Lense thirring effect

The Lense-Thirring-Effect , also called Frame-Dragging-Effect , is a physical effect predicted in 1918 by the mathematician Josef Lense and the physicist Hans Thirring , which results from the general theory of relativity . It falls into the class of gravitomagnetic effects. The Lense-Thirring-Effect describes the influence of a rotating mass on the local inertial system . In simplified terms, this can be imagined in such a way that the rotating mass pulls the space around it like a viscous liquid. This twists spacetime .

In the derivation by Thirring, the correspondence with Einstein (1917) played an important role and Einstein already calculated the effect within the framework of his predecessor theories for general relativity. The root of these considerations lies in Mach's principle , which Einstein saw implemented in it.

Experimental evidence

See also : The Lense-Thirring Effect as a test of general relativity

LOCATION

It is currently still being discussed whether the scientists led by Ignazio Ciufolini from the University of Lecce and Erricos Pavlis from the University of Maryland in Baltimore succeeded in proving the effect experimentally in 2004 . To do this, they precisely measured the orbits of the geodetic satellites LAGEOS  1 and 2 . Their position and location should be influenced by the rotating mass of the earth . The accuracy of the tests with the LAGEOS satellites is currently controversial, estimates range from 10% to 20–30% and even more. In 2013, G. Renzetti published a review article about attempts to measure the Lense-Thirring effect with earth satellites .

The two satellites were put into orbit in 1976 and 1992 in order to determine small effects on the earth's surface such as the drifting of the continents , post-glacial uplift processes and seasonal fluctuations in the earth's rotation . Their position can be measured with the help of reflected laser beams to an accuracy of 1 to 3 cm, so that the twisting of space-time can be determined quantitatively with the approximately 400 kg heavy earth satellite. According to the theoretical prediction of the general theory of relativity, the twisting angles of spacetime due to the rotating mass of the earth move at around 12 millionths of a degree or -39.2 milli- arcseconds per year. If the effect actually exists, the two satellites must follow the curved trajectories of twisted spacetime.

Despite possible sources of error due to the inconsistent gravitational field of the earth, the centimeter-precise position determinations of the LAGEOS satellites were sufficient in the opinion of the experimenters to be able to prove the relativistic effect.

Gravity Probe B

Another detection experiment was carried out between August 28, 2004 and August 14, 2005 using the NASA Gravity Probe B research satellite . In the opinion of the experimenters, this experiment has also succeeded in proving the Lense-Thirring effect in the meantime, despite an unexpected source of error. It soon became clear that the desired accuracy of 1% of the effect size had been missed by at least a factor of 2. The final evaluation resulted in a value that was up to 5% of the prediction. The most recent evaluations (April 2011) of the data again confirmed the effect.

LARES

In February 2012, the LARES mission started on board the first Vega rocket with the primary objective of finally confirming the effect. The mission was designed to run until 2016, but will continue beyond that. After evaluating the data of the first 3.5 years, the predictions of the general theory of relativity are confirmed with increased accuracy. The accuracy that can actually be achieved is controversial.

Effects

The Lense-Thirring-Effect is responsible for the enormous luminosity of quasars . It enables the plasma of the accretion disk , which falls into the mostly rotating black hole in the center of the quasar, to have a stable orbit just outside the Schwarzschild radius . As a result, the plasma can become hotter than with a non-rotating black hole and consequently radiate more strongly.

In addition, the magnetic fields twisted together with the plasma are probably responsible for the strong acceleration and focusing of the jets .

More precise formulation

Corotation of locally non-rotating measuring buoys sitting on a fixed r in the reference system of a distant observer who is stationary relative to the fixed stars.

The rotational angular velocity of the space around a rotating charged and central ground with the spin parameters and the electric charge resulting in Boyer-Lindquist coordinates with with ${\displaystyle \omega }$ ${\displaystyle a}$ ${\displaystyle Q}$ ${\displaystyle G=M=c=K=1}$

${\displaystyle \Omega ={\frac {{\rm {d}}\phi }{{\rm {d}}t}}=-{\frac {g_{t\phi }}{g_{\phi \phi }}}={\frac {a\left(2r-Q^{2}\right)}{\chi }}}$

with the terms

${\displaystyle \chi =\left(a^{2}+r^{2}\right)^{2}-a^{2}\ \sin ^{2}\theta \ \Delta }$

