  The discovery and timing of radio pulsars within the Galactic centre is a
fundamental aspect of the SKA Science Case, responding to the topic of "Strong
Field Tests of Gravity with Pulsars and Black Holes" (Kramer et al. 2004;
Cordes et al. 2004). Pulsars have in many ways proven to be excellent tools for
testing the General theory of Relativity and alternative gravity theories (see
Wex (2014) for a recent review). Timing a pulsar in orbit around a companion,
provides a unique way of probing the relativistic dynamics and spacetime of
such a system. The strictest tests of gravity, in strong field conditions, are
expected to come from a pulsar orbiting a black hole. In this sense, a pulsar
in a close orbit ($P_{\rm orb}$ < 1 yr) around our nearest supermassive black
hole candidate, Sagittarius A* - at a distance of ~8.3 kpc in the Galactic
centre (Gillessen et al. 2009a) - would be the ideal tool. Given the size of
the orbit and the relativistic effects associated with it, even a slowly
spinning pulsar would allow the black hole spacetime to be explored in great
detail (Liu et al. 2012). For example, measurement of the frame dragging caused
by the rotation of the supermassive black hole, would allow a test of the
"cosmic censorship conjecture." The "no-hair theorem" can be tested by
measuring the quadrupole moment of the black hole. These are two of the prime
examples for the fundamental studies of gravity one could do with a pulsar
around Sagittarius A*. As will be shown here, SKA1-MID and ultimately the SKA
will provide the opportunity to begin to find and time the pulsars in this
extreme environment.
