We examine the role of space-time geometry in the non-adiabatic collapse of a star dissipating energy in the form of radial heat flow, studying its evolution under different initial conditions. The collapse of a star filled with a homogeneous perfect fluid is compared with that of a star filled with inhomogeneous imperfect fluid under anisotropic pressure. Both the configurations are spherically symmetric. However, in the latter case, the physical space 𝑡 = constant of the configurations endowed with spheroidal or pseudospheroidal geometry is assumed to be inhomogeneous. It is observed that as long as the collapse is shear-free, its evolution depends only on the mass and size of the star at the onset of collapse.

In this paper, we present a formalism to generate a family of interior solutions to the Einstein–Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner–Nordström space–time. By reducing the Einstein–Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.

Exact solutions to Einstein–Maxwell systems play an important role in relativistic astrophysics. In this paper, a new technique to generate exact solutions to the Einstein–Maxwell system is proposed. Corresponding to a spherically symmetric charged fluid sphere, by specifying the electric field and for a particular form of the metric potential grr , a new solution is obtained in terms of hypergeometric functions. Subsequently, for specific choice of model parameters, many closed-form solutions are developed. In the process, it is possible to regain a number of well-known stellar models which had been developed earlier with or without the presence of charge following the Vaidya and Tikekar ansatz for compact stars (J. Astrophys. Astron. 3:325 (1982); J. Math. Phys. 31:2454 (1990)).It is shown that the new class of solutions can be used as viable models for compact stars for a wide range of values of the model parameters. Physical behaviour of the resultant stellar configurations are studied.