The Reality of Gravitational Repulsion, Its Impact in the Kerr Field and on Astrophysics

Employing Boyer-Lindquist coordinates we show that the Kerr solution to the field equations of General Relativity leads to the conclusion that relativistic particles experience gravitational repulsion, $\frac{{\text{d}}^{2}r}{\text{d}{t}^2}>0$ , in the weak-field regime, i.e., as measured by distant observers. We consider only particles moving in axial motion or in the equatorial plane in the Kerr field. In both cases to the first order in weak fields relativistic particles experience gravitational acceleration, ${\text{d}}^{2}r/\text{d}{t}^2=+2g$ , where $g=\frac{GM}{r^2}$ . We reconcile the asymptotic result of McGruder (1982) and Krori & Barua (1985) with a systematic weak-field expansion, and identify higher-order Kerr corrections. The influence of rotation only becomes apparent in the second order. Implications for ultra-relativistic particles, ultra-high-energy cosmic rays, and compact astrophysical sources are discussed. After showing that gravitational repulsion exists in the Kerr field, we make it clear that gravitational repulsion corresponds to physical reality in both the Schwarzschild and Kerr fields.