Asymptotes of solutions of a perfect fluid coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry

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 = kρ, can be reduced to solving a master equation of the form,For k = 0 and k = −1/3 the general solutions are obtained and their main local and global properties are studied in detail.

Gravitational collapse of phantom fluid in (2 + 1)-dimensions

“…Along this vein, self-similar solutions of the Einstein field equations have attracted a great deal of attention. This is not only because the simplification of the problem, but also because of their relevance to astrophysics [3][4][5][6][7][8][9] and critical phenomena in gravitational collapse [10][11][12][13][14][15][16][17][18][19][20][21][22].…”