${\displaystyle \Sigma =r^{2}+a^{2}\ \cos ^{2}\theta }$

${\displaystyle \Delta =r^{2}-2\ r+a^{2}+Q^{2}}$

${\displaystyle t}$refers to the time coordinate of an observer at a great distance from the rotating mass. The angle denotes the degree of latitude with the zero point at the north pole, the Kerr's rotation parameter of the central mass, and the radial distance from the center of gravity of the same. ${\displaystyle \theta }$ ${\displaystyle a}$ ${\displaystyle r}$

The local speed with which a local observer would have to move against the vortex of spacetime in order to remain stationary relative to the distant observer is

${\displaystyle v_{\perp }=\omega \ {\bar {R}}\ \varsigma }$

With

${\displaystyle {\bar {R}}={\sqrt {|g_{\phi \phi }|}}={\sqrt {\frac {\chi }{\Sigma }}}\ \sin \theta }$

for the radius of gyration and

${\displaystyle \varsigma ={\frac {{\rm {d}}t}{{\rm {d}}\tau }}={\sqrt {|g^{tt}|}}={\sqrt {\frac {\chi }{\Delta \ \Sigma }}}}$

for gravitational time dilation, where the time coordinate of a corotating, but angular momentum-free observer on site denotes. ${\displaystyle \tau }$

A distant stationary observer, however, observes a transverse speed of

${\displaystyle u_{\perp }=\omega \ {\sqrt {x^{2}+y^{2}}}}$

on a locally stationary measuring buoy, whereby the Cartesian - and - values ​​are derived from the rule ${\displaystyle x}$ ${\displaystyle y}$

${\displaystyle x={\sqrt {r^{2}+a^{2}}}\sin \theta \ \cos \phi \ ,\ y={\sqrt {r^{2}+a^{2}}}\sin \theta \ \sin \phi \ ,\ z=r\cos \theta }$

surrender.

literature

• Remo Ruffini, Costantino Sigismondi: Nonlinear gravitodynamics - the Lense – Thirring effect; a documentary introduction to current research. World Scientific, Singapore 2003, ISBN 981-238-347-6 .
• Bernhard Wagner: Gravitoelectromagnetism and Lense-Thirring Effect. Dipl.-Arb. University of Graz, 2002.

