arXiv subjects
Publications and source records attributed to Vyacheslav Dokuchaev.
The higher derivative gravitational theories exhibit new phenomena absent in General Relativity. One of them is the possible formation of the so called double layer which is the pure gravitational phenomenon and can be interpreted, in a sense, as the gravitational shock wave. In this paper we show how some very important features of the double layer equations of motion can be extracted straight from the least action principle.
How the supermassive black hole SgrA* in the Milky Way Center looks like for a distant observer? It depends on the black hole highlighting by the surrounding hot matter. The black hole shadow (the photon capture cross-section) would be viewed if there is a stationary luminous background. The black hole event horizon is invisible directly (per se). Nevertheless, a more compact (with respect to black hole shadow) projection of the black hole event horizon on the celestial sphere may be reconstructed by detecting the highly red-shifted photons emitted by the non-stationary luminous matter plunging into the black hole and approaching to the event horizon. It is appropriate to call this reconstructed projection of the event horizon on the celestial sphere for a distant observer as the ``lensed event horizon image'', or simply the ``event horizon image''. This event horizon image is placed on the celestial sphere within the position of black hole shadow. Amazingly, the event horizon image is a gravitationally lensed projection on the celestial sphere of the whole surface of the event horizon globe. In result, the black holes may be viewed at once from both the front and back sides. The lensed event horizon image may be considered as a genuine silhouette of the black hole. For example, a dark northern hemisphere of the event horizon image is the simplest model for a black hole silhouette in the presence of a thin accretion disk.
The main results are the following. We derived the matching conditions for the spherically symmetric singular hypersurface (in our case it is equivalent to the world line) in the Weyl$+$Einstein gravity. It was found, that the residual extrinsic curvature tensor of this surface must be continuous on the singular hypersurface. The result is the same as that found by Senovilla, it is dictated by the very possibility to have the double layer, but the jump in the normal derivative of the radius may be not zero. It was found that in the presence of the double layer, the matching conditions contain an arbitrary function, and this result is quite new and very important. One of the consequences of such freedom is that the trace of the extrinsic curvature tensor of the singular hypersurface is necessarily equal to zero. We suggested the physical interpretation for the $S_0^n$ and $S_n^n$ components of the surface matter energy-momentum tensor of the shell. In General Relativity they are zero by virtue of the Einstein equations. In the quadratic gravity they are not necessarily zero. Our interpretation is that these components describe the energy flow $(S^{0n})$ and the momentum transfer $(S^{nn})$ of the particles produced by the double layer itself. Moreover, the requirement of the zero trace of the extrinsic curvature tensor (mentioned above) implies that $S_n^n=0$, and this fact also support our suggestion, because it means that for the observer sitting on the shell, the particles will be seen created by pairs, and the sum of their momentum transfers must zero. We derived also the matching conditions for the null hypersurface, and this is, again, quite new. We found that the null-double layer in the Weyl$+$ Einstein gravity does not exist at all.
We study a black hole in an expanding Universe during the radiation-dominated stage. In the case when the black hole radius is much smaller than the cosmological horizon, we present a solution of the Einstein equations for the metric, the matter density and velocity distributions. At distances much smaller than the cosmological horizon the solution features quasi-stationary accretion, while at large distances the solution asymptotes the homogeneous radiation dominated FLRW. We discuss how our solution is related to the McVittie solution. The obtained results can be applied, in particular, for the formation of dark matter density spikes around primordial black holes, and for the evolution of dark matter clumps during the radiation-dominated stage.
The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity theories. We are interested in the special and physically important case when all the quadratic in curvature tensor (Riemann tensor) and its contractions (Ricci tensor and scalar curvature) terms are present in the form of the square of Weyl tensor. By definition, the energy-momentum tensor of the thin shell is proportional to Dirac delta-function. We constructed the theory of the spherically symmetric thin shells for three types of gravitational theories with the shell: (1) General Relativity; (2) Pure conformal (Weyl) gravity where the gravitational part of the total Lagrangian is just the square of the Weyl tensor; (3) Weyl+Einstein gravity. The results are compared with these in General Relativity (Israel equations). We considered in details the shells immersed in the vacuum. Some peculiar properties of such shells are found. In particular, for the traceless (= massless) shells it is shown that their dynamics can not be derived from the matching conditions and, thus, is completely arbitrary. On the contrary, in the case of the Weyl+Einstein gravity the trajectory of the same type of shell is completely restored even without knowledge of the outside solution.
