Self-gravitating general-relativistic cosmic strings

We examine the coupled Einstem-Euler-Lagrange equations for nonstationary cosmic strings. Self-consistent solutions to all the equations are found under the assumption that the energy-momentum tensor is of the formT _t ^t =T _z ^z while all other components vanish. It is shown that the strings are necessarily static in this case and that the scalar field potential must be of the usual quartic form with the coupling constants satisfying e²=8.     

Self-gravitating bosons at nonzero temperature

A system of charged bosons at finite temperature and chemical potential is studied in a general-relativistic framework. We assume that the boson fields interact only gravitationally. At sufficiently low temperature the system exists in two phases: the gas and the condensate. By studying the condensation process numerically we determine the critical temperature T_c at which the condensate emerges. As the temperature decreases, the system eventually settles down in the ground state of a cold boson star.     

Self-gravitating darkon fluid with anisotropic scaling

The fluid model for the dark sector of the universe (darkon fluid), introduced previously in Phys. Rev. D 80, 083513, 2009, is reformulated as a modified model involving only variables from the physical phase space. The Lagrangian of the model does not possess a free particle limit and hence the particles it describes, darkons, exist only as a self-gravitating fluid. This darkon fluid presents a dynamical realization of the zero-mass Galilean algebra extended by anisotropic dilational symmetry with dynamical exponent z=\frac53z=\frac{5}{3}. The model possesses cosmologically relevant solutions which are identical to those in the previous paper. We derive also the equations for the cosmological perturbations at early times and determine their solutions. In addition, we discuss also some implications of adding higher spatial-derivative terms.     

Self-gravitating radiation in anti-de sitter space

Equilibrium configurations of self-gravitating massless thermal radiation inside spherical boxes of radiusR in asymptotically anti-de Sitter space (A = -3/b ₂) are constructed numerically for a range of central densities. For each box radius considered (R/b = 0, 1/2, 1, 2, 4, ), there is a unique configuration with maximal total mass and entropy, and another (at a lower central density) with maximum asymptotic red-shifted temperature. With the box removed toR=, the maximum total mass and entropy of self-gravitating thermal radiation areM _max 0.4598b0.7964(–A)^–1/2 andS _max1.3560a ^1/4 b ^3/2 3.0910a ^1/4(–A)^–3/4, and the maximum red-shifted temperature is     

Self-gravitating scalar field with cubic nonlinearity

For a self-gravitating massless conformally invariant scalar field a solution is obtained to the Einstein equations for which the geometry of space-time remains arbitrary. For a scalar field with cubic nonlinearity, a static solution to the Einstein equations possessing plane symmetry is found. A cosmological model with nonlinear scalar field in the class of conformally flat Friedmann metrics is investigated. An example is given of an exact solution to the equations of the gravitational field with singularity in the infinite past.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 18–22, December, 1980.     

Self-gravitating fluid systems and galactic dark matter

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space–times that are seeded by galactic dark matter. To this end, we identify a class of space–times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space–time is seen to be the Bertrand space–time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two-fluid models, we show that our galactic space–times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.     

Self-gravitating strings and string/black hole correspondence

In a recent essay, we discussed the possibility of using polymer sizing to model the collapse of a single, long excited string to a black hole. In this letter, we apply this idea to bring further support to string/black hole correspondence. In particular, we reproduce Horowitz and Polchinki's results for self-gravitating fundamental strings and speculate on the nature of the quantum degrees of freedom of black holes in string theory.     

Self-gravitating three-dimensional solitons in nonlinear scale-invariant electrodynamics

A scale-invariant nonlinear modification of Maxwellian electrodynamics within general relativity is proposed. The starting point is the Mie model and its scale-invariant generalization in flat space-timeE ₄. We prove that all static, spherically symmetrical regular field configurations in this new theory, as well as those in the Mie model, possess negative energy. In search of solitonlike solutions with positive masses, we take into account their proper gravitational fields. We show first that in Riemannian space any gauge-invariant electrodynamic theory does not admit regular solutions. Supposing the gauge invariance to be broken inside the particle, we prove the existence of static particlelike solutions with spherical symmetry and positive energy in the scale-invariant electrodynamics described by a Lagrangian density of the form =-Y(I)R/(2)-W(I)F F _u/2+2X(I)R A A , withY, W, andX arbitrary functions of the invariantI=A A . The correspondence with the Maxwellian theory is required.     

