163 research outputs found
Series solutions for a static scalar potential in a Salam-Sezgin Supergravitational hybrid braneworld
The static potential for a massless scalar field shares the essential
features of the scalar gravitational mode in a tensorial perturbation analysis
about the background solution. Using the fluxbrane construction of [8] we
calculate the lowest order of the static potential of a massless scalar field
on a thin brane using series solutions to the scalar field's Klein Gordon
equation and we find that it has the same form as Newton's Law of Gravity. We
claim our method will in general provide a quick and useful check that one may
use to see if their model will recover Newton's Law to lowest order on the
brane.Comment: 5 pages, no figure
Strong Interactions and Stability in the DGP Model
The model of Dvali, Gabadadze, and Porrati (DGP) gives a simple geometrical
setup in which gravity becomes 5-dimensional at distances larger than a length
scale \lambda_{DGP}. We show that this theory has strong interactions at a
length scale \lambda_3 ~ (\lambda_{DGP}^2 / M_P)^{1/3}. If \lambda_{DGP} is of
order the Hubble length, then the theory loses predictivity at distances
shorter than \lambda_3 ~ 1000 km. The strong interaction can be viewed as
arising from a longitudinal `eaten Goldstone' mode that gets a small kinetic
term only from mixing with transverse graviton polarizations, analogous to the
case of massive gravity. We also present a negative-energy classical solution,
which can be avoided by cutting off the theory at the same scale scale
\lambda_3. Finally, we examine the dynamics of the longitudinal Goldstone mode
when the background geometry is curved.Comment: 24 pages, LaTeX2e, no figure
Brane Junctions in the Randall-Sundrum Scenario
We present static solutions to Einstein's equations corresponding to branes
at various angles intersecting in a single 3-brane. Such configurations may be
useful for building models with localized gravity via the Randall-Sundrum
mechanism. We find that such solutions may exist only if the mechanical forces
acting on the junction exactly cancel. In addition to this constraint there are
further conditions that the parameters of the theory have to satisfy. We find
that at least one of these involves only the brane tensions and cosmological
constants, and thus can not have a dynamical origin. We present these
conditions in detail for two simple examples. We discuss the nature of the
cosmological constant problem in the framework of these scenarios, and outline
the desired features of the brane configurations which may bring us closer
towards the resolution of the cosmological constant problem.Comment: 15 pages, LaTeX. 4 postscript figures included. Typo corrected and
reference adde
Spatial infinity in higher dimensional spacetimes
Motivated by recent studies on the uniqueness or non-uniqueness of higher
dimensional black hole spacetime, we investigate the asymptotic structure of
spatial infinity in n-dimensional spacetimes(). It turns out that the
geometry of spatial infinity does not have maximal symmetry due to the
non-trivial Weyl tensor {}^{(n-1)}C_{abcd} in general. We also address static
spacetime and its multipole moments P_{a_1 a_2 ... a_s}. Contrasting with four
dimensions, we stress that the local structure of spacetimes cannot be unique
under fixed a multipole moments in static vacuum spacetimes. For example, we
will consider the generalized Schwarzschild spacetimes which are deformed black
hole spacetimes with the same multipole moments as spherical Schwarzschild
black holes. To specify the local structure of static vacuum solution we need
some additional information, at least, the Weyl tensor {}^{(n-2)}C_{abcd} at
spatial infinity.Comment: 6 pages, accepted for publication in Physical Review D, published
versio
Domain Walls of D=8 Gauged Supergravities and their D=11 Origin
Performing a Scherk-Schwarz dimensional reduction of D=11 supergravity on a
three-dimensional group manifold we construct five D=8 gauged maximal
supergravities whose gauge groups are the three-dimensional (non-)compact
subgroups of SL(3,R). These cases include the Salam-Sezgin SO(3) gauged
supergravity. We construct the most general half-supersymmetric domain wall
solutions to these five gauged supergravities. The generic form is a triple
domain wall solution whose truncations lead to double and single domain wall
solutions. We find that one of the single domain wall solutions has zero
potential but nonzero superpotential.
