Matter ouside a Static Higher-dimensional Black Hole

We considered matter fields composed of a perfect fluid in the static higher-dimensional spherically symmetric asymptotically flat black hole spacetime. The proof of the nonexistence of perfect fluid matter in such a background was provided under the auxiliary condition, which can be interpreted as a relation connecting the stellar mass and the black hole mass in question.
Comment: 14 pages, RevTex, to be published in Phys.Rev.D15