A family of exact models for radiating matter

Abstract

In this paper, the cosmological constant and electric charge are incorporated in the Einstein–Maxwell field equations. Two approaches are used to investigate the problem. First, the boundary condition is expressed as a generalized Riccati equation in one of the gravitational potentials. New classes of exact solutions are found by writing the Riccati equation in linear, Bernoulli, and inhomogeneous forms. Our solutions contain previous results in the absence of the cosmological constant and charge. Second, it is possible to preserve the form of the generalized Riccati equation by introducing a transformation called the horizon function. This transformation simplifies the generalized Riccati equation. We generate new solutions to the transformed Riccati equation when one of the metric functions serves as a generating function. We also obtain other families of new classes of exact solutions, where the horizon function serves as a generating function. Interestingly, new uncharged solutions, not contained in previous studies, arise as special cases of the inhomogeneous Riccati equation in both approaches.

Radiating composite stars with electromagnetic fields

“…These physical quantities determine the evolution of the radiating star in general relativity. Our result emphasises the importance of taking into consideration different matter distributions in the energy momentum tensor (1), for the interior, and the matter tensor (20), for the exterior. The matter variables q, μ,μ, and l directly affect the pressure p at the stellar surface.…”

“…The null vectorl a is a double null eigenvector of the energy momentum tensor (20). The nonzero components of ( 20) are…”

“…Also, the condition for vanishing shear was made by Charan et al [14], and the shear-free condition has been investigated in different physical scenarios [15][16][17]. Particular models are known which have nonzero shear [18][19][20][21]. Abebe and Maharaj [22] found charged radiating stars using Lie symmetry infinitesimal generators to exactly solve the boundary condition.…”

Embedding with Vaidya geometry

“…The interior matter distribution is heat conducting and the exterior spacetime is given by the conventional Vaidya metric. For comprehensive treatments of recent exact solutions for radiating stellar models see Abebe and Maharaj [52], Mohanlal et al [53] and Mohamed et al [54][55][56]. The generalized Vaidya spacetime may also be used to model a radiating star in general relativity.…”

First Integrals of Shear-Free Fluids and Complexity

“…The general framework for the study of physically acceptable dissipating systems in spherical symmetry was undertaken in several works [17][18][19][20][21]. Some particular exact models have been found using this framework [22][23][24][25]. The special case of vanishing shear provides new insights into the behaviour of gravity, and some particular radiating stellar models have been generated [26][27][28][29].…”