359 research outputs found

### Post-Newtonian Expansion of the Ingoing-Wave Regge-Wheeler Function

We present a method of post-Newtonian expansion to solve the homogeneous
Regge-Wheeler equation which describes gravitational waves on the Schwarzschild
spacetime. The advantage of our method is that it allows a systematic iterative
analysis of the solution. Then we obtain the Regge-Wheeler function which is
purely ingoing at the horizon in closed analytic form, with accuracy required
to determine the gravitational wave luminosity to (post)$^{4}$-Newtonian order
(i.e., order $v^8$ beyond Newtonian) from a particle orbiting around a
Schwarzschild black hole. Our result, valid in the small-mass limit of one
body, gives an important guideline for the study of coalescing compact
binaries. In particular, it provides basic formulas to analytically calculate
detailed waveforms and luminosity, including the tail terms to
(post)$^3$-Newtonian order, which should be reproduced in any other
post-Newtonian calculations.Comment: 31 pages, KUNS 124

### Newton's law on an Einstein "Gauss-Bonnet" brane

It is known that Newton's law of gravity holds asymptotically on a flat
"brane" embedded in an anti-de Sitter "bulk" ; this was shown not only when
gravity in the bulk is described by Einstein's theory but also in Einstein
"Lanczos Lovelock Gauss-Bonnet"'s theory. We give here the expressions for the
corrections to Newton's potential in both theories, in analytic form and valid
for all distances. We find that in Einstein's theory the transition from the
1/r behaviour at small r to the 1/r^2 one at large r is quite slow. In the
Einstein Gauss-Bonnet case on the other hand, we find that the correction to
Newton's potential can be small for all r. Hence, Einstein Gauss-Bonnet
equations in the bulk (rather than simply Einstein's) induce on the brane a
better approximation to Newton's law.Comment: typos corrected, reference added, version to be published in Progress
of Theoretical Physic

### Stability of Q-balls and Catastrophe

We propose a practical method for analyzing stability of Q-balls for the
whole parameter space, which includes the intermediate region between the
thin-wall limit and thick-wall limit as well as Q-bubbles (Q-balls in false
vacuum), using the catastrophe theory. We apply our method to the two concrete
models, $V_3=m^2\phi^2/2-\mu\phi^3+\lambda\phi^4$ and
$V_4=m^2\phi^2/2-\lambda\phi^4+\phi^6/M^2$. We find that $V_3$ and $V_4$ Models
fall into {\it fold catastrophe} and {\it cusp catastrophe}, respectively, and
their stability structures are quite different from each other.Comment: 9 pages, 4 figures, some discussions and references added, to apear
in Prog. Theor. Phy

### Conformal transformations and Nordstr\"om's scalar theory of gravity

As we shall briefly recall, Nordstr\"om's theory of gravity is
observationally ruled out. It is however an interesting example of non-minimal
coupling of matter to gravity and of the role of conformal transformations. We
show in particular that they could be useful to extend manifolds through
curvature singularities.Comment: 9 pages, no figure, prepared for the Proceedings of YKIS2010, to be
published in Progress of Theoretical Physics Supplemen

### Quantum Fluctuations for de Sitter Branes in Bulk AdS(5)

The vacuum expectation value of the square of the field fluctuations of a
scalar field on a background consisting of {\it two} de Sitter branes embedded
in an anti-de Sitter bulk are considered. We apply a dimensional reduction to
obtain an effective lower dimensional de Sitter space equation of motion with
associated Kaluza-Klein masses and canonical commutation relations. The case of
a scalar field obeying a restricted class of mass and curvature couplings,
including massless, conformal coupling as a special case, is considered. We
find that the local behaviour of the quantum fluctuations suffers from surface
divergences as we approach the brane, however, if the field is {\it
constrained} to its value on the brane from the beginning then surface
divergences disappear. The ratio of $$ between the Kaluza-Klein
spectrum and the lowest eigenvalue mode is found to vanish in the limit that
one of the branes goes to infinity.Comment: 14 pages, no figures, to appear in Prog. Theor. Phy

### Gradient expansion approach to nonlinear superhorizon perturbations

Using the gradient expansion approach, we formulate a nonlinear cosmological
perturbation theory on super-horizon scales valid to $O(\epsilon^2)$, where
$\epsilon$ is the expansion parameter associated with a spatial derivative. For
simplicity, we focus on the case of a single perfect fluid, but we take into
account not only scalar but also vector and tensor modes. We derive the general
solution under the uniform-Hubble time-slicing. In doing so, we identify the
scalar, vector and tensor degrees of freedom contained in the solution. We then
consider the coordinate transformation to the synchronous gauge in order to
compare our result with the previous result given in the literature. In
particular, we find that the tensor mode is invariant to $O(\epsilon^2)$ under
the coordinate transformation.Comment: 15 pages, no figures. V2: minor changes, typos corrected; V3:Section
I, Introduction and minor change to match version to appear in Prog. Theor.
Phys

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