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 $U^s=(U_i^s)$ belonging to $R^{n+1}$ and obeying inequalities $U_1^s=q_s>0$, $s=1,\dots ,m$. 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 $q=1,2,\dots$ 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 $D=2+d_0$.

30 pages, LaTex, one table, no figures. Revised version: a table and several paragraphs and relations are added, several typos are eliminated, 7 references are added. To be published in Philosophical Transactions of the Royal Society A