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

TL;DR

The paper constructs a family of spherically symmetric solutions in a multicomponent anisotropic fluid model, generalizing black brane solutions with connections to Lie algebras and supergravity.

Contribution

It introduces new solutions governed by moduli functions satisfying nonlinear equations, extending known black brane solutions to more general multicomponent fluid models.

Findings

Existence of solutions with horizons for specific parameters q.

Solutions related to semisimple Lie algebras.

Generalizations of known supergravity black brane solutions.

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 $D = 2 + d_0$.