Upon uplifting to 11 dimensions each domain wall becomes a purely
gravitational 1/2 BPS solution. The corresponding metric has a 7+4 split with a
Minkowski 7-metric and a 4-metric that corresponds to a gravitational
instanton. These instantons generalize the SO(3) metric of Belinsky, Gibbons,
Page and Pope (which includes the Eguchi-Hanson metric) to the other Bianchi
types of class A.Comment: 23 pages, 1 figure, minor changes, references adde
Classical confinement of test particles in higher-dimensional models: stability criteria and a new energy condition
We review the circumstances under which test particles can be localized
around a spacetime section \Sigma_0 smoothly contained within a codimension-1
embedding space M. If such a confinement is possible, \Sigma_0 is said to be
totally geodesic. Using three different methods, we derive a stability
condition for trapped test particles in terms of intrinsic geometrical
quantities on \Sigma_0 and M; namely, confined paths are stable against
perturbations if the gravitational stress-energy density on M is larger than
that on \Sigma_0, as measured by an observed travelling along the unperturbed
trajectory. We confirm our general result explicitly in two different cases:
the warped-product metric ansatz for (n+1)-dimensional Einstein spaces, and a
known solution of the 5-dimensional vacuum field equation embedding certain
4-dimensional cosmologies. We conclude by defining a confinement energy
condition that can be used to classify geometries incorporating totally
geodesic submanifolds, such as those found in thick braneworld and other
5-dimensional scenarios.Comment: 9 pages, REVTeX4, in press in Phys. Rev.
A Note on Solitons in Brane Worlds
We obtain the zero mode effective action for gravitating objects in the bulk
of dilatonic domain walls. Without additional fields included in the bulk
action, the zero mode effective action reproduces the action in one lower
dimensions obtained through the ordinary Kaluza-Klein (KK) compactification,
only when the transverse (to the domain wall) component of the bulk metric does
not have non-trivial term depending on the domain wall worldvolume coordinates.
With additional fields included in the bulk action, non-trivial dependence of
the transverse metric component on the domain wall worldvolume coordinates
appears to be essential in reproducing the lower-dimensional action obtained
via the ordinary KK compactification. We find, in particular, that the
effective action for the charged (p+1)-brane in the domain wall bulk reproduces
the action for the p-brane in one lower dimensions.Comment: 13 pages, LaTe
Dynamical compactification from de Sitter space
We show that D-dimensional de Sitter space is unstable to the nucleation of
non-singular geometries containing spacetime regions with different numbers of
macroscopic dimensions, leading to a dynamical mechanism of compactification.
These and other solutions to Einstein gravity with flux and a cosmological
constant are constructed by performing a dimensional reduction under the
assumption of q-dimensional spherical symmetry in the full D-dimensional
geometry. In addition to the familiar black holes, black branes, and
compactification solutions we identify a number of new geometries, some of
which are completely non-singular. The dynamical compactification mechanism
populates lower-dimensional vacua very differently from false vacuum eternal
inflation, which occurs entirely within the context of four-dimensions. We
outline the phenomenology of the nucleation rates, finding that the
dimensionality of the vacuum plays a key role and that among vacua of the same
dimensionality, the rate is highest for smaller values of the cosmological
constant. We consider the cosmological constant problem and propose a novel
model of slow-roll inflation that is triggered by the compactification process.Comment: Revtex. 41 pages with 24 embedded figures. Minor corrections and
added reference
Multi-dimensional classical and quantum cosmology: Exact solutions, signature transition and stabilization
We study the classical and quantum cosmology of a -dimensional
spacetime minimally coupled to a scalar field and present exact solutions for
the resulting field equations for the case where the universe is spatially
flat. These solutions exhibit signature transition from a Euclidean to a
Lorentzian domain and lead to stabilization of the internal space, in contrast
to the solutions which do not undergo signature transition. The corresponding
quantum cosmology is described by the Wheeler-DeWitt equation which has exact
solutions in the mini-superspace, resulting in wavefunctions peaking around the
classical paths. Such solutions admit parametrizations corresponding to metric
solutions of the field equations that admit signature transition.Comment: 15 pages, two figures, to appear in JHE
Goldberger-Wise variations: stabilizing brane models with a bulk scalar
Braneworld scenarios with compact extra-dimensions need the volume of the
extra space to be stabilized. Goldberger and Wise have introduced a simple
mechanism, based on the presence of a bulk scalar field, able to stabilize the
radius of the Randall-Sundrum model. Here, we transpose the same mechanism to
generic single-brane and two-brane models, with one extra dimension and
arbitrary scalar potentials in the bulk and on the branes. The single-brane
construction turns out to be always unstable, independently of the bulk and
brane potentials. In the case of two branes, we derive some generic criteria
ensuring the stabilization or destabilization of the system.Comment: 8 pages, 2 figures. 1 figure and one subsection added. version
published on PR
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