Brandon Carter has made outstanding contributions to relativity theory and astrophysics. He provided key mathematical theorems leading to the understanding that any stationary rotating black hole must conform to Kerr geometry. He made a deep analysis of this Kerr geometry, discovering an important hitherto unsuspected constant of the geodesic orbits, obtaining their equations explicitly in terms of quadratures, and showing that the scalar wave equation on a Kerr space is separable.
Brandon has also made significant contributions to the study of causality properties of black hole and other space–time models. He co-authored a seminal paper on black hole thermodynamics and has made other significant contributions to the study of black holes. In addition, he has worked on general relativistic elasticity, providing a comprehensive theoretical treatment and applying it, in particular, to the study of neutron stars and starquake glitches. He has also made a penetrating analysis of the role played by the pure number constants of nature in astrophysical processes.