  If a lot of dark matter particles accumulate near the black hole, then the
chances of detecting dark matter signals near a black hole are greatly
increased. These effects may be observed by the Event Horizon Telescope (EHT),
Tianqin project, Taiji project, Laser Interferometer Space Antenna (LISA) and
Laser Interferometer Gravitational-Wave Observatory (LIGO). In this work, we
explore the effects of dark matter spikes on black hole space-time. For the
Schwarzschild-like black hole case, we consider Newton$'$s approximation and
perturbation approximation. This makes it possible to use Xu$'$s method to
solve the Einstein field equation, and extend Schwarzschild-like black hole to
Kerr-like black hole (BH) via Newman-Janis (NJ) algorithm. By analyzing the
dark matter spike on the black hole event horizon (EH), stationary limit
surfaces (SLS), ergosphere and energy-momentum tensors (EMT), we found that
compared with the dark matter halo, the dark matter spike would have a higher
effect on the black hole by several orders of magnitude. Therefore, if there is
a dark matter spike near the black hole, it is very possible to test the dark
matter model through gravitational wave (GW) observation and EHT observation.