Self-gravitating static massive vector field in general relativity

A static spherically symmetric solution is found to the combined system of Einstein's equations and the equation of a massive vector field, the cosmological term being taken into account. It is shown that such a self-gravitating configuration forms a closed inhomogeneous cosmological model.Translated from Izvestiya Vysshlkh Uchebnykh Zavedenii, Fizika, No. 4, pp. 56–59, April, 1980.     

Self-consistent Solutions of Canonical Proper Self-gravitating Quantum Systems

Generic self-gravitating quantum solutions that are not critically dependent on the specifics of microscopic interactions are presented. The solutions incorporate curvature effects, are consistent with the universality of gravity, and have appropriate correspondence with Newtonian gravitation. The results are consistent with known experimental results that indicate the maintenance of the quantum coherence of gravitating systems, as expected through the equivalence principle.     

Self-gravitating wave fields in a Gödel space

The properties of self-gravitating wave fields with integral spin (scalar and vector), compatible with a Gödel type space, are investigated. The simultaneous systems of Einstein's gravitational field equations and the equations corresponding to wave fields in Gödel's metric are solved. For the scalar field, the solutions are obtained for different types of interaction Lagrangians for the gravitational and scalar fields. It is shown that for a massive vector field the relations obtained between the constants lead, within the scope of the strong gravitation theory, to the classical expression for the spin of elementary particles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 59–63, October, 1981.The authors are grateful to the participants of the theoretical seminar conducted by D. Ivanenko for discussing the results of this work.     

Self-gravitating Brownian particles in two dimensions: the case of N = 2 particles

We study the motion of N = 2 overdamped Brownianparticles in gravitational interaction in a space of dimensiond = 2. This is equivalent to the simplified motion of twobiological entities interacting via chemotaxis when time delay anddegradation of the chemical are ignored. This problem also bearssimilarities with the stochastic motion of two point vorticesin viscous hydrodynamics [O. Agullo, A. Verga, Phys. Rev. E 63,056304 (2001)]. We analytically obtain the probability density offinding the particles at a distance r from each other at timet. We also determine the probability that the particles havecoalesced and formed a Dirac peak at time t(i.e. the probability that the reduced particle has reached r = 0at time t). Finally, we investigate the meansquare separation \(\langle\) r ² \(\rangle\) and discuss the proper formof the virial theorem for this system. The reduced particle has anormal diffusion behavior for small times with a gravity-modifieddiffusion coefficient \(\langle\) r ² \(\rangle\) = r ₀ ² + (4k _B /ξ μ)(T–\(T_{*}\))t, wherek _B \(T_{*}\) = Gm ₁ m ₂/2 is a critical temperature, and an anomalousdiffusion for large times \(\langle\) r ² \(\rangle\) \(\propto\) \(t^{1-T_*/T}\). As a by-product, our solution also describes thegrowth of the Dirac peak (condensate) that forms at large time inthe post collapse regime of the Smoluchowski-Poisson system (orKeller-Segel model in biology) for T < T _c = GMm/(4k _B ). We find thatthe saturation of the mass of the condensate to the total mass isalgebraic in an infinite domain and exponential in a boundeddomain. Finally, we provide the general form of the virial theoremfor Brownian particles with power law interactions.     

Self-gravitating ring of matter in orbit around a black hole: the innermost stable circular orbit

We study analytically a black-hole-ring system which is composed of a stationary axisymmetric ring of particles in orbit around a perturbed Kerr black hole of mass $M$ . In particular, we calculate the shift in the orbital frequency of the innermost stable circular orbit (ISCO) due to the finite mass $m$ of the orbiting ring. It is shown that for thin rings of half-thickness $r\ll M$ , the dominant finite-mass correction to the characteristic ISCO frequency stems from the self-gravitational potential energy of the ring (a term in the energy budget of the system which is quadratic in the mass $m$ of the ring). This dominant correction to the ISCO frequency is of order $O(\mu \ln (M/r))$ , where $\mu \equiv m/M$ is the dimensionless mass of the ring. We show that the ISCO frequency increases (as compared to the ISCO frequency of an orbiting test-ring) due to the finite-mass effects of the self-gravitating ring.     

Macroscopic Form of the First Law of Thermodynamics for an Adibatically Evolving <Emphasis Type="Italic">Non-singular</Emphasis> Self-gravitating Fluid

We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve proper volume element rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation as well as particle number conservation equation. It is also emphasized that we are considering here a non-singular fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum gravity which apparently suggests thermodynamical properties even for a (singular) black hole. Having made such a clarification, we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified that such a global first law of thermodynamics, for a non-singular fluid, has not been formulated earlier.