An analysis is given of thermoelastic noise ͑thermal noise due to thermoelastic dissipation͒ in finite sized test masses of laser interferometer gravitational-wave detectors. Finite-size effects increase the thermoelastic noise by a modest amount; for example, for the sapphire test masses tentatively planned for LIGO-II and plausible beam-spot radii, the increase is Շ10 percent. As a side issue, errors are pointed out in the currently used formulas for conventional, homogeneous thermal noise ͑noise associated with dissipation which is homogeneous and described by an imaginary part of the Young's modulus͒ in finite sized test masses. Correction of these errors increases the homogeneous thermal noise by Շ5 percent for LIGO-II-type configurations.

A B S T R A C TEquilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion-induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high-density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.

We study the self-force acting on static electric or scalar charges inside or outside a spherical, massive, thin shell. The regularization of the self-force is done using the recently proposed mode sum regularization prescription. In all cases the self-force acting on the charge is repulsive. We find that in the scalar case the force is quadratic in the mass of the shell, and is a second post-Newtonian effect. For the electric case the force is linear in the shell's mass, and is a first post-Newtonian effect. When the charge is outside the shell our results correct the known zero self-force in the scalar case or the known repulsive, inverse-cubic force law in the electric case, for the finite size of the shell. When the charge is near the center of the shell the charge undergoes harmonic oscillations.

We study the self-force acting on a particle endowed with scalar charge, which is held static ͑with respect to an undragged, static observer at infinity͒ outside a stationary, axially symmetric black hole. We find that the acceleration due to the self-force is in the same direction as the black hole's spin, and diverges when the particle approaches the outer boundary of the black hole's ergosphere. This acceleration diverges more rapidly approaching the ergosphere's boundary than the particle's acceleration in the absence of the self-force. At the leading order this self-force is a (post) 2 -Newtonian effect. For scalar charges with high charge-to-mass ratio, the acceleration due to the self-force starts dominating over the regular acceleration already far from the black hole. The self-force is proportional to the rate at which the black hole's rotational energy is dissipated. This self-force is local ͑i.e., only the Abraham-Lorentz-Dirac force and the local coupling to Ricci curvature contribute to it͒. The non-local, tail part of the self-force is zero.

The dynamical instability of new-born neutron stars is studied by evolving the linearized hydrodynamical equations. The neutron stars considered in this paper are those produced by the accretion induced collapse of rigidly rotating white dwarfs. A dynamical bar-mode (m = 2) instability is observed when the ratio of rotational kinetic energy to gravitational potential energy β of the neutron star is greater than the critical value β d ≈ 0.25. This bar-mode instability leads to the emission of gravitational radiation that could be detected by gravitational wave detectors. However, these sources are unlikely to be detected by LIGO II interferometers if the event rate is less than 10 −6 per year per galaxy. Nevertheless, if a significant fraction of the pre-supernova cores are rapidly rotating, there would be a substantial number of neutron stars produced by the core collapse undergoing bar-mode instability. This would greatly increase the chance of detecting the gravitational radiation.PACS: 04.30. Db, 95.30.Sf, 97.60.Jd