hamiltonian Formulation of Scalar Field Collapse in Einstein Gauss Bonnet Gravity
We compute the Hamiltonian for spherically symmetric scalar field collapse in
Einstein-Gauss-Bonnet gravity in D dimensions using slicings that are regular
across future horizons. We first reduce the Lagrangian to two dimensions using
spherical symmetry. We then show that choosing the spatial coordinate to be a
function of the areal radius leads to a relatively simple Hamiltonian
constraint whose gravitational part is the gradient of the generalized mass
function. Next we complete the gauge fixing such that the metric is the
Einstein-Gauss-Bonnet generalization of non-static Painleve-Gullstrand
coordinates. Finally, we derive the resultant reduced equations of motion for
the scalar field. These equations are suitable for use in numerical simulations
of spherically symmetric scalar field collapse in Gauss-Bonnet gravity and can
readily be generalized to other matter fields minimally coupled to gravity.Comment: 14 pages, 0 figure
Scalar cosmological perturbations in the Gauss-Bonnet braneworld
We study scalar cosmological perturbations in a braneworld model with a bulk
Gauss-Bonnet term. For an anti-de Sitter bulk, the five-dimensional
perturbation equations share the same form as in the Randall-Sundrum model,
which allows us to obtain metric perturbations in terms of a master variable.
We derive the boundary conditions for the master variable from the generalized
junction conditions on the brane. We then investigate several limiting cases in
which the junction equations are reduced to a feasible level. In the low energy
limit, we confirm that the standard result of four-dimensional Einstein gravity
is reproduced on large scales, whereas on small scales we find that the
perturbation dynamics is described by the four-dimensional Brans-Dicke theory.
In the high energy limit, all the non-local contributions drop off from the
junction equations, leaving a closed system of equations on the brane. We show
that, for inflation models driven by a scalar field on the brane, the
Sasaki-Mukhanov equation holds on the high energy brane in its original
four-dimensional form.Comment: 18 pages, v2: minor changes, reference added, v3: comments and
references added, accepted for publication in JCA