Year: 2015
Type: dissertation
Abstract: We study shear-free heat conducting spherically symmetric gravitating \nfluids defined in four \nand higher dimensional spacetimes. We analyse models that are both uncharged and charged \nvia the pressure isotropy condition emanating from the Einstein field equations and the \nEinstein-Maxwell system respectively. Firstly, we consider the uncharged model defined in \nhigher dimensions, and we use the algorithm due to Deng to generate new exact solutions. \nThree new metrics are identified which contain the results of four dimensions as special cases. \nWe show graphically that the matter variables are well behaved and the speed of sound is \ncausal. Secondly, we use Lie's group theoretic approach to study the condition of pressure \nisotropy of a charged relativistic model in four dimensions. The Lie symmetry generators \nthat leave the equation invariant are found. We provide exact solutions to the gravitational \npotentials using the symmetries admitted by the equation. The new exact solutions contain \nearlier results without charge. We show that new charged solutions related to the Lie \nsymmetries, that are generalizations of conformally \nat metrics, may be generated using \nthe algorithm of Deng. Finally, we extend our study to find models of charged gravitating \n \nfluids defined in higher dimensional manifolds. The Lie symmetry generators related to the \ngeneralized pressure isotropy condition are found, and exact solutions to the gravitational \npotentials are generated. The new exact solutions contain earlier results obtained in four \ndimensions. Using particular Lie generators, we are able to provide forms for the gravitational \npotentials or reduce the order of the master equation to a first order nonlinear differential \nequation. Exact expressions for the temperature pro les, from the transport equation for \nboth the causal and noncausal cases, in higher dimensions are obtained, generalizing previous \nresults. In summary, the Deng algorithm and Lie analysis prove to be useful approaches \nin generating new models for gravitating \nfluids.
Author: Y. Nyonyi
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2412383395