Slowly rotating black holes in the novel Einstein–Maxwell-scalar theory

We investigate a slowly rotating black hole solution in a novel Einstein–Maxwell-scalar theory, which is prompted by the classification of general Einstein–Maxwell-scalar theory. The gyromagnetic ratio of this black hole is calculated, and it increases as the second free parameter $$\beta $$ β increases, but decreases with the increasing parameter $$\gamma \equiv \frac{2 \alpha ^{2}}{1+\alpha ^2}$$ γ ≡ 2 α 2 1 + α 2 . In the Einstein–Maxwell-dilaton (EMD) theory, the parameter $$\beta $$ β vanishes but the free parameter $$\alpha $$ α governing the strength of the coupling between the dilaton and the Maxwell field remains. The gyromagnetic ratio is always less than 2, the well-known value for a Kerr–Newman (KN) black hole as well as for a Dirac electron. Scalar hairs reduce the magnetic dipole moment in dilaton theory, resulting in a drop in the gyromagnetic ratio. However, we find that the gyromagnetic ratio of two can be realized in this Einstein–Maxwell-scalar theory by increasing $$\beta $$ β and the charge-to-mass ratio Q/M simultaneously (recall that the gyromagnetic ratio of KN black holes is independent of Q/M). The same situation also applies to the angular velocity of a locally non-rotating observer. Moreover, we analyze the period correction for circular orbits in terms of charge-to-mass ratio, as well as the correction of the radius of the innermost stable circular orbits. It is found the correction increases with $$\beta $$ β but decreases with Q/M. Finally, the total radiative efficiency is investigated, and it can vanish once the effect of rotation is considered.

On the double copy for spinning matter

We explore various tree-level double copy constructions for amplitudes including massive particles with spin. By working in general dimensions, we use that particles with spins s ≤ 2 are fundamental to argue that the corresponding double copy relations partially follow from compactification of their massless counterparts. This massless origin fixes the coupling of gluons, dilatons and axions to matter in a characteristic way (for instance fixing the gyromagnetic ratio), whereas the graviton couples universally reflecting the equivalence principle. For spin-1 matter we conjecture all-order Lagrangians reproducing the interactions with up to two massive lines and we test them in a classical setup, where the massive lines represent spinning compact objects such as black holes. We also test the amplitudes via CHY formulae for both bosonic and fermionic integrands. At five points, we show that by applying generalized gauge transformations one can obtain a smooth transition from quantum to classical BCJ double copy relations for radiation, thereby providing a QFT derivation for the latter. As an application, we show how the theory arising in the classical double copy of Goldberger and Ridgway can be naturally identified with a certain compactification of $$ \mathcal{N} $$ N = 4 Supergravity.

Lense–Thirring precession and gravito–gyromagnetic ratio

The geodesics of bound spherical orbits i.e. of orbits performing Lense–Thirring precession, are obtained in the case of the $$\varLambda $$ Λ term within the gravito-electromagnetic formalism. It is shown that the presence of the $$\varLambda $$ Λ -term in the equations of gravity leads to both relativistic and non-relativistic corrections in the equations of motion. The contribution of the $$\varLambda $$ Λ -term in the Lense–Thirring precession is interpreted as an additional relativistic correction and the gravito–gyromagnetic ratio is defined.

Dirac Theory of the Electron

This chapter explores applications drawn from Dirac theory of the electron. In the treatment of electrons, it uses the following: an electron has spin 1/2; its magnetic dipole moment is very nearly twice that of the orbital model in which charge and mass move together; and the spin-orbit interaction is a factor of two off the value arrived at by the heuristic argument in the Chapter 7. The factor of two in the last effect is recovered if one does the Lorentz transformations in a more careful (and correct) way, but it is easier to get it from the relativistic Dirac equation. This equation applied to an electron also says the particle has spin 1/2, as observed, and it says the gyromagnetic ratio in equation (23.11) is g = 2. The small difference from the observed value is accounted for by the quantum treatment of the electromagnetic field.