On Spherically Symmetric Solutions with Horizon in Model with Multicomponent Anisotropic Fluid

A family of spherically symmetric solutions in the model with mcomponent multicomponent anisotropic fluid is considered. The metric of the solution depends on parameters qs > 0, s = 1, . . . ,m, relating radial pressures and the densities and contains (n− 1)m parameters corresponding to Ricci-flat “internal space” metrics and obeying certain m(m − 1)/2 (“orthogonality”) relations. For qs = 1 (for all s) and certain equations of state (pi = ±ρs) the metric coincides with the metric of intersecting black brane solution in the model with antisymmetric forms. A family of solutions with (regular) horizon corresponding to natural numbers qs = 1, 2, . . . is singled out. Certain examples of “generalized simulation” of intersecting M -branes in D = 11 supergravity are considered. The post-Newtonian parameters β and γ corresponding to the 4-dimensional section of the metric are calculated. PACS number(s): 04.20.Jb, 04.50.+h, 04.70.Bw