Extremal Black Hole in a Nonlinear Newtonian Theory of Gravity

Abstract

This work investigates an upper-limit of charge for a black hole in a nonlinear Newtonian theory of gravity. The charge is accumulated via protons fired isotropically at the black hole. This theoretical study of gravity (known as ‘pseudo-Newtonian’) is a forced merger of special relativity and Newtonian gravity. Whereas the source of Newton’s gravity is purely mass, pseudo-Newtonian gravity includes effects of fields around the mass, giving a more complete picture of how gravity behaves. Interestingly, pseudo-Newtonian gravity predicts such relativistic phenomena as black holes and deviations from Kepler’s laws, but of course, provides a less accurate picture than general relativity. Though less accurate, it offers an easier approach to understanding some results of general relativity, and merits interest due to its simplicity. The method of study applied here examines the predictions of pseudo-Newtonian gravity for a particle interacting with a highly charged black hole. A black hole with a suitable charge will reach an upper limit (expressed by pseudo-Newtonian gravity) in charge capacity before Coulomb’s law repels like-charge particles away from the hole. In particular, this work attempts to push pseudo-Newtonian gravity to its extreme and discover how its results differ from general relativistic predictions involving the same proton bombardment. It is found that the results for an upper limit of charge in general relativity and this nonlinear theory of Newtonian gravity differ by a factor of four. This may give insight into the importance of space-time curvature effects on the description of particle dynamics around a black hole