1,235 research outputs found

### On some geometric features of the Kramer interior solution for a rotating perfect fluid

Geometric features (including convexity properties) of an exact interior
gravitational field due to a self-gravitating axisymmetric body of perfect
fluid in stationary, rigid rotation are studied. In spite of the seemingly
non-Newtonian features of the bounding surface for some rotation rates, we
show, by means of a detailed analysis of the three-dimensional spatial
geodesics, that the standard Newtonian convexity properties do hold. A central
role is played by a family of geodesics that are introduced here, and provide a
generalization of the Newtonian straight lines parallel to the axis of
rotation.Comment: LaTeX, 15 pages with 4 Poscript figures. To be published in Classical
and Quantum Gravit

### Vacuum Polarization on the Schwarzschild Metric with a Cosmic String

We consider the problem of the renormalization of the vacuum polarization in
a symmetry space-time with axial but not spherical symmetry, Schwarzschild
space-time threaded by an infinite straight cosmic string. Unlike previous
calculations, our framework to compute the renormalized vacuum polarization
does not rely on special properties of Legendre functions, but rather has been
developed in a way that we expect to be applicable to Kerr space-time

### Quasi-local contribution to the scalar self-force: Non-geodesic Motion

We extend our previous calculation of the quasi-local contribution to the
self-force on a scalar particle to general (not necessarily geodesic) motion in
a general spacetime. In addition to the general case and the case of a particle
at rest in a stationary spacetime, we consider as examples a particle held at
rest in Reissner-Nordstrom and Kerr-Newman space-times. This allows us to most
easily analyse the effect of non-geodesic motion on our previous results and
also allows for comparison to existing results for Schwarzschild spacetime.Comment: 11 pages, 1 figure, corrected typo in Eq. 2.

### On the ill-posed character of the Lorentz integral transform

An exact inversion formula for the Lorentz integral transform (LIT) is
provided together with the spectrum of the LIT kernel. The exponential increase
of the inverse Fourier transform of the LIT kernel entering the inversion
formula explains the ill-posed character of the LIT approach. Also the
continuous spectrum of the LIT kernel, which approaches zero points necessarily
to the same defect. A possible cure is discussed and numerically illustrated.Comment: 13 pages, 3 figure

### Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case

In our previous paper \cite{co1} we have shown that the theory of circulant
matrices allows to recover the result that there exists $p+1$ Mutually Unbiased
Bases in dimension $p$, $p$ being an arbitrary prime number. Two orthonormal
bases $\mathcal B, \mathcal B'$ of $\mathbb C^d$ are said mutually unbiased if
$\forall b\in \mathcal B, \forall b' \in \mathcal B'$ one has that $| b\cdot
b'| = \frac{1}{\sqrt d}$ ($b\cdot b'$ hermitian scalar product in $\mathbb
C^d$). In this paper we show that the theory of block-circulant matrices with
circulant blocks allows to show very simply the known result that if $d=p^n$
($p$ a prime number, $n$ any integer) there exists $d+1$ mutually Unbiased
Bases in $\mathbb C^d$. Our result relies heavily on an idea of Klimov, Munoz,
Romero \cite{klimuro}. As a subproduct we recover properties of quadratic Weil
sums for $p\ge 3$, which generalizes the fact that in the prime case the
quadratic Gauss sums properties follow from our results

### MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems

CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric
systems of linear equations. When these methods are applied to an incompatible
system (that is, a singular symmetric least-squares problem), CG could break
down and SYMMLQ's solution could explode, while MINRES would give a
least-squares solution but not necessarily the minimum-length (pseudoinverse)
solution. This understanding motivates us to design a MINRES-like algorithm to
compute minimum-length solutions to singular symmetric systems.
MINRES uses QR factors of the tridiagonal matrix from the Lanczos process
(where R is upper-tridiagonal). MINRES-QLP uses a QLP decomposition (where
rotations on the right reduce R to lower-tridiagonal form). On ill-conditioned
systems (singular or not), MINRES-QLP can give more accurate solutions than
MINRES. We derive preconditioned MINRES-QLP, new stopping rules, and better
estimates of the solution and residual norms, the matrix norm, and the
condition number.Comment: 26 pages, 6 figure

### Features of gravitational waves in higher dimensions

There are several fundamental differences between four-dimensional and
higher-dimensional gravitational waves, namely in the so called braneworld
set-up. One of them is their asymptotic behavior within the Cauchy problem.
This study is connected with the so called Hadamard problem, which aims at the
question of Huygens principle validity. We investigate the effect of braneworld
scenarios on the character of propagation of gravitational waves on FRW
background.Comment: to appear in ERE09 proceeding

### Transport in Transitory, Three-Dimensional, Liouville Flows

We derive an action-flux formula to compute the volumes of lobes quantifying
transport between past- and future-invariant Lagrangian coherent structures of
n-dimensional, transitory, globally Liouville flows. A transitory system is one
that is nonautonomous only on a compact time interval. This method requires
relatively little Lagrangian information about the codimension-one surfaces
bounding the lobes, relying only on the generalized actions of loops on the
lobe boundaries. These are easily computed since the vector fields are
autonomous before and after the time-dependent transition. Two examples in
three-dimensions are studied: a transitory ABC flow and a model of a
microdroplet moving through a microfluidic channel mixer. In both cases the
action-flux computations of transport are compared to those obtained using
Monte Carlo methods.Comment: 30 pages, 16 figures, 1 table, submitted to SIAM J. Appl. Dyn. Sy

### Regularization of static self-forces

Various regularization methods have been used to compute the self-force
acting on a static particle in a static, curved spacetime. Many of these are
based on Hadamard's two-point function in three dimensions. On the other hand,
the regularization method that enjoys the best justification is that of
Detweiler and Whiting, which is based on a four-dimensional Green's function.
We establish the connection between these methods and find that they are all
equivalent, in the sense that they all lead to the same static self-force. For
general static spacetimes, we compute local expansions of the Green's functions
on which the various regularization methods are based. We find that these agree
up to a certain high order, and conjecture that they might be equal to all
orders. We show that this equivalence is exact in the case of ultrastatic
spacetimes. Finally, our computations are exploited to provide regularization
parameters for a static particle in a general static and spherically-symmetric
spacetime.Comment: 23 pages, no figure

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