  We consider deformation of the d+2 dimensional asymptotically flat
Schwarzschild black hole spacetime with the induced metric on a d-sphere at
$r=r_c$ held fixed. This is done without taking the near horizon limit. The
deformation is determined so that the $\Lambda=0$ vacuum Einstein equation is
satisfied and the metric is regular on the horizon. In this paper the velocity
of a dual fluid $v^i$ is assumed to be a Killing field and small, and the
deformed metric is obtained up to $O(v^2)$. At this order of hydrodynamic
expansion the dual fluid is an ideal one. The structure of the metric is fairly
different from the near horizon result of Bredberg and Strominger in
arXiv:1106.3084.