We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the "usual" hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by "the particle creation law", proportional to the square of the Weyl tensor (following the famous result by Ya.B.Zel`dovich and A. A.Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein--Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A. D.Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the "empty vacuum", there may exist the "dynamical vacuum", which is nothing more but the Dirac sea.
Neutralino annihilation in the Galactic halo is the most definite observational signature proposed for indirect registration of the SUSY Dark Matter (DM) candidate particles. The corresponding annihilation signal (in the form of gamma-rays, positrons and antiprotons) may be boosted for one or three orders of magnitude due to the clustering of cold DM particles into the small-scale and very dense self-gravitating clumps. We discuss the formation of these clumps from the initial density perturbations and their successive fate in the Galactic halo. Only a small fraction of these clumps, $\sim0.1$%, in each logarithmic mass interval $Δ\log M\sim1$ survives the stage of hierarchical clustering. We calculate the probability of surviving the remnants of dark matter clumps in the Galaxy by modelling the tidal destruction of the small-scale clumps by the Galactic disk and stars. It is demonstrated that a substantial fraction of clump remnants may survive through the tidal destruction during the lifetime of the Galaxy. The resulting mass spectrum of survived clumps is extended down to the mass of the core of the cosmologically produced clumps with a minimal mass. The survived dense remnants of tidally destructed clumps provide an amplification (boosting) of the annihilation signal with respect to the diffuse DM in the Galactic halo. We describe the anisotropy of clump distribution caused by the tidal destruction of clumps in the Galactic disk.
What happened to the central cores of tidally destructed dark matter clumps in the Galactic halo? We calculate the probability of surviving of the remnants of dark matter clumps in the Galaxy by modelling the tidal destruction of the small-scale clumps. It is demonstrated that a substantial fraction of clump remnants may survive through the tidal destruction during the lifetime of the Galaxy if the radius of a core is rather small. The resulting mass spectrum of survived clumps is extended down to the mass of the core of the cosmologically produced clumps with a minimal mass. Since the annihilation signal is dominated by the dense part of the core, destruction of the outer part of the clump affects the annihilation rate relatively weakly and the survived dense remnants of tidally destructed clumps provide a large contribution to the annihilation signal in the Galaxy. The uncertainties in minimal clump mass resulting from the uncertainties in neutralino models are discussed.
We describe the anisotropy of dark matter clump distribution caused by tidal destruction of clumps in the Galactic disk. A tidal destruction of clumps with orbit planes near the disk plane occurs more efficiently as compared with destruction of clumps at near-polar orbits. A corresponding annihilation of dark matter particles in small-scale clumps produces the anisotropic gamma-ray signal with respect to the Galactic disk. This anisotropy is rather small, 9%, and superimposed on that due to off-centering position of the Sun in the Galaxy. The anisotropy of annihilation signal with respect to the Galactic disk provides a possibility to discriminate dark matter annihilation from the diffuse gamma-ray backgrounds of other origin.
A mass function of small-scale dark matter clumps is calculated in the standard cosmological scenario with an inflationary-produced primordial fluctuation spectrum and with a hierarchical clustering. We take into account the tidal destruction of clumps at early stages of structure formation starting from a time of clump detachment from the Universe expansion. Only a small fraction of these clumps, ~0.1-0.5%, in each logarithmic mass interval $Δ\log M\sim1$ survives the stage of hierarchical clustering. The surviving clumps can be disrupted further in the galaxies by tidal interactions with stars. We performed the detailed calculations of the tidal destruction of clumps by stars in the Galactic bulge and halo and by the Galactic disk itself. It is shown that the Galactic disc provides the dominant contribution to the tidal destruction of small-scale clumps outside the bulge. The results obtained are crucial for calculations of the dark matter annihilation signal in the Galaxy.
We describe the possible scenarios for the evolution of a thin spherically symmetric self-gravitating phantom shell around the Schwarzschild black hole. The general equations describing the motion of the shell with a general form of equation of state are derived and analyzed. The different types of space-time R- and T-regions and shell motion are classified depending on the parameters of the problem. It is shown that in the case of a positive shell mass there exist three scenarios for the shell evolution with an infinite motion and two distinctive types of collapse. Analogous scenarios were classified for the case of a negative shell mass. In particular this classification shows that it is impossible for the physical observer to detect the fantom energy flow. We shortly discuss the importance of our results for astrophysical applications.
