6,733 research outputs found
Stability of Higher-Dimensional Schwarzschild Black Holes
We investigate the classical stability of the higher-dimensional
Schwarzschild black holes against linear perturbations, in the framework of a
gauge-invariant formalism for gravitational perturbations of maximally
symmetric black holes, recently developed by the authors. The perturbations are
classified into the tensor, vector, and scalar-type modes according to their
tensorial behaviour on the spherical section of the background metric, where
the last two modes correspond respectively to the axial- and the polar-mode in
the four-dimensional situation. We show that, for each mode of the
perturbations, the spatial derivative part of the master equation is a
positive, self-adjoint operator in the -Hilbert space, hence that the
master equation for each tensorial type of perturbations does not admit
normalisable negative-modes which would describe unstable solutions.
On the same Schwarzschild background, we also analyse the static perturbation
of the scalar mode, and show that there exists no static perturbation which is
regular everywhere outside the event horizon and well-behaved at spatial
infinity. This checks the uniqueness of the higher-dimensional spherically
symmetric, static, vacuum black hole, within the perturbation framework.
Our strategy for the stability problem is also applicable to the other
higher-dimensional maximally symmetric black holes with non-vanishing
cosmological constant. We show that all possible types of maximally symmetric
black holes (thus, including the higher-dimensional Schwarzschild-de Sitter and
Schwarzschild-anti-de Sitter black holes) are stable against the tensor and the
vector perturbations.Comment: 19 pages, 9 figures, references and comments on the generalised black
hole case are added, minor changes in text, version to appear in PT
Second-order Gauge Invariant Cosmological Perturbation Theory: -- Einstein equations in terms of gauge invariant variables --
Along the general framework of the gauge invariant perturbation theory
developed in the papers [K. Nakamura, Prog. Theor. Phys. {\bf 110} (2003), 723;
{\it ibid}, {\bf 113} (2005), 481.], we formulate the second order gauge
invariant cosmological perturbation theory in a four dimensional homogeneous
isotropic universe. We consider the perturbations both in the universe
dominated by the single perfect fluid and in that dominated by the single
scalar field. We derive the all components of the Einstein equations in the
case where the first order vector and tensor modes are negligible. All
equations are derived in terms of gauge invariant variables without any gauge
fixing. These equations imply that the second order vector and tensor modes may
be generated due to the mode-mode coupling of the linear order scalar
perturbations. We also briefly discuss the main progress of this work by the
comparison with some literatures.Comment: 58 pages, no figure. Complete version of gr-qc/0605107; some typos
are corrected (v2); References and some typos are corrected. To be appeard
Progress of Theoretical Physic
De Sitter ground state of scalar-tensor gravity and its primordial perturbation
Scalar-tensor gravity is one of the most competitive gravity theory to
Einstein's relativity. We reconstruct the exact de Sitter solution in
scalar-tensor gravity, in which the non-minimal coupling scalar is rolling
along the potential. This solution may have some relation to the early
inflation and present acceleration of the universe. We investigated its
primordial quantum perturbation around the adiabatic vacuum. We put forward for
the first time that exact de Sitter generates non-exactly scale invariant
perturbations. In the conformal coupling case, this model predicts that the
tensor mode of the perturbation (gravity wave) is strongly depressed.Comment: 9 page
Slow-roll inflationary senario in the maximally extended background
During the inflationary epoch,geometry of the universe may be described by
quasi-de Sitter space. On the other hand,maximally extended de Sitter metric in
the comoving coordinates accords with a special FLRW model with positive
spatial curvature,so in this article we focus on the positively curved
inflationary paradigm.For this purpose,first we derive the power spectra of
comoving curvature perturbation and primordial gravitational waves in a
positively curved FLRW universe according to the slowly rolling inflationary
senario. It can be shown that the curvature spectral index in this model
automatically has a small negative running parameter which is compatible with
observational measurements.Then,by taking into account the curvature factor,we
investigate the relative amplitude of the scalar and tensor perturbations.It
would be clarified that the tensor-scalar ratio for this model against the
spatially flat one,depends on the waelength of the perturbative models
directly.Comment: 21 pages,n o figure
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