We are all familiar with the concept of celestial bodies orbiting around one another, such as the Earth orbiting around the Sun. According to Newton, the Earth’s orbit traces out an ellipse in a plane which cuts through the centre of the Sun. Even when the effects of Einstein’s theory of general relativity are included, this picture continues to hold true to a very good approximation.
However, the situation changes when a planet is orbiting near a rotating Kerr black hole. Due to the black hole’s rotation, the orbits can trace out paths which are different from what we are familiar with. Spherical orbits are a special class of these non-planar orbits. They are so-called because they trace out paths which lie on spheres.
Assoc Prof Edward Teo has studied the properties of these spherical orbits in detail. This is important in modelling the motion of planets and stars around a Kerr black hole. This information is useful, for instance, in modelling the emission of gravitational waves by a neutron star or small black hole as it falls into a supermassive black hole.
This recent research extends the work that Assoc Prof Teo did in 2003 on spherical photon orbits. In particular, he has found analytic solutions for the paths of these orbits, which enable them to be generated quickly and efficiently.
This work was published in General Relativity and Gravitation (January 2021).