  We present a model for launching relativistic jets in active galactic nuclei
(AGN) from an accreting Kerr black hole (BH) as an effect of the rotation of
the space-time, where the gravitational energy of the accretion disc inside the
ergosphere, which can be increased by the BH rotational energy transferred to
the disc via closed magnetic field lines that connect the BH to the disc
(BH-disc magnetic connection), is converted into jet energy. The main role of
the BH-disc magnetic connection is to provide the source of energy for the jets
when the mass accretion rate is very low. We assume that the jets are launched
from the disc inside the BH ergosphere, where the rotational effects of the
space-time become much stronger, being further accelerated by magnetic
processes. The rotation of the space-time channels a fraction of the disc
energy (i.e., the gravitational energy of the disc plus the rotational energy
of the BH which is deposited into the disc by magnetic connection) into a
population of particles that escape from the disc surfaces, carrying away mass,
energy and angular momentum in the form of jets, allowing the remaining disc
gas to accrete. In the limit of the spin-down power regime, the model proposed
here can be regarded as a variant of the Blandford-Znajek mechanism, where the
BH rotational energy is transferred to the disc inside the ergosphere and then
used to drive the jets. We use general-relativistic conservation laws to
calculate the mass flow rate into the jets, the launching power of the jets and
the angular momentum transported by the jets for BHs with a spin parameter $a_*
\geqslant 0.95$. We found that a stationary state of the BH ($a_* = $ const)
can be reached if the mass accretion rate is larger than $\dot{m} \sim 0.001$.
In addition, the maximum AGN lifetime can be much longer than $\sim 10^{7}$ yr
when using the BH spin-down power.
