On generalized black brane solutions in the model with multicomponent anisotropic fluid

Abstract

A family of spherically $O(d_0 + 1)$-symmetric solutions in the model with $m$-component anisotropic fluid is obtained. The metrics are defined on a manifold which contains a product of $n-1$ Ricci-flat ``internal'' spaces. The equation of state for any $s$-th component is defined by a vector $U^s = (U^s_i)$ belonging to $R^{n + 1}$ and obeying inequalities $U^s_1 = q_s > 0$, $s = 1, \ldots,m$. The solutions are governed by moduli functions $H_s$ which are solutions to (master) non-linear differential equations with certain boundary conditions imposed. It is shown that for coinciding $q_s = q$ there exists a subclass of solutions with a horizon when $q = 1, 2, \ldots$ and $U^s$-vectors correspond to certain semisimple Lie algebras. An extension of these solutions to block-orthogonal set of vectors $U^s$ with natural parameters $q_s$ coinciding inside blocks is also proposed. $q$-analogues of black brane/hole solutions are presented, e.g. generalising $M_2 \cap M_5$ dyonic solution in $D =11$ supergravity and Myers-Perry charged black hole solution in dimension $D = 2 + d_0$.