291 research outputs found
Relativistic Stellar Pulsations With Near-Zone Boundary Conditions
A new method is presented here for evaluating approximately the pulsation
modes of relativistic stellar models. This approximation relies on the fact
that gravitational radiation influences these modes only on timescales that are
much longer than the basic hydrodynamic timescale of the system. This makes it
possible to impose the boundary conditions on the gravitational potentials at
the surface of the star rather than in the asymptotic wave zone of the
gravitational field. This approximation is tested here by predicting the
frequencies of the outgoing non-radial hydrodynamic modes of non-rotating
stars. The real parts of the frequencies are determined with an accuracy that
is better than our knowledge of the exact frequencies (about 0.01%) except in
the most relativistic models where it decreases to about 0.1%. The imaginary
parts of the frequencies are determined with an accuracy of approximately M/R,
where M is the mass and R is the radius of the star in question.Comment: 10 pages (REVTeX 3.1), 5 figs., 1 table, fixed minor typos, published
in Phys. Rev. D 56, 2118 (1997
Generalized r-Modes of the Maclaurin Spheroids
Analytical solutions are presented for a class of generalized r-modes of
rigidly rotating uniform density stars---the Maclaurin spheroids---with
arbitrary values of the angular velocity. Our analysis is based on the work of
Bryan; however, we derive the solutions using slightly different coordinates
that give purely real representations of the r-modes. The class of generalized
r-modes is much larger than the previously studied `classical' r-modes. In
particular, for each l and m we find l-m (or l-1 for the m=0 case) distinct
r-modes. Many of these previously unstudied r-modes (about 30% of those
examined) are subject to a secular instability driven by gravitational
radiation. The eigenfunctions of the `classical' r-modes, the l=m+1 case here,
are found to have particularly simple analytical representations. These r-modes
provide an interesting mathematical example of solutions to a hyperbolic
eigenvalue problem.Comment: 12 pages, 3 figures; minor changes and additions as will appear in
the version to be published in Physical Review D, January 199
On the Geometry of Planar Domain Walls
The Geometry of planar domain walls is studied. It is argued that the planar
walls indeed have plane symmetry. In the Minkowski coordinates the walls are
mapped into revolution paraboloids.Comment: 11 paghoj, Late
Second-order rotational effects on the r-modes of neutron stars
Techniques are developed here for evaluating the r-modes of rotating neutron
stars through second order in the angular velocity of the star. Second-order
corrections to the frequencies and eigenfunctions for these modes are evaluated
for neutron star models. The second-order eigenfunctions for these modes are
determined here by solving an unusual inhomogeneous hyperbolic boundary-value
problem. The numerical techniques developed to solve this unusual problem are
somewhat non-standard and may well be of interest beyond the particular
application here. The bulk-viscosity coupling to the r-modes, which appears
first at second order, is evaluated. The bulk-viscosity timescales are found
here to be longer than previous estimates for normal neutron stars, but shorter
than previous estimates for strange stars. These new timescales do not
substantially affect the current picture of the gravitational radiation driven
instability of the r-modes either for neutron stars or for strange stars.Comment: 13 pages, 5 figures, revte
Classical and Quantum Equations of Motion for a BTZ Black String in AdS Space
We investigate gravitational collapse of a -dimensional BTZ black
string in AdS space in the context of both classical and quantum mechanics.
This is done by first deriving the conserved mass per unit length of the
cylindrically symmetric domain wall, which is taken as the classical
Hamiltonian of the black string. In the quantum mechanical context, we take
primary interest in the behavior of the collapse near the horizon and near the
origin (classical singularity) from the point of view of an infalling observer.
In the absence of radiation, quantum effects near the horizon do not change the
classical conclusions for an infalling observer, meaning that the horizon is
not an obstacle for him/her. The most interesting quantum mechanical effect
comes in when investigating near the origin. First, quantum effects are able to
remove the classical singularity at the origin, since the wave function is
non-singular at the origin. Second, the Schr\"odinger equation describing the
behavior near the origin displays non-local effects, which depend on the energy
density of the domain wall. This is manifest in that derivatives of the
wavefunction at one point are related to the value of the wavefunction at some
other distant point.Comment: 9 pages, 1 figure. Minor Clarification and corrections. Accepted for
Publication in JHE
Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions
We address the generalized thermodynamics and the collapse of a system of
self-gravitating Langevin particles exhibiting anomalous diffusion in a space
of dimension D. The equilibrium states correspond to polytropic distributions.
