My friend asked me about the geometry of a moving black hole with constant velocity. My first attempt to cast its metric tensor was:
$1.$ Start with Schwarzschild metric in spherical coordinates $(t,r,\theta,\phi)$.
$2.$ Perform a coordinate transformation for cartesian coordinates $(t,r,\theta,\phi) \to (t,x,y,z)$.
$3.$ Finally, perform a boost in just the $x$-direction $(t,x,y,z) \to (\gamma(t'-vx'),\gamma(x' -vt'),y',z')$.
I didn't finish the calculations but my question is that if I follow the steps of my reasoning above, will I reach a metric tensor $g$ that describes a black hole moving with a constant velocity?
