A different approach to anisotropic spherical collapse with shear and heat radiation

Abstract

In order to study the type of collapse, mentioned in the title, we introduce a physically meaningful object, called the horizon function. It directly enters the expressions for many of the stellar characteristics. The main junction equation, which governs the collapse, transforms into a Riccati equation with simple coefficients for the horizon function. We integrate this equation in the geodesic case. The same is done in the general case when one or another of the coefficients vanish. It is shown how to build classes of star models in this formulation of the problem and simple solutions are given.

Riccati equations for bounded radiating systems

“…Equation (8) has been integrated for geodesic motion by Ivanov [14], and in particular cases with nongeodesic motion and shear in [13].…”

“…Abebe et al [11] obtained a generalized class of Euclidean stars, with a barotropic equation of state, using the method of Lie symmetries on differential equations. The usual Lie method may be extended to include exponential Lie symmetry generators which produce the most general exact solutions as recently demonstrated by Mohanlal et al [12] Another interesting approach was followed by Ivanov [13] in which he introduced a new variable called the horizon function. This method has the advantage of substantially reducing the complexity of the boundary condition and the horizon function can be related to physical features of the radiating star.…”

“…For example, in the previous study, general radiating stars have been studied by Abebe et al [11] and a set of new exact solutions have been found. Recently, Ivanov [13] studied the same problem by introducing a horizon function. This horizon function transforms the junction condition to a simpler form.…”

“…II we derive the partial differential equation governing the stellar boundary. To simplify the boundary condition, we apply the transformation introduced by Ivanov [13] in Sect. VI that we can regain known results from our analysis.…”

Radiating stars with exponential Lie symmetries

“…A generalized class of Euclidean stars, containing metrics with an equation of state, was discussed by Abebe et al [16] using the Lie method of infinitesimal generators. In a recent approach Ivanov [17] introduced a horizon function that transforms the boundary condition to a simpler form; exact solutions also arise in this approach.…”