Lense-Thirring effect is the frame-dragging of spacetime caused by the rotation of a massive body, such as a black hole or planet.Austrian physicists Josef Lense and Hans Thirring in 1918, just three years after the creation of GR, found an exact solution for the weak field of a slowly rotating sphere. They showed that the spacetime metric acquires additional components that cause test bodies to precess. The gravitational field of a rotating object splits into a static part (like that of a Newtonian sphere) and a 'gravitomagnetic' part, producing forces similar to magnetic ones. Thus the concept of gravitomagnetism was born.
Josef Lense and Hans Thirring in 1918 first derived the formula for gyroscope precession in a rotating gravitational field from Einstein's equations. Their work 'Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie' laid the foundations of gravitomagnetism. For a long time, the effect remained unconfirmed due to its extreme smallness for planets. Only in 2004–2011 did the satellite missions Gravity Probe B and LAGEOS/LARES confirm the GR prediction with an accuracy of about 10%.
The effect is taken into account in high-precision satellite positioning (e.g., orbit corrections in GPS/GLONASS systems). For compact objects like neutron stars and black holes, frame-dragging can cause observable precession of accretion disks and jets. In strong fields, the weak-field approximation is inapplicable, and numerical solutions of the full Einstein equations are required.
The Lense–Thirring effect is accounted for in GPS navigation satellites and measured using high-precision gyroscopes like Gravity Probe B to test General Relativity.
The Lense–Thirring effect is so tiny that the gyroscopes of Gravity Probe B had to be the most spherical objects ever made by humans, with deviations from a perfect sphere of only 40 atomic layers.
| \Delta\Omega | variable | precession rate of orbital nodes — angular velocity radian per second |
| \chi | variable | dimensionless spin parameter of central body — dimensionless spin parameter |
| e | variable | orbital eccentricity — eccentricity |
| r_g | variable | gravitational radius of central body — length metre |
| a | variable | semi-major axis of orbit — length metre |












