Tests of ideas at the frontier of physics, whether in the realm of dark matter detection or quantum gravity, are hard to conduct on Earth. For example, accelerator energies are many orders of magnitude too low to directly test GUT-scale physics and the even more prohibitive compactification scale of extra spatial dimensions. But astrophysical “laboratories” have no such limits. On the other hand, astrophysical systems can be complex. We will discuss a relatively “simple” binary system consisting of a Kerr black hole and pulsar. The pulsar, acting as a precision orbiting clock, would enable measurements that can test specific predictions beyond the standard model. We will consider the case of black hole superradiance which allows axions to be generated in a cloud around a Kerr black hole. This cloud drains the rotational kinetic energy, and thus mass, emitting gravitational waves in the process. Axions are central to many theoretical ideas at the frontier of physics including as a dark matter candidate and are a prediction of models of quantum gravity such as string theory. We will discuss how precision measurements of the changing orbital period of the system (at the level accomplished in the case of the binary pulsar) can test this axion production process, and set limits on the mass scale of the axions produced. The Square Kilometer Array will be able to discover and observe black hole-pulsar binaries and will be able to search for axions in such systems.