  Spinning black holes store rotational energy that can be extracted. When a
black hole is immersed in an externally supplied magnetic field, reconnection
of magnetic field lines within the ergosphere can generate negative energy
(relative to infinity) particles that fall into the black hole event horizon
while other particles escape stealing energy from the black hole. We show
analytically that energy extraction via magnetic reconnection is possible when
the black hole spin is high (dimensionless spin $a\sim1$) and the plasma is
strongly magnetized (plasma magnetization $\sigma_0>1/3$). The parameter space
region where energy extraction is allowed depends on the plasma magnetization
and the orientation of the reconnecting magnetic field lines. For $\sigma_0 \gg
1$, the asymptotic negative energy at infinity per enthalpy of the decelerated
plasma that is swallowed by a maximally rotating black hole is found to be
$\epsilon^\infty_- \simeq - \sqrt{\sigma_0/3}$. The accelerated plasma that
escapes to infinity and takes away black hole energy asymptotes the energy at
infinity per enthalpy $\epsilon^\infty_+ \simeq \sqrt{3\sigma_0}$. We show that
the maximum power extracted from the black hole by the escaping plasma is
$P_{\rm extr}^{\rm max} \sim 0.1 M^2\sqrt{\sigma_0}\,w_0$ (here, $M$ is the
black hole mass and $w_0$ is the plasma enthalpy density) for the collisionless
plasma regime and one order of magnitude lower for the collisional regime.
Energy extraction causes a significant spindown of the black hole when $a \sim
1$. The maximum efficiency of the plasma energization process via magnetic
reconnection in the ergosphere is found to be $\eta_{\rm max} \simeq 3/2$.
Since fast magnetic reconnection in the ergosphere should occur intermittently
in the scenario proposed here, the associated emission within a few
gravitational radii from the black hole is expected to display a bursty nature.
