Malaysian Journal of Mathematical Sciences, April 2019, Vol. 13(S)
Special Issue: 3rd International Conference on Mathematical Sciences and Statistics (ICMSS2018)
The Two Techniques for Generating Perfect Fluid Sphere
Ngampitipan, T. and Boonserm, P.
Corresponding Email: tritos.ngampitipan@gmail.com
Received date: -
Accepted date: -
Abstract:
The Einstein field equation is the second-order partial differential equation. It relates spacetime curvature to matter. In general, the exact solutions cannot be obtained because the equation is so complicated. One of the popular assumptions to reduce the complexity of the equation is that matter is a static, spherically symmetric, perfect fluid. In this way, the Einstein field equation is transformed to a second-order differential equation with variable coefficients. In this paper, we are interested in solutions about regular singular points. Therefore, the method of Frobenius can be applied. Moreover, the reduced Einstein equation is of the Riccati form. With the property of the Riccati equation, we can find the general solutions if the particular solutions are specified.
Keywords: Differential equation with variable coefficients, Einstein field equation, method of Frobenius, perfect fluid, Riccati equation
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