We propose the model of first quasars formation around the cluster of rimordial black holes (PBHs). It is supposed, that mass fraction of the universe ~10^-3 is composed of the compact clusters of PBHs, produced during the phase transitions in the early universe. The clusters of PBHs become the centers of dark matter condensation. As a result, the galaxies with massive central black holes are formed. In the process of galaxies formation the central black holes are growing due to accretion. This accretion is acompaned by the early quasar activity.
We describe the model of protogalaxy formation around the cluster of primordial black holes with a minimum extension of standard cosmological model. Namely, it is supposed, that a mass fraction of the universe ~10^-3 is composed of the compact clusters of primordial (relict) black holes produced during the phase transitions in the early universe. These clusters are the centers of the dark matter (DM) condensations. As a result the protogalaxies with a mass 2x10^8Msun form at the redshift z=15. These induced protogalaxies contain the central black holes of mass ~10^5Msun and look like the dwarf spheroidal galaxies with a central density spike. Subsequent merging of the induced protogalaxies and ordinary DM haloes leads to the standard scenario of the large scale structure formation. Black holes merging gives the nowadays supermassive black holes and reproduces the observed correlations between their masses and velocity dispersions in the bulges.
We study the cosmological origin of small-scale DM clumps in the hierarchical scenario with the most conservative assumption of adiabatic Gaussian fluctuations. The mass spectrum of small-scale clumps with M<10^3Msun is calculated with tidal destruction of the clumps taken into account within the hierarchical model of clump structure. Only 0.1-0.5% of small clumps survive the stage of tidal destruction in each logarithmic mass interval. The mass distribution of clumps has a cutoff at Mmin due to diffusion of DM particles out of a fluctuation and free streaming at later stage. Mmin is a model dependent quantity. In the case the neutralino DM, considered as a pure bino, Mmin~10^-8 Msun. The evolution of density profile in a DM clump does not result in the singularity because of formation of the core under influence of tidal interaction. The radius of the core is ~0.1R, where R is radius of the clump. The applications for annihilation of DM particles in the Galactic halo are studied. The number density of clumps as a function of their mass, radius and distance to the Galactic center is presented. The enhancement of annihilation signal due to clumpiness, valid for arbitrary DM particles, is calculated. In spite of small survival probability, the global annihilation signal in most cases is dominated by clumps, with major contribution given by small clumps. The enhancement due to large clumps with M>10^6 Msun is very small.
We calculate the gravitational radiation from a cusp of the chiral cosmic strings as a function of the current on the string in the limit of small values of the current. The smoothing of the cosmic string cusp due to the presence of the superconducting current on the string leads to the different behavior of the gravitational radiation from the cusp as compared with the non-superconducting (ordinary) string. The difference between the gravitational energy radiation from the chiral cusp and the ordinary one is proportional to the value of the current on the string. It is shown that there is a high-frequency cutoff in the spectrum of the gravitational radiation from the chiral string. The frequency cutoff depends on the value of the string current. This effect is crucial for the detection of gravitation wave bursts from cosmic strings: the rather large current on the string would lower the amplitude of the incoming signal.
Chiral cosmic string loop tends to the stationary (vorton) configuration due to the energy loss into the gravitational and electromagnetic radiation. We describe the asymptotic behaviour of near stationary chiral loops and their fading to vortons. General limits on the gravitational and electromagnetic energy losses by near stationary chiral loops are found. For these loops we estimate the oscillation damping time. We present solvable examples of gravitational radiation energy loss by some chiral loop configurations. The analytical dependence of string energy with time is found in the case of the chiral ring with small amplitude radial oscillations.
The gravitational lensing of a relativistic fireball can produce the time delayed multiple images with quite different spectra and temporal patterns in contrast with a nonrelativistic source and hence can imitate the source recurrence. In particular, the enigmatic four multiple gamma-ray bursts detected during two days at October 1996 in the same sky region may be due to a single fireball event multiply imaged by the foreground galactic nucleus or cluster of galaxies.