On limiting velocity with Weber-like potentials

This work analyses the problem of a charge moving perpendicularly to the plates of a charged capacitor. The results obtained from the current theoretical framework (Maxwell–Lorentz electromagnetism and special relativity theory) are compared with the results obtained from Weber’s electrodynamic potential, with the Phipps’s potential and a new potential proposed here. The aim of this comparison is to analyse the causes of the inability of these Weber-like potentials to predict the existence of a limiting velocity for this problem, as special relativity theory does indeed predict and many experimental results confirm. To overcome this incapacity, the need to employ an effective potential to solve the capacitor problem is shown. In the adoption of this strategy, it is shown that the potential proposed here reproduces the same relativistic result. Finally, the origin and possible interpretation of the aforementioned effective potential are analysed.

MODIFIED NEWTONIAN POTENTIALS FOR OPTICALLY THIN ACCRETION DISKS AROUND BLACK HOLES

The use of modified Newtonian potentials to describe the gravitational field around black holes has proven successful. I will present here an investigation of the accuracy of several modified Newtonian potentials proposed in the literature, by comparing the result with the exact relativistic solution. I will do so for optically thin accretion disks that are more sensitive to the form of the potential than optically thick standard disks. I find that simple modified Newtonian potentials capture the essential features of general relativity, and the results from using the modified Newtonian potentials deviate from the relativistic result only by 20% at most for nonrotating black holes. For rotating black holes the accuracy depends on the rotation of the black hole.