Regularity of a inverse problem for generic parabolic equations

The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary value inputs.Comment: 9 page

The wave function of a gravitating shell

We have calculated a discrete spectrum and found an exact analytical solution in the form of Meixner polynomials for the wave function of a thin gravitating shell in the Reissner-Nordstrom geometry. We show that there is no extreme state in the quantum spectrum of the gravitating shell, as in the case of extreme black hole.Comment: 7 pages, 1 figur

Calorimetry of gamma-ray bursts: echos in gravitational waves

Black holes surrounded by a disk or torus may drive the enigmatic cosmological gamma-ray bursts (GRBs). Equivalence in poloidal topology to pulsar magnetospheres shows a high incidence of the black hole-luminosity $L_H$ into the surrounding magnetized matter. We argue that this emission is re-radiated into gravitational waves at $L_{GW}\simeq L_H/3$ in frequencies of order 1kHz, winds and, potentially, MeV neutrinos. The total energy budget and input to the GRB from baryon poor jets are expected to be standard in this scenario, consistent with recent analysis of afterglow data. Collimation of these outflows by baryon rich disk or torus winds may account for the observed spread in opening angles up to about $35^o$. This model may be tested by future LIGO/VIRGO observations.Comment: To appear in ApJ

Mechanism for the Suppression of Intermediate-Mass Black Holes

A model for the formation of supermassive primordial black holes in galactic nuclei with the simultaneous suppression of the formation of intermediate-mass black holes is presented. A bimodal mass function for black holes formed through phase transitions in a model with a "Mexican hat" potential has been found. The classical motion of the phase of a complex scalar field during inflation has been taken into account. Possible observational manifestations of primordial black holes in galaxies and constraints on their number are discussed.Comment: 12 pages, 2 figure

Gravitational radiation from rotating monopole-string systems

We study the gravitational radiation from a rotating monopole-antimonopole pair connected by a string. While at not too high frequencies the emitted gravitational spectrum is described asymptotically by $P_n\propto n^{-1}$, the spectrum is exponentially suppressed in the high-frequency limit, $P_n\propto \exp(-n/n_{\rm cr})$. Below $n_{\rm cr}$, the emitted spectrum of gravitational waves is very similar to the case of an oscillating monopole pair connected by a string, and we argue therefore that the spectrum found holds approximately for any moving monopole-string system. As application, we discuss the stochastic gravitational wave background generated by monopole-antimonopole pairs connected by strings in the early Universe and gravitational wave bursts emitted at present by monopole-string networks. We confirm that advanced gravitational wave detectors have the potential to detect a signal for string tensions as small as $G\mu\sim 10^{-13}$.Comment: 8 pages, 2 figures, revtex4; v2: minor corrections, matches published versio

Gamma Ray Bursts from the Evolved Galactic Nuclei

A new cosmological scenario for the origin of gamma ray bursts (GRBs) is proposed. In our scenario, a highly evolved central core in the dense galactic nucleus is formed containing a subsystem of compact stellar remnants (CSRs), such as neutron stars and black holes. Those subsystems result from the dynamical evolution of dense central stellar clusters in the galactic nuclei through merging of stars, thereby forming (as has been realized by many authors) the short-living massive stars and then CSRs. We estimate the rate of random CSR collisions in the evolved galactic nuclei by taking into account, similar to Quinlan & Shapiro (1987), the dissipative encounters of CSRs, mainly due to radiative losses of gravitational waves, which results in the formation of intermediate short-living binaries, with further coalescence of the companions to produce GRBs. We also consider how the possible presence of a central supermassive black hole, formed in a highly evolved galactic nucleus, influences the CSR binary formation. This scenario does not postulate ad hoc a required number of tight binary neutron stars in the galaxies. Instead, it gives, for the most realistic parameters of the evolved nuclei, the expected rate of GRBs consistent with the observed one, thereby explaining the GRB appearance in a natural way of the dynamical evolution of galactic nuclei. In addition, this scenario provides an opportunity for a cosmological GRB recurrence, previously considered to be a distinctive feature of GRBs of a local origin only. We also discuss some other observational tests of the proposed scenario.Comment: 25 pages, LATEX, uses aasms4.sty, accepted by Ap

Dynamical Friction of a Circular-Orbit Perturber in a Gaseous Medium

We investigate the gravitational wake due to, and dynamical friction on, a perturber moving on a circular orbit in a uniform gaseous medium using a semi-analytic method. This work is a straightforward extension of Ostriker (1999) who studied the case of a straight-line trajectory. The circular orbit causes the bending of the wake in the background medium along the orbit, forming a long trailing tail. The wake distribution is thus asymmetric, giving rise to the drag forces in both opposite (azimuthal) and lateral (radial) directions to the motion of the perturber, although the latter does not contribute to orbital decay much. For subsonic motion, the density wake with a weak tail is simply a curved version of that in Ostriker and does not exhibit the front-back symmetry. The resulting drag force in the opposite direction is remarkably similar to the finite-time, linear-trajectory counterpart. On the other hand, a supersonic perturber is able to overtake its own wake, possibly multiple times, and develops a very pronounced tail. The supersonic tail surrounds the perturber in a trailing spiral fashion, enhancing the perturbed density at the back as well as far front of the perturber. We provide the fitting formulae for the drag forces as functions of the Mach number, whose azimuthal part is surprisingly in good agreement with the Ostriker's formula, provided Vp t=2 Rp, where Vp and Rp are the velocity and orbital radius of the perturber, respectively.Comment: 28 pages, 9 figures, accepted for publication in Astrophysical Journa

Supernovae - Optical Precursors of Short Gamma-Ray Bursts

The probability of observing "supernova - gamma-ray burst" (GRB) pair events and recurrent GRBs from one galaxy in a time interval of several years has been estimated. Supernova explosions in binary systems accompanied by the formation of a short-lived pair of compact objects can be the sources of such events. If a short GRB is generated during the collision of a pair, then approximately each of ~300 short GRBs with redshift z must have an optical precursor - a supernova in the observer's time interval <2(1+z)yr. If the supernova explosion has the pattern of a hypernova, then a successive observation of long and short GRBs is possible. The scenario for the generation of multiple GRBs in collapsing galactic nuclei is also discussed.Comment: 12 pages, 1 figure; this paper has the e-precursor arXiv:1101.3298 [astro-ph.HE

Gravitational Wave Bursts from Collisions of Primordial Black Holes in Clusters

The rate of gravitational wave bursts from the mergers of massive primordial black holes in clusters is calculated. Such clusters of black holes can be formed through phase transitions in the early Universe. The central black holes in clusters can serve as the seeds of supermassive black holes in galactic nuclei. The expected burst detection rate by the LISA gravitational wave detector is estimated.Comment: 10 pages, 2 figure

Possible types of the evolution of vacuum shells around the de Sitter space

All possible evolution scenarios of a thin vacuum shell surrounding the spherically symmetric de Sitter space have been determined and the corresponding global geometries have been constructed. Such configurations can appear at the final stage of the cosmological phase transition, when isolated regions (islands) of the old vacuum remain. The islands of the old vacuum are absorbed by the new vacuum, expand unlimitedly, or form black holes and wormholes depending on the sizes of the islands as well as on the density and velocity of the shells surrounding the islands.Comment: 3 pages, 1 figur