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- Title
Charged Shear-Free Fluids and Complexity in First Integrals.
- Authors
Gumede, Sfundo C.; Govinder, Keshlan S.; Maharaj, Sunil D.
- Abstract
The equation y x x = f (x) y 2 + g (x) y 3 is the charged generalization of the Emden-Fowler equation that is crucial in the study of spherically symmetric shear-free spacetimes. This version arises from the Einstein–Maxwell system for a charged shear-free matter distribution. We integrate this equation and find a new first integral. For this solution to exist, two integral equations arise as integrability conditions. The integrability conditions can be transformed to nonlinear differential equations, which give explicit forms for f (x) and g (x) in terms of elementary and special functions. The explicit forms f (x) ∼ 1 x 5 1 − 1 x − 11 / 5 and g (x) ∼ 1 x 6 1 − 1 x − 12 / 5 arise as repeated roots of a fourth order polynomial. This is a new solution to the Einstein-Maxwell equations. Our result complements earlier work in neutral and charged matter showing that the complexity of a charged self-gravitating fluid is connected to the existence of a first integral.
- Subjects
NONLINEAR differential equations; MAXWELL equations; INTEGRALS; SPECIAL functions; INTEGRAL equations; FLUIDS; EINSTEIN-Maxwell equations
- Publication
Entropy, 2022, Vol 24, Issue 5, pN.PAG
- ISSN
1099-4300
- Publication type
Article
- DOI
10.3390/e24050645