Twisted partial actions of Hopf algebras

In this work, the notion of a twisted partial Hopf action is introduced as a unified approach for twisted partial group actions, partial Hopf actions and twisted actions of Hopf algebras. The conditions on partial cocycles are established in order to construct partial crossed products, which are also related to partially cleft extensions of algebras. Examples are elaborated using algebraic groups

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

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

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

Vacuum shell in the Schwarzschild-de Sitter world

We construct the classification scheme for all possible evolution scenarios and find the corresponding global geometries for dynamics of a thin spherical vacuum shell in the Schwarzschild-de Sitter metric. This configuration is suitable for the modelling of vacuum bubbles arising during cosmological phase transitions in the early Universe. The distinctive final types of evolution from the local point of view of a rather distant observer are either the unlimited expansion of the shell or its contraction with a formation of black hole (with a central singularity) or wormhole (with a baby universe in interior).Comment: 15 pages, 8 figure

Dynamical Friction in a Gaseous Medium

Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber M_p traveling at velocity V through a uniform gaseous medium of density rho_0 and sound speed c_s. This drag force acts in the direction -\hat V, and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion (M=V/c_s>1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion (M<1), the wake is confined to a sphere of radius c_s t centered a distance V t behind the perturber. Inside the wake, surfaces of constant density are hyperboloids or oblate spheroids for supersonic or subsonic perturbers, respectively, with the density maximal nearest the perturber. The dynamical drag force has the form F_df= - I 4\pi (G M_p)^2\rho_0/V^2. We evaluate I analytically; its limits are I\to M^3/3 for M>1. We compare our results to the Chandrasekhar formula for dynamical friction in a collisionless medium, noting that the gaseous drag is generally more efficient when M>1 but less efficient when M<1. To allow simple estimates of orbit evolution in a gaseous protogalaxy or proto-star cluster, we use our formulae to evaluate the decay times of a (supersonic) perturber on a near-circular orbit in an isothermal \rho\propto r^{-2} halo, and of a (subsonic) perturber on a near-circular orbit in a constant-density core. We also mention the relevance of our calculations to protoplanet migration in a circumstellar nebula.Comment: 17 pages, 5 postscript figures, to appear in ApJ 3/1/9

Swift J164449.3+573451 event: generation in the collapsing star cluster?

We discuss the multiband energy release in a model of a collapsing galactic nucleus, and we try to interpret the unique super-long cosmic gamma-ray event Swift J164449.3+573451 (GRB 110328A by early classification) in this scenario. Neutron stars and stellar-mass black holes can form evolutionary a compact self-gravitating subsystem in the galactic center. Collisions and merges of these stellar remnants during an avalanche contraction and collapse of the cluster core can produce powerful events in different bands due to several mechanisms. Collisions of neutron stars and stellar-mass black holes can generate gamma-ray bursts (GRBs) similar to the ordinary models of short GRB origin. The bright peaks during the first two days may also be a consequence of multiple matter supply (due to matter release in the collisions) and accretion onto the forming supermassive black hole. Numerous smaller peaks and later quasi-steady radiation can arise from gravitational lensing, late accretion of gas onto the supermassive black hole, and from particle acceleration by shock waves. Even if this model will not reproduce exactly all the Swift J164449.3+573451 properties in future observations, such collapses of galactic nuclei can be available for detection in other events.Comment: 7 pages, replaced by the final versio