On black hole solutions in a model with anisotropic fluid (Q1886174)

The authors considered a family of spherically symmetric solutions in a model with spacetime \[ M=\mathbb R\times (M_0=S^{d_0})\times(M_1^{d_1}=\mathbb R)\times M_2^{d_2}\times\dots\times M_n^{d_n}, \] where \(M_n^{d_n}\) is a Ricci-flat manifold and with 1-component anisotropic fluid when the equations of state are \[ p_r=-\rho(2q-1)^{-1},\;p_0=\rho(2q-1)^{-1},\;p_i=(1-(1U_i)/d_i)\rho/(2q-1). \] For \(q=1\) and certain equation of state \((p_i=\pm\rho)\) the metric coincides that of the black brane (or black hole) solution in the model with antisymmetric forms without dilatons. For positive integers \(q=1,2,\dots\) they obtained a family of black hole solutions. Some examples of solutions with horizons, e.g., (fluid) generalizations of charged black hole and \(2M, 5M\) black brane solutions are considered. The authors also calculated the post-Newtonian parameters, corresponding the 4-dimensional section of the metric, and the Hawking temperature for possible estimations of observable effects of extra dimensions.