The index n of the polytrope is related to the exponent of anomalous diffusion.
We consider a high-friction limit and reduce the problem to the study of the
nonlinear Smoluchowski-Poisson system. We show that the associated Lyapunov
functional is the Tsallis free energy. We discuss in detail the equilibrium
phase diagram of self-gravitating polytropes as a function of D and n and
determine their stability by using turning points arguments and analytical
methods. When no equilibrium state exists, we investigate self-similar
solutions describing the collapse. These results can be relevant for
astrophysical systems, two-dimensional vortices and for the chemotaxis of
bacterial populations. Above all, this model constitutes a prototypical
dynamical model of systems with long-range interactions which possesses a rich
structure and which can be studied in great detail.Comment: Submitted to Phys. Rev.
Gravitational Radiation from Nonaxisymmetric Instability in a Rotating Star
We present the first calculations of the gravitational radiation produced by
nonaxisymmetric dynamical instability in a rapidly rotating compact star. The
star deforms into a bar shape, shedding of its mass and
of its angular momentum. The gravitational radiation is calculated in the
quadrupole approximation. For a mass M and radius km, the gravitational waves have frequency kHz and amplitude
at the distance of the Virgo Cluster. They carry off
energy and radiate angular momentum .Comment: 16 pages, LaTeX with REVTEX macros, reprints available - send mailing
address to [email protected]. Published: PRL 72, 1314 (1994
Stability of the r-modes in white dwarf stars
Stability of the r-modes in rapidly rotating white dwarf stars is
investigated. Improved estimates of the growth times of the
gravitational-radiation driven instability in the r-modes of the observed DQ
Her objects are found to be longer (probably considerably longer) than 6x10^9y.
This rules out the possibility that the r-modes in these objects are emitting
gravitational radiation at levels that could be detectable by LISA. More
generally it is shown that the r-mode instability can only be excited in a very
small subset of very hot (T>10^6K), rather massive (M>0.9M_sun) and very
rapidly rotating (P_min<P<1.2P_min) white dwarf stars. Further, the growth
times of this instability are so long that these conditions must persist for a
very long time (t>10^9y) to allow the amplitude to grow to a dynamically
significant level. This makes it extremely unlikely that the r-mode instability
plays a significant role in any real white dwarf stars.Comment: 5 Pages, 5 Figures, revte
Flat World of Dilatonic Domain Walls
We study dilatonic domain walls specific to superstring theory.
Along with the matter fields and metric the dilaton also changes its value in
the wall background. We found supersymmetric (extreme) solutions which in
general interpolate between isolated superstring vacua with non-equal value of
the matter potential; they correspond to the static, planar domain walls with
{\it flat} metric in the string (sigma model) frame.
We point out similarities between the space-time of dilatonic walls and that
of charged dilatonic black holes. We also comment on non-extreme solutions
corresponding to expanding bubbles.Comment: 11 pgs (+2 figures available upon request), UPR-560-
The Power of Brane-Induced Gravity
We study the role of the brane-induced graviton kinetic term in theories with
large extra dimensions. In five dimensions we construct a model with a
TeV-scale fundamental Planck mass and a {\it flat} extra dimension the size of
which can be astronomically large. 4D gravity on the brane is mediated by a
massless zero-mode, whereas the couplings of the heavy Kaluza-Klein modes to
ordinary matter are suppressed. The model can manifest itself through the
predicted deviations from Einstein theory in long distance precision
measurements of the planetary orbits. The bulk states can be a rather exotic
form of dark matter, which at sub-solar distances interact via strong 5D
gravitational force. We show that the induced term changes dramatically the
phenomenology of sub-millimeter extra dimensions. For instance, high-energy
constraints from star cooling or cosmology can be substantially relaxed.Comment: 24 pages, 4 eps figures; v2 typos corrected; v3 1 ref. added; PRD
versio
- …