Test and theory of frame-dragging and gravitomagnetism

Frame-dragging or dragging of inertial frames and gravitomagnetism [1-3] are intriguing phenomena of the general theory of relativity (GR) with spectacular astrophysical effects in the vicinities of spinning black holes and great relevance in the emission of gravitational waves by spinning black holes. I first report on the 2026 test [4] of frame-dragging obtained with the laser-ranged satellite LARES 2 (LAser RElativity Satellite 2, launched in 2022) of the Italian Space Agency (ASI) together with the NASA laser-ranged satellite LAGEOS (Laser Geodynamics Satellite, lunched in 1976). Using these two satellites, it was achieved a test of frame-dragging with an unprecedentedly small relative uncertainty at the level of one part in a thousand only. Then, after a brief description of GR tests and of the need for further tests of GR, I report some of its previous experimental verifications, and particularly those obtained with the laser-ranged satellites LARES 1, LAGEOS and LAGEOS 2 [5-7]. After the experimental verifications of frame-dragging and Earth's gravitomagnetism, I present a description of the theory of frame-dragging on gyroscopes and test-particles, and several miscellaneous effects due to frame-dragging, including some intriguing effects on the flow of time, clocks and electromagnetic waves, and including its effects inside a rotating massive sphere and its potential effects related to gravitational lensing. Finally, I describe the Chern-Simons theory which may explain Dark Energy, Quintessence and the accelerated expansion of the universe. This theory, which has been shown to be equivalent to a type of String theory, predicts a different frame-dragging effect than GR, I then finally describe on the constraints of Chern-Simons theory and of some other modified theories of gravity obtained with the LARES 2 satellite.