Lense–Thirring precession

Lense–Thirring precession
Name	Lense–Thirring precession
Caption	Frame-dragging effect near a rotating mass
Discoverers	Josef Lense; Hans Thirring
Year	1918
Field	General relativity; Astrophysics

Lense–Thirring precession is a general relativistic frame-dragging effect predicted for a test particle orbiting a rotating massive body. It was derived by Josef Lense and Hans Thirring in 1918 and is relevant to precision tests of Albert Einstein's General relativity and to observations of compact objects such as Sun, Earth, Jupiter, Saturn, Neutron star, Black hole, and Supermassive black hole systems. The prediction connects to landmark experiments and missions including Gravity Probe B, LAGEOS, LARES, and observations of the accretion flows in Sagittarius A* and M87.

Introduction

Lense–Thirring precession arises when the angular momentum of a rotating mass drags spacetime, producing precession of gyroscopes and orbital nodes; this links to the theoretical framework developed by Albert Einstein and refined by Karl Schwarzschild and Roy Kerr. The effect appears alongside other post-Newtonian phenomena tested by experiments such as Perihelion precession of Mercury studies, Eddington's 1919 expedition, and modern satellite missions like GRACE and GOCE. It is central to interpretations of timing measurements from Pulsar binaries such as PSR B1913+16 and to imaging efforts by the Event Horizon Telescope consortium observing M87* and Sagittarius A*.

Theoretical background

Derived within the weak-field, slow-rotation approximation to General relativity, Lense–Thirring precession follows from the gravitomagnetic components of the linearized Einstein field equations developed in analogy with James Clerk Maxwell's electrodynamics. The original calculation by Josef Lense and Hans Thirring extended the Schwarzschild metric treatment to a rotating source and presaged the exact rotating solution found by Roy Kerr. Connections exist to conservation laws studied by Noether and to the post-Newtonian formalism advanced by researchers at institutions such as Princeton University, Cambridge University, and Max Planck Society. Frame-dragging effects are distinct from geodetic precession measured in the context of Lunar Laser Ranging and the Mercury perihelion problem investigated historically by Le Verrier and Urbain Le Verrier's contemporaries.

Mathematical formulation

In the weak-field limit the Lense–Thirring angular precession Ω_LT of an orbit or gyroscope is proportional to the central body's angular momentum J and inversely proportional to r^3, where r is the orbital radius; this analytic form is derived from the linearized metric perturbations introduced in the original Lense–Thirring papers and later formalized in the post-Newtonian expansions used by Chandrasekhar and Robert Dicke. Precise expressions employ tensorial language from Einstein field equations and make use of coordinate systems related to those used by Roy Kerr in the Kerr metric. Perturbative calculations have been performed by groups at MIT, Caltech, and Stanford University to connect Ω_LT to measurable quantities such as node drift and pericenter advance in satellite orbits and to predict frame-dragging timescales for Accretion disk precession around Black hole candidates in Active galactic nucleus models associated with Seyfert galaxy observations.

Observational evidence and experiments

Direct tests of frame-dragging include the gyro measurements of Gravity Probe B led by teams from Stanford University and NASA and laser-ranging analyses of the passive satellites LAGEOS and LARES pursued by research groups in Italy and at University of Maryland. Analyses of relativistic timing in binary pulsar systems such as PSR J0737−3039 and earlier work on PSR B1913+16 by Russell Hulse and Joseph Taylor provide indirect constraints on relativistic spin-orbit couplings. Very-long-baseline interferometry efforts by collaborations around Very Long Baseline Array and the Event Horizon Telescope have reported signatures consistent with frame-dragging influencing jet-launch regions in M87 and the vicinity of Sagittarius A*. Laboratory proposals and proposed missions from agencies such as European Space Agency and Roscosmos continue to refine measurement strategies and error budgets.

Astrophysical and practical implications

Lense–Thirring precession influences accretion disk alignment and the Bardeen–Petterson effect invoked in models of Quasar and X-ray binary behavior; researchers at Harvard University, University of Cambridge, and Institute for Advanced Study have modeled its role in jet collimation observed in Radio galaxy and Blazar systems. In compact-object astrophysics the effect affects spin evolution of Black hole binary mergers studied by collaborations such as LIGO Scientific Collaboration and Virgo Collaboration and interpreted using numerical relativity codes developed at Max Planck Institute for Gravitational Physics. On Earth, frame-dragging corrections matter for high-precision geodesy practiced by National Geospatial-Intelligence Agency and for orbit determination used by European Space Agency missions and by companies operating Global Positioning System constellations.

Measurement techniques and instrumentation

Key measurement techniques include spaceborne gyroscopes exemplified by Gravity Probe B, laser ranging to satellites like LAGEOS and LARES using networks coordinated by International Laser Ranging Service, and very-long-baseline interferometry observations by arrays such as Very Large Telescope and Atacama Large Millimeter/submillimeter Array contributing to Event Horizon Telescope imaging. Data analysis pipelines integrate models from Jet Propulsion Laboratory, relativistic ephemerides from Jet Propulsion Laboratory's DE series, and covariance studies developed at NASA and ESA centers. Future instrumentation proposals from Square Kilometre Array consortia and next-generation space interferometers envisage improved sensitivity to gravitomagnetic signatures in both Solar System and extragalactic settings.

Category:General relativity