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

Exemplar variance supports robust learning of facial identity

Differences in the visual processing of familiar and unfamiliar faces have prompted considerable interest in face learning, the process by which unfamiliar faces become familiar. Previous work indicates that face learning is determined in part by exposure duration; unsurprisingly, viewing faces for longer affords superior performance on subsequent recognition tests. However, there has been further speculation that exemplar variation, experience of different exemplars of the same facial identity, contributes to face learning independently of viewing time. Several leading accounts of face learning, including the averaging and pictorial coding models, predict an exemplar variation advantage. Nevertheless, the exemplar variation hypothesis currently lacks empirical support. The present study therefore sought to test this prediction by comparing the effects of unique exemplar face learning - a condition rich in exemplar variation - and repeated exemplar face learning œ a condition that equates viewing time, but constrains exemplar variation. Crucially, observers who received unique exemplar learning displayed better recognition of novel exemplars of the learned identities at test, than observers in the repeated exemplar condition. These results have important theoretical and substantive implications for models of face learning and for approaches to face training in applied contexts

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

Gravitational Radiation Instability in Hot Young Neutron Stars

We show that gravitational radiation drives an instability in hot young rapidly rotating neutron stars. This instability occurs primarily in the l=2 r-mode and will carry away most of the angular momentum of a rapidly rotating star by gravitational radiation. On the timescale needed to cool a young neutron star to about T=10^9 K (about one year) this instability can reduce the rotation rate of a rapidly rotating star to about 0.076\Omega_K, where \Omega_K is the Keplerian angular velocity where mass shedding occurs. In older colder neutron stars this instability is suppressed by viscous effects, allowing older stars to be spun up by accretion to larger angular velocities.Comment: 4 Pages, 2 Figure

Ultralight Scalars and Spiral Galaxies

We study some possible astrophysical implications of a very weakly coupled ultralight dilaton-type scalar field. Such a field may develop an (approximately stable) network of domain walls. The domain wall thickness is assumed to be comparable with the thickness of the luminous part of the spiral galaxies. The walls provide trapping for galactic matter. This is used to motivate the very existence of the spiral galaxies. A zero mode existing on the domain wall is a massless scalar particle confined to 1+2 dimensions. At distances much larger than the galaxy/wall thickness, the zero-mode exchange generates a logarithmic potential, acting as an additional term with respect to Newton's gravity. The logarithmic term naturally leads to constant rotational velocities at the periphery. We estimate the scalar field coupling to the matter energy-momentum tensor needed to fit the observable flat rotational curves of the spiral galaxies. The value of this coupling turns out to be reasonable -- we find no contradiction with the existing data.Comment: 19 pages, 2 eps figures; extra references and two important Comments adde

Instability of a membrane intersecting a black hole

The stability of a Nambu-Goto membrane at the equatorial plane of the Reissner-Nordstr{\o}m-de Sitter spacetime is studied. The covariant perturbation formalism is applied to study the behavior of the perturbation of the membrane. The perturbation equation is solved numerically. It is shown that a membrane intersecting a charged black hole, including extremely charged one, is unstable and that the positive cosmological constant strengthens the instability.Comment: 12 pages, 3 figures, to be published in Physical Review

Gravitational field of vacuumless defects

It has been recently shown that topological defects can arise in symmetry breaking models where the scalar field potential $V(\phi)$ has no minima and is a monotonically decreasing function of $|\phi|$. Here we study the gravitational fields produced by such vacuumless defects in the cases of both global and gauge symmetry breaking. We find that a global monopole has a strongly repulsive gravitational field, and its spacetime has an event horizon similar to that in de Sitter space. A gauge monopole spacetime is essentially that of a magnetically charged black hole. The gravitational field of a global string is repulsive and that of a gauge string is attractive at small distances and repulsive at large distances. Both gauge and global string spacetimes have singularities at a finite distance from the string core.Comment: 19 pages, REVTeX, 6 Postscript figure