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Frame dragging is the phenomenon whereby a rotating mass drags the surrounding spacetime — and anything in it — in the direction of its rotation. The Lense-Thirring effect (1918) is the leading-order frame-dragging effect in linearized GR: a rotating mass with angular momentum J produces off-diagonal metric components g_{0i} proportional to the gravitomagnetic potential, analogous to the magnetic vector potential in electromagnetism. This causes precession of gyroscopes (geodetic + Lense-Thirring precession), dragging of orbital planes, and the impossibility of static observers near rotating black holes (the ergosphere). Frame dragging was experimentally confirmed by Gravity Probe B (2011), which measured the precession of gyroscopes in Earth orbit, and by LAGEOS satellite observations of orbital plane precession. It is the gravitational analog of the magnetic field: just as moving charges create magnetic fields, moving masses create gravitomagnetic fields.
In electromagnetism, a stationary charge creates an electric field, while a moving charge (current) creates a magnetic field. The gravitoelectromagnetic analogy in linearized GR draws a parallel: a stationary mass creates the Newtonian gravitational field (gravitoelectric field, encoded in g₀₀), while a rotating mass creates a gravitomagnetic field (encoded in the off-diagonal metric components g₀ᵢ). The gravitomagnetic field is the mathematical content of frame dragging: spacetime near a rotating mass is "twisted" in the direction of rotation, affecting the trajectories of particles, the orientation of gyroscopes, and the orbits of satellites.
The Lense-Thirring effect, predicted by Josef Lense and Hans Thirring in 1918, is the leading-order frame-dragging effect. For a slowly rotating body with angular momentum J, the gravitomagnetic vector potential is A_g ~ GJ×r/(c²r³), analogous to the magnetic vector potential of a magnetic dipole. This produces two observable effects on a gyroscope in orbit: Lense-Thirring precession (the gyroscope's spin axis precesses around the direction of J, at a rate proportional to GJ/(c²r³)) and a contribution to the orbital plane precession of satellites (the orbital angular momentum vector precesses, causing the orbital plane to slowly rotate). Both effects are extremely small for Earth — milliarcseconds per year — because Earth's gravitomagnetic field is weak (GJ_⊕/(c²R_⊕³) ~ 10⁻¹⁴ rad/s).
Gravity Probe B, launched in 2004, was specifically designed to measure these effects. The spacecraft carried four superconducting gyroscopes (niobium-coated quartz spheres, the most perfectly spherical objects ever manufactured) in a polar orbit around Earth. After years of data analysis to account for unexpected systematic effects, the results confirmed geodetic precession (6601.8 ± 18.3 mas/yr, predicted: 6606.1 mas/yr) and Lense-Thirring precession (37.2 ± 7.2 mas/yr, predicted: 39.2 mas/yr). The LAGEOS and LAGEOS II satellite laser-ranging experiments independently confirmed the Lense-Thirring orbital precession to about 10% precision by tracking the slow drift of the satellites' orbital planes.
Near rapidly rotating compact objects, frame dragging becomes dramatic. In the Kerr metric describing a rotating black hole, the ergosphere — the region between the outer horizon and the static limit surface — is where frame dragging is so strong that no observer can remain stationary relative to distant stars. All observers must co-rotate with the black hole, regardless of their rocket thrust. This extreme frame dragging also shifts the innermost stable circular orbit (ISCO) — prograde orbits (rotating with the black hole) can get closer than retrograde orbits, which affects the accretion efficiency and X-ray emission of matter spiraling into the black hole. Observing these differences through X-ray spectroscopy of accretion disks provides a way to measure black hole spin, complementing gravitational wave measurements. Frame dragging is thus not merely a theoretical curiosity: it is an observationally confirmed effect with practical astrophysical consequences.