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.
Highlights
Radiating stellar models have been studied in many different physical situations over the years
We find that the addition of charge and cosmological constant to the Einstein field equations leads to several families of exact solutions to the Riccati equations that arise
This paper consists of two important approaches that discuss the boundary condition for a radiating star in general relativity with cosmological constant and electric charge
Summary
Radiating stellar models have been studied in many different physical situations over the years. The junction conditions at the stellar surface were completed by Santos, who showed that the presence of heat flow must be taken into account so that the interior can match to the exterior Vaidya metric at the boundary. A second approach to solving the boundary condition at the stellar surface is to exploit physical properties, such as the formation of horizons This approach was first suggested by Ivanov for anisotropic spherical collapse for geodesic particles with shear. These solutions are helpful in describing gravitational collapse scenarios in radiating stars In this process, the interior heat conducting matter loses energy across the stellar boundary in the form of null radiation to the exterior. Two tables showing new gravitational potentials and previous results are provided
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