Quadratic-in-spin Hamiltonian at $$ \mathcal{O} $$(G2) from scattering amplitudes

We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through $$ \mathcal{O} $$ O (G2) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory to consider non-minimal coupling of the spinning objects to gravity. At the order that we consider, we establish the validity of the formula proposed in [1] that relates the impulse and spin kick in a scattering event to the eikonal phase.

Rolling spinners on the water surface

Angular momentum of spinning bodies leads to their remarkable interactions with fields, waves, fluids, and solids. Orbiting celestial bodies, balls in sports, liquid droplets above a hot plate, nanoparticles in optical fields, and spinning quantum particles exhibit nontrivial rotational dynamics. Here, we report self-guided propulsion of magnetic fast-spinning particles on a liquid surface in the presence of a solid boundary. Above some critical spinning frequency, such particles generate localized 3D vortices and form composite “spinner-vortex” quasiparticles with nontrivial, yet robust dynamics. Such spinner-vortices are attracted and dynamically trapped near the boundaries, propagating along the wall of any shape similarly to “liquid wheels.” The propulsion velocity and the distance to the wall are controlled by the angular velocity of the spinner via the balance between the Magnus and wall repulsion forces. Our results offer a new type of surface vehicles and provide a powerful tool to manipulate spinning objects in fluids.

Classical potential for general spinning bodies

In this paper we compute the spin-dependent terms of the gravitational potential for general spinning bodies at the leading Newton’s constant G and to all orders in spin. We utilize the on-shell approach, which extracts the classical potential directly from the scattering amplitude. For spinning particles, extra care is required due to the fact that the spin space of each particle is independent. Once the appropriate matching procedures are applied, taking the classical-spin limit we obtain the potential for general spinning bodies. When the Wilson coefficients are set to unity, we successfully reproduced the potential for the Kerr black hole. Interestingly, for finite spins, we find that the finite-spin deviations from Kerr Wilson coefficients cancel with that in the matching procedure, reproducing the Kerr potential without the need for taking the classical-spin limit. Finally, we find that when cast into the chiral basis, the spin-dependence of minimal coupling exhibits factorization, allowing us to take the classical-spin limit straight forwardly.

Evidences of the charge fundamental asymmetry

There is an infinitesimal small non polarizable electric inertial charge in the individual atoms or in a number neutral matter included to equal number of the electrons and protons. We refer to the pure calculations verified by the experimental laboratorial results, also planetary phenomena and cosmic observations. This inertial electric charge is origin of a part of the measurable magnetic field in addition to self-consistent dynamo, together as complementary origins to generate very complex magnetism of the celestial bodies. Ultimately we refer to the null results of the test experiments for the spinning bodies magnetic field and we see that neither used bodies in the experiments have been number neutral (no equal number of the electrons and protons), nor the simple formula of the Patrick Blackett is accurate in detail. But we have extracted a new formula in agreement for all spinning bodies magnetic fields, in agreement with both terrestrial and cosmic bodies. We verify the effect of electric charge asymmetry in expanding universe and acceleration of the universe expansion and anisotropy of cosmic microwave background and singularity paradox and solar wind and acceleration of solar wind and corona high temperature puzzle as an equilibrium between the gravity and antigravity and mysterious heat generation of the Sun and planets interiors and missing neutrino and the comets plasma tail outward direction and pendulums mysterious precessions and some other mysteries phenomena too.

Spinning bodies in general relativity

A covariant Hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of Hamiltonians accounting for specific properties and interactions of spinning bodies. The dynamics for a minimal and a specific non-minimal Hamiltonian is discussed. An independent derivation of the equations of motion from an appropriate energy–momentum tensor is provided. It is shown how to derive constants of motion, both background-independent and background-dependent ones.