Everything about Frame Dragging totally explained
Albert Einstein's theory of
general relativity predicts that rotating bodies drag
spacetime around themselves in a phenomenon referred to as
frame-dragging. The rotational frame-dragging effect was first derived from the theory of general relativity in
1918 by the Austrian physicists
Joseph Lense and
Hans Thirring, and is also known as the
Lense-Thirring effect. Lense and Thirring predicted that the rotation of an object would alter space and time, dragging a nearby object out of position compared to the predictions of Newtonian physics. The predicted effect is incredibly small — about one part in a few trillion. In order to detect it, it's necessary to look at a very massive object, or build an instrument that's incredibly sensitive. More generally, the subject of field effects caused by moving matter is known as
gravitomagnetism.
Frame dragging effects
Rotational frame-dragging (the Lense-Thirring effect) appears in the
general principle of relativity and similar theories in the vicinity of rotating massive objects. Under the Lense-Thirring effect, the frame of reference in which a clock ticks the fastest is one which is rotating around the object as viewed by a distant observer. This also means that light traveling in the direction of rotation of the object will move around the object faster than light moving against the rotation as seen by a distant observer. It is now the best-known effect, partly thanks to the
Gravity Probe B experiment.
Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the "rotational" effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging (but see Einstein, 1921).
Static mass increase is a third effect noted by Einstein in the same paper. The effect is an increase in inertia of a body when other masses are placed nearby. While not strictly a frame dragging effect (the term frame dragging isn't used by Einstein), it's demonstrated by Einstein to derive from the same equation of general relativity. Again, a tiny effect difficult to confirm experimentally.
Experimental tests of frame-dragging
In 1976 Van Patten and Everitt proposed to implement a dedicated mission aimed to measure the Lense-Thirring node precession of a pair of counter-orbiting spacecraft to be placed in terrestrial polar orbits and endowed with drag-free apparatus. A somewhat equivalent, cheaper version of such an idea was put forth in 1986 by Ciufolini who proposed to launch a passive, geodetic satellite in an orbit identical to that of the LAGEOS satellite, launched in 1976, apart from the orbital planes which should have been displaced by 180 deg apart: the so-called butterfly configuration. The measurable quantity was, in this case, the sum of the nodes of LAGEOS and of the new spacecraft, later named LAGEOS III, LARES, WEBER-SAT. Although extensively studied by various groups, such an idea hasn't yet been implemented. The butterfly configuration would allow, in principle, to measure not only the sum of the nodes but also the difference of the perigees, although such Keplerian orbital elements are more affected by the non-gravitational perturbations like the direct solar radiation pressure: the use of the active, drag-free technology would be required. Other proposed approaches involved the use of a single satellite to be placed in near polar orbit of low altitude, but such a strategy has been shown to be unfeasible. In order to enhance the possibilities of being implemented, it has been recently claimed that LARES/WEBER-SAT would be able to measure the effects induced by the multidimensional braneworld model by Dvali, Gabadaze and Porrati and to improve by two orders of magnitude the present-day level of accuracy of the equivalence principle. Such claims have been shown to be highly unrealistic.
Limiting ourselves to the scenarios involving existing orbiting bodies, the first proposal to use the LAGEOS satellite and the Satellite Laser Ranging (
SLR) technique to measure the Lense-Thirring effect dates back to 1977-1978. Tests have started to be effectively performed by using the
LAGEOS and
LAGEOS II satellites in 1996, according to a strategy involving the use of a suitable combination of the nodes of both satellites and the perigee of
LAGEOS II. The latest tests with the
LAGEOS satellites have been performed in 2004-2006 by discarding the perigee of
LAGEOS II and using a linear combination involving only the nodes of both the spacecraft.
Although the predictions of general relativity are compatible with the experimental results, the realistic evaluation of the total error raised a debate. Another test of the Lense-Thirring effect in the gravitational field of Mars, performed by suitably interpreting the data of the Mars Global Surveyor (MGS) spacecraft, has been recently reported. Also such a test raised a debate. Attempts to detect the Lense-Thirring effect induced by the Sun's rotation on the orbits of the inner planets of the Solar System have been reported as well: the predictions of general relativity are compatible with the estimated corrections to the perihelia precessions, although the errors are still large. The system of the Galilean satellites of Jupiter was investigated as well, following the original suggestion by Lense and Thirring.
The
Gravity Probe B experiment is currently under way to experimentally measure another gravitomagnetic effect, for example the
Schiff precession of a gyroscope, to an expected 1% accuracy or better. Unfortunately, it seems that such an ambitious goal won't be achieved: indeed, first preliminary results released in April 2007 point toward a so far obtained accuracy of 256-128%, with the hope of reaching about 13% in December 2007.
A 1% measurement of the Lense-Thirring effect in the gravitational field of the Earth
could be obtained by launching at least two entirely new satellites, preferably endowed with active mechanisms of compensation of the non-gravitational forces, in rather eccentric orbits, as stated in 2005 by Iorio. Recently, the Italian Space Agency (ASI) has announced that the LARES satellite will be launched with a VEGA rocket at the end of 2008
(External Link
).
The goal of LARES is to measure the Lense-Thirring effect to 1%, but there are doubts that this can be achieved.
Recently, an indirect test of the gravitomagnetic interaction accurate to 0.1% has been reported by Murphy et al with the Lunar Laser Ranging (
LLR) technique, but Kopeikin questioned the ability of
LLR to be sensible to gravitomagnetism.
Astronomical evidence
Relativistic jets may provide evidence for the reality of frame-dragging.
Gravitomagnetic forces produced by the Lense-Thirring effect (frame dragging) within the
ergosphere of
rotating black holes combined with the energy extraction mechanism by Sir
Roger Penrose which describes the geometry of
spacetime in the vicinity of a mass
M rotating with
angular momentum J
»
where the purely temporal component
gtt of the metric changes sign from positive to negative. The space between these two surfaces is called the
ergosphere. A moving particle experiences a positive
proper time along its
worldline, its path through
spacetime. However, this is impossible within the ergosphere, where
gtt is negative, unless the particle is co-rotating with the interior mass
M with an angular speed at least of Ω. However, as seen above, frame-dragging occurs about every rotating mass and at every radius
r and colatitude θ, not only within the ergosphere.
Further Information
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