A relativistic core-envelope model on pseudospheroidal space-time

A core-envelope model for superdense matter distribution with the feature- core consisting of anisotropic fluid distribution and envelope with isotropic fluid distribution is reported on the background of pseudospheroidal space-time. The physical plausibility of the model is examined analytically and numerically.     

Gravitational collapse in higher-dimensional charged-Vaidya space-time

We analyze here the gravitational collapse of higher-dimensional charged-Vaidya spacetime. We show that singularities arising in a charged null fluid in higher dimension are always naked violating at least strong cosmic censorship hypothesis (CCH), though not necessarily weak CCH. We show that earlier conclusions on the occurrence of naked singularities in four-dimensional case can be extended essentially in the same manner in 5D case also     

Nonstatic perfect fluid sphere in higher-dimensional space-time

It is shown that in the case of a spherical nonstatic fluid distribution undergoing shear-free motion the field equations in higher dimensional space-time can be reduced to a single second-order differential equation involving an arbitrary function of the radial co-ordinate. This result extends to higher dimensions a similar one obtained by Wyman and Faulkes earlier for 4D space-time. Solving this differential equation a number of new solutions is found, and the dynamical behaviour of one of the models is briefly discussed. The ansatz is later generalised to include the electromagnetic field as well.     

Oscillating solutions in higher-dimensional cosmology

Behaviour characteristics of the mixmaster model of the early universe can be reproduced in ten dimensions by the low-energy superstring theory. The three-index tensor field H can produce, in the variation of the sizes of three-dimensional spaces, the characteristic jumping between Kasner solutions near a singularity. Behaviour which would otherwise by chaotic is moderated by the dilaton field of the ten-dimensional theory.     

Relativistic particles on quantum space-time

We discuss alternatives to the usual quantization of a relativistic particle which result in discrete spectra for position and time operators.     

Plane-wave solutions in higher-dimensional Kaluza-Klein theories

Exact solutions representing mixed plane-gravitational waves and planewaves of scalar fields and non-Abelian gauge fields in higher-dimensional Kaluza-Klein theories are obtained under the generalized higher-dimensional harmonic condition. Two special cases are discussed.     

Inflationary solutions in higher-dimensional quantum cosmology

This paper studies a massive scalar field in a (n+2)-dimensional spherically symmetric space-time withR×S×S _n topology. The Hamilton-Jacobi function is constructed from the Wick-rotated action of the solution of Einstein's field equations by analytic continuation. Solutions are obtained by solving the Hamilton-Jacobi equation in the Lorentzian region, and inflation is exhibited.     

Relativistic quantum statistical mechanics in two-dimensional space-time

We construct for a boson field in two-dimensional space-time with polynomial or exponential interactions and without cut-offs, the positive temperature state or the Gibbs state at temperature 1/β. We prove that at positive temperatures i.e. β<∞, there is no phase transitions and the thermodynamic limit exists and is unique for all interactions. It turns out that the Schwinger functions for the Gibbs state at temperature 1/β is after interchange of space and time equal to the Schwinger functions for the vacuum or temperature zero state for the field in a periodic box of length β, and the lowest eigenvalue for the energy of the field in a periodic box is simply related to the pressure in the Gibbs state at temperature 1/β.     

Gauge theory of gravitation in higher-dimensional space-time and its dimensional reduction

It is shown that the Euler invariant type action of an O(d) gauge theory in d dimensions is a surface term and becomes the (d − 1)-dimensional gauge theory of gravitation. Its Kaluza-Klein dimensional reduction gives a theory which contains the ordinary Einstein gravity.     

Relativistic fluid sphere on pseudo-spheroidal space-time

A new exact closed form solution of Einstein's field equations is reported describing the space-time in the interior of a fluid sphere in equilibrium. The physical 3-space,t=constant of its space-time has the geometry of a 3-pseudo spheroid. The suitability of this solution for describing the model of a relativistic superdense star is discussed and the stability of the model under radial pulsations is examined.     