See also

• Geodetic effect

Individual evidence

1. ↑ Josef Lense, Hans Thirring: About the influence of the self-rotation of the central body on the movement of the planets and moons according to Einstein's theory of gravity. In: Physikalische Zeitschrift. 19, 1918, pp. 156-163.
2. ^ Herbert Pfister, On the history of the so-called Lense-Thirring effect, General Relativity and Gravitation, Volume 39, 2007, pp. 1735-1748
3. ^ ^{A b} I. Ciufolini, A. Paolozzi, EC Pavlis, JC Ries, R. Koenig, RA Matzner, G. Sindoni, H. Neumayer: General Relativity and John Archibald Wheeler (=  Astrophysics and Space Science Library . Volume 367 ). SpringerLink, 2010, Gravitomagnetism and Its Measurement with Laser Ranging to the LAGEOS Satellites and GRACE Earth Gravity Models, p. 371-434 , doi : 10.1007 / 978-90-481-3735-0_17 .
4. ^ ^{A b} L. Iorio: An Assessment of the Systematic Uncertainty in Present and Future Tests of the Lense-Thirring Effect with Satellite Laser Ranging . In: Space Science Reviews . tape 148 , 2009, p. 363 , doi : 10.1007 / s11214-008-9478-1 , arxiv : 0809.1373 , bibcode : 2009SSRv..148..363I .
5. ↑ ^{a b} L. Iorio, HIM Lichtenegger, ML Ruggiero, C. Corda: Phenomenology of the Lense-Thirring effect in the solar system . In: Astrophysics and Space Science . tape 331 , no. 2 , 2011, p. 351 , doi : 10.1007 / s10509-010-0489-5 , arxiv : 1009.3225 , bibcode : 2011Ap & SS.331..351I .
6. ↑ L. Iorio, ML Ruggiero, C. Corda: Novel considerations about the error budget of the LAGEOS-based tests of frame-dragging with GRACE geopotential models . In: Acta Astronautica . tape 91 , no. 10-11 , 2013, pp. 141 , doi : 10.1016 / j.actaastro.2013.06.002 .
7. ^ G. Renzetti: History of the attempts to measure orbital frame-dragging with artificial satellites . In: Central European Journal of Physics . tape 11 , no. 5 , May 2013, p. 531-544 , doi : 10.2478 / s11534-013-0189-1 .
8. ↑ Stanford University Status Report on Gravity Probe B (Spring 2008)
9. ↑ CWF Everitt et al: Gravity Probe B: Final results of a space experiment to test general relativity. In: Physical Review Letters.
10. ↑ Earth bends spacetime like a ball a sheet. In: Welt online. May 6, 2011.
11. ↑ GP-B STATUS UPDATE - May 4, 2011 einstein.stanford.edu, accessed on May 13, 2011.
12. ↑ ASI website ( Memento of the original dated February 13, 2012 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. to the LARES mission 
13. ^ Herbert J. Kramer: Status of LARES mission. In: eoportal.org. Accessed February 4, 2018 . 
14. ↑ Ignazio Ciufolini et al .: A test of general relativity using the LARES and LAGEOS satellites and a GRACE Earth gravity model . In: Eur. Phys. J. C . tape 76 , no. 3 , 2016, p. 120 , doi : 10.1140 / epjc / s10052-016-3961-8 .
15. ↑ L. Iorio: Towards a 1% measurement of the Lense-Thirring effect with LARES? In: Advances in Space Research . tape 43 , no. 7 , 2009, p. 1148–1157 , doi : 10.1016 / j.asr.2008.10.016 , arxiv : 0802.2031 , bibcode : 2009AdSpR..43.1148I .
16. ↑ L. Iorio: Will the recently approved LARES mission be able to measure the Lense – Thirring effect at 1%? In: General Relativity and Gravitation . tape 41 , no. 8 , 2009, p. 1717–1724 , doi : 10.1007 / s10714-008-0742-1 , arxiv : 0803.3278 , bibcode : 2009GReGr..41.1717I .
17. ↑ Lorenzo Iorio: Recent Attempts to Measure the General Relativistic Lense-Thirring Effect with Natural and Artificial Bodies in the Solar System . In: PoS ISFTG . tape 017 , 2009, arxiv : 0905.0300 , bibcode : 2009isft.confE..17I .
18. ^ L. Iorio: On the impact of the atmospheric drag on the LARES mission . In: Acta Physica Polonica B . tape 41 , no. 4 , 2010, p. 753-765 ( edu.pl ).
19. ^ A. Paolozzi, I. Ciufolini, C. Vendittozzi: Engineering and scientific aspects of LARES satellite . In: Acta Astronautica . tape 69 , no. 3–4 , 2011, ISSN  0094-5765 , pp. 127-134 , doi : 10.1016 / j.actaastro.2011.03.005 .
20. ^ I. Ciufolini, A. Paolozzi, EC Pavlis, J. Ries, R. Koenig, G. Sindoni, H. Neumeyer: Testing Gravitational Physics with Satellite Laser Ranging . In: European Physical Journal Plus . tape 126 , no. 8 , 2011, p. 72 , doi : 10.1140 / epjp / i2011-11072-2 , bibcode : 2011EPJP..126 ... 72C .
21. ^ I. Ciufolini, EC Pavlis, A. Paolozzi, J. Ries, R. Koenig, R. Matzner, G. Sindoni, KH Neumayer: Phenomenology of the Lense-Thirring effect in the Solar System: Measurement of frame-dragging with laser ranged satellites . In: New Astronomy . tape 17 , no. 3 , August 3, 2011, p. 341–346 , doi : 10.1016 / j.newast.2011.08.003 , bibcode : 2012NewA ... 17..341C .
22. ↑ G. Renzetti: Are higher degree even zonals really harmful for the LARES / LAGEOS frame-dragging experiment? In: Canadian Journal of Physics . tape 90 , no. 9 , 2012, p. 883–888 , doi : 10.1139 / p2012-081 , bibcode : 2012CaJPh..90..883R .
23. ^ G. Renzetti: First results from LARES: An analysis . In: New Astronomy . tape 23-24 , 2013, pp. 63–66 , doi : 10.1016 / j.newast.2013.03.001 , bibcode : 2013NewA ... 23 ... 63R .
24. ^ Scott A. Hughes: Nearly horizon skimming orbits of Kerr black holes , page 5 ff.
25. ↑ Andrei & Valeri Frolov: Rigidly rotating ZAMO surfaces in the Kerr spacetime ( arxiv : 1408.6316v1 )