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Asymptotics of Solutions of a Perfect Fluid Coupled with a Cosmological Constant in Four-Dimensional Spacetime with Toroidal Symmetry

Gregory A. Benesh·Anzhong Wang
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Abstract

Asymptotics of solutions of a perfect fluid when coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry are studied. In particular, it is found that the problem of self-similar solutions of the first kind for a fluid with the equation of state, $p = k ρ$, can be reduced to solving a master equation of the form, $$ 2 F(q, k)\frac{q''(ξ)}{q'(ξ)} - G(q,k) q'(ξ) = \frac{4}ξ. $$ For $k = 0$ and $k = -1/3$ the general solutions are obtained and their main local and global properties are studied in detail.

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Gregory A. Benesh, Anzhong Wang. 2005-10-27. Asymptotics of Solutions of a Perfect Fluid Coupled with a Cosmological Constant in Four-Dimensional Spacetime with Toroidal Symmetry. https://doi.org/10.1007/s10714-005-0224-7

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