We investigate the integrability of cosmic strings in Bianchi III spacetime using a symmetry analysis. The behaviour of the model is reduced to the solution of a single second order nonlinear differential equation. We show that this equation has a rich structure and admits an infinite family of solutions. Our class of solutions extends special cases previously obtained by Tikekar and Patel [Gen. Relativ. Gravit.24, 397 (1992)].

We investigate the integrability of cosmic strings in Bianchi II, VIII and IX space-times using a Lie symmetry analysis. The behaviour of the gravitational field is governed by solutions of a single second order nonlinear differential equation. We demonstrate that this equation is integrable and admits an infinite family of physically reasonable solutions. Particular solutions obtained by other authors are shown to be special cases of our class of solutions.

Following the techniques used by Letelier and Stachel some new physically relevant stationary solutions of string cosmology with magnetic field are presented. In these solutions, the flow vector of matter has non-zero rotation and the cosmological constant is taken to be non-zero. Previously known solutions are derived as particular cases from our class of solutions. Some string models with vanishing cosmological constant are also discussed.

The junction conditions for a magnetohydrodynamic fluid sphere undergoing dissipative gravitational collapse in the form of a radial heat flux with shear are obtained. These conditions extend particular results of earlier treatments. We demonstrate that the pressure is proportional to the magnitude of the heat flux as is the case in shear-free models. However in our case the gravitational potentials must be solutions of the Einstein-Maxwell system of equations. The mass function m(v) is increased by a factor related to the charge Q of the radiating star. Physical quantities relating to the local conservation of momentum and surface redshift are obtained.

We investigate the propagation equations for the expansion, vorticity and shear for perfect fluid space-times which are geodesic. It is assumed that space-time admits a conformal Killing vector which is inheriting so that fluid flow lines are mapped conformally. Simple constraints on the electric and magnetic parts of the Weyl tensor are found for conformal symmetry. For homothetic vectors the vorticity and shear are free; they vanish for nonhomothetic vectors. We prove a conjecture for conformal symmetries in the special case of inheriting geodesic flows: there exist no proper conformal Killing vectors (ψ_;ab ≠ 0) for perfect fluids except for Robertson-Walker space-times. For a nonhomothetic vector field the propagation of the quantity ln (R_ab u^au^b) along the integral curves of the symmetry vector is homogeneous.

We study the junction condition relating the pressure to heat flux at the boundary of an accelerating and expanding spherically symmetric radiating star. We transform the junction condition to an ordinary differential equation by making a separability assumption on the metric functions in the space–time variables. The condition of separability on the metric functions yields several new exact solutions. A class of shear-free models is found which contains a linear equation of state and generalizes a previously obtained model. Four new shearing models are obtained; all the gravitational potentials can be written explicitly. A brief physical analysis indicates that the matter variables are well behaved.

We consider an uncharged anisotropic stellar model with two distinct equations of state in general relativity. The core layer has a quark matter distribution with a linear equation of state. The envelope layer has a matter distribution which is quadratic. The interfaces between the core, envelope and the vacuum exterior regions are smoothly matched. We find radii, masses and compactifications for five different compact objects which are consistent with other investigations. In particular, the properties of the pulsar object PSR J1614-2230 are studied. The metric functions and the matter distribution are regular throughout the star. In particular, it is shown that the radii associated with the core and the envelope can change for different parameter values.