Yu. V. Grats

Self-forces in the spacetime of multiple cosmic strings

We calculate the electromagnetic self-force on a stationary linear distribution of 4-current in the spacetime of multiple cosmic strings. It is shown that if the current is infinitely thin and stretched along a line which is parallel to the strings, the problem admits an explicit solution. We show that the topological contribution to the self-forces on the multistring space is not equal to the superposition of the individual contributions of the separate strings.

SELF-ACTION ON A CURRENT WITH INTERNAL STRUCTURE IN COSMIC STRING SPACE–TIMES

We calculate the topological self-energy of the stationary linear distribution of a four-current with zero total current and a charge per unit length in the space–time of a straight cosmic string. It is shown that if the structure of a current is determined in the first approximation by its electric and magnetic dipole moments, then the self-force is not equal to zero and the current is also affected by the action of a moment of force which has a topological nature. The generalization of the obtained results for the space–time of multiple cosmic string is also discussed.

Problem of bremsstrahlung in: The case of gravitational interaction

A study is made of scalar bremsstrahlung associated with the gravitational and electromagnetic scattering of point particles. It is shown that the interaction between the gravitational field and the scalar field leads to a significant change in the spectral and angular distribution of the radiated energy when there is gravitational interaction of the radiating particles as compared with the case of electromagnetic interaction. The information that the low-frequency approximation can give for this problem is also discussed.

Electrostatics in a locally flat space with conical singularities

We calculate the potential of a pointlike source in a multicenter three-dimensional space-time and obtain general relations between the values of the regularized self-energy, force, and force moment. The self-action effects as well as the relative contribution of higher multipoles infinitely increase as the angle deficit increases. The results obtained are generalized to a system of parallel cosmic strings one of which carries a current. The case of string with a finite thickness is also considered.

Vacuum interaction of conic singularities

In the (tr log)-formalism, we consider the problem of the vacuum interaction of conic singularities in a D-dimensional (D ≥ 3) space–time. We show that the interaction energy regularized by dimensional regularization contains neither ultraviolet divergences nor divergences associated with the nonintegrable nature of the vacuum mean of the energy–momentum tensor operator. In the case of four space–time dimensions, the result coincides with those obtained previously in a local approach.

Gravitational radiation from Coulomb collisions

The problem is considered of gravitational bremsstrahlung radiation from collisions between nonrelativistic charged particles at arbitrary values of the Born parameter ¦e1e2¦/hv (with exact Coulomb wave functions). It is shown that the existing estimates of this type of radiation from the solar plasma are far too high as they are based on equations for the cross section which are not applicable at the given temperature. A new estimate is derived.

Casimir Energy in Contact-Interaction Models

The problem of Casimir interaction between two δd-like (d = 1, 2, and 3) sources in Minkowski space is examined on the basis of the ln det formalism. The result obtained for the case of two semitransparent plates (d = 1) coincides with the earlier result based on an alternative approach. The earlier assertion that there is no vacuum interaction between linear (d = 2) sources is disproved. An expression for the Casimir energy for two pointlike (d = 3) sources is obtained.

Electrostatic self-force in the field of an (n + 1)-dimensional black hole: Dimensional regularization

The self-energy of a classical charged particle localized at a relatively large distance outside the event horizon of an (n + 1)-dimensional Schwarzschild–Tangherlini black hole for an arbitrary n ≥ 3 is calculated. An expression for the electrostatic Green function is derived in the first two orders of the perturbation theory. Dimensional regularization is proposed to be used to regularize the corresponding formally divergent expression for the self-energy. The derived expression for the renormalized self-energy is compared with the results of other authors.

Vacuum polarization in the field of a multidimensional global monopole

An approximate expression for the Euclidean Green function of a massless scalar field in the spacetime of a multidimensional global monopole has been derived. Expressions for the vacuum expectation values 〈ϕ2〉ren and 〈T00〉ren have been derived by the dimensional regularization method. Comparison with the results obtained by alternative regularization methods is made.

Gravitational properties of vacuumless defects in the Randall-Sundrum universe

Topological defects can arise in symmetry-breaking models where the scalar field potential V(|ϕ|) has no minima and is some monotonically decreasing function of |ϕ|. These so-called vacuumless defects are quite different from analogous “usual” defects. We investigate the gravitational field outside a global vacuumless string and a global vacuumless monopole embedded in the brane of the Randall-Sundrum one-brane model. Leading-order corrections to the metric around vacuumless defects on the brane are determined.