Abstract
A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions.
Highlights
In many studies, the concept of complexity has been applied to topics such as entropy and information
Several investigations have been initiated involving the concept of complexity in self-gravitating systems in general relativity and some modified theories of gravity [2,3,4,5,6,7,8,9,10,11,12]
Jasim et al [13] studied a strange star model in a special case of Lovelock theory, namely Einstein–Gauss–Bonnet gravity, and showed that such theories are consistent with the concept of complexity
Summary
The concept of complexity has been applied to topics such as entropy and information. Shear-free matter distributions arise as a special case and deserve special attention because of their applicability to stellar models, and they have been used to model both static and radiating stars In this investigation, we consider the behaviour of shear-free fluids in a spherical spacetime. Seeking exact solutions to the Einstein field equations has been the subject of study in many astrophysical and cosmological applications. When seeking exact solutions to the Einstein field equations, it is usual to assume spherical symmetry for spacetimes and the absence of shear for the matter distribution. These assumptions greatly simplify the field equations while ensuring that the results are still physically meaningful.
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