The Conservative Field of Coupled Newton–Coulomb Sources: Component Coupling Constants, Mass ⇌ Charge Cross-Forces, and Radiation from Reissner--Nordström Black-Hole Mergers

We investigate a combined conservative field in which classical gravitational and electrostatic sources also exhibit mutual interactions. Hitherto neglected, the coupling between mass and charge may be necessary for constructing a unified conservative force field generated by a single underlying source. We determine the coupling constant of the cross-field components as the geometric mean (G-M) of Newton’s G and Coulomb’s K constants, in both SI units and dimensionless form. Consequently, for two identical objects, the cross-force (F×) is the G-M of the familiar Newton (Fg) and Coulomb (Fe) forces, so that F×=sqrt(Fg Fe), where Fg ≪ F× ≪ Fe. Remarkably, such cross-forces should be measurable in torsion-balance experiments involving a suspended neutral mass interacting with a partially ionized gas. Furthermore, we apply our new formulation to estimate the dimensionless amplitude ||h_αβ^TT|| of gravitational waves emitted by inspiraling Reissner–Nordström (RN) black-hole binaries, expressed in terms of ratios of the four fundamental lengths of the problem: the distance to the binary D, the binary separation R, the Schwarzschild radius RS ∝ 2M of mass M, and the RN charge (Q) length scale LQ ∝ 2Q. In this classical setting with speeds much lower than the speed of light c in vacuum, the surprising appearance of the maximum relativistic tension force Fmax=c^4/(4G) is duly noted.