Charged anisotropic star on paraboloidal space-time

The charged anisotropic star on paraboloidal space-time is reported by choosing a particular form of radial pressure and electric field intensity. The non-singular solution of Einstein–Maxwell system of equation has been derived and it is shown that the model satisfies all the physical plausibility conditions. It is observed that in the absence of electric field intensity, the model reduces to a particular case of uncharged Sharma and Ratanpal model. It is also observed that the parameter used in the electric field intensity directly affects mass of the star.     

Relativistic star clusters with high central redshift

Collisionless star clusters in dynamical equilibrium are of current interest in general relativity and astrophysics. A step-function distribution is chosen for star clusters. The corresponding equation of state is analogous to a Fermi-gas equation. These clusters are found to be pulsationally unstable for a central redshift ofZ _c ⩾ 0·54. Further, a model of clusters is developed in which the core has an extremely relativistic equation of state. These structures are unstable forZ _c ⩾ 2·55 when we use Chandrasekhar’s technique to study their pulsational stability.     

Relativistic wave mechanics of spinless particles in a curved space-time

Starting from the Klein-Gordon equation, the single-particle approximation for a reiativistic scalar particle in the presence of external electromagnetic and gravitational fields is performed. The nonrelativistic limit is obtained by a Foldy-Wouthuysen transformation on a Schrödinger-type equation. The results are then compared with those obtained in classical mechanics.     

Relativistic string model in a space-time of a constant curvature

The relativistic string model is investigated in a space-time of a constant curvature (de Sitter universe). The fundamental differential quadratic forms of the world surface of the string are considered as the dynamical variables. The coefficients of these forms obey two nonlinear equations $$\varphi _{,11} - \varphi _{,22} = e^\varphi \cos \theta + Ke^{ - \varphi } ,\theta _{,11} - \theta _{,22} = e^\varphi \sin \theta .$$ The Lax representation for this system is obtained.     

Classical solutions of higher-dimensional nonlinear sigma models on spheres

We construct several classical solutions of higher-dimensional nonlinear sigma models on spheres. These solutions are characterized by typical topological maps, in particular, four famous Hopf maps and the universal maps of theK-theory.Dedicated to the late Professor Shichiro Oka.     

A class of wormhole solutions to higher-dimensional general relativity

An ansatz is given which reduces the equations of sourceless (n+p)-dimensional general relativity to those ofn-dimensional general relativity coupled to a repulsiveO(p) scalar field. Regular solutions are obtained for (n=2,p=3,n=3,p=2), and (n=3, p=4). All these solutions have the wormhole topology.     

Riccion from higher-dimensional space-time with D-dimensional sphere as a compact manifold and one-loop renormalization

Lagrangian density of riccions is obtained with the quartic self-interacting potential using higher-derivative gravitational action in (4 +D)-dimensional space-time withS ^D as a compact manifold. It is found that the resulting four-dimensional theory for riccions is one-loop multiplicatively renormalizable. Renormalization group equations are solved and its solutions yield many interesting results such as (i) dependence of extra dimensions on the enegy mass scale showing that these dimensions increase with the increasing mass scale up toD = 6, (ii) phase transition at 3.05 × 10¹⁶ GeV and (iii) dependence of gravitational and other coupling constants on energy scale. Results also suggest that space-time above 3.05 × 10¹⁶ GeV should be fractal. Moreover, dimension of the compact manifold decreases with the decreasing energy mass scale such thatD = 1 at the scale of the phase transition. Results imply invisiblity of S¹ at this scale (which is 3.05 × 10¹⁶ GeV).     

Triplet interactions in star polymer solutions

We analyze the effective triplet interactions between the centers of star polymers in a good solvent. Using an analytical short-distance expansion inspired by scaling theory, we deduce that the triplet part of the three-star force is attractive but only 11% of the pairwise part even for a close approach of three star polymers. We have also performed extensive computer simulations for different arm numbers f to extract the effective triplet force. The simulation data show good correspondence with the theoretical predictions. Our results justify the effective pair potential picture even beyond the star polymer overlap concentration. Received 1 September 1999 and Received in final form 18 January 2000