Gravitational wave

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A gravitational wave is a wave in spacetime that is triggered by an accelerated mass. The term itself was first coined by Henri Poincaré in 1905. According to the theory of relativity , nothing can move faster than the speed of light . Local changes in the gravitational field can therefore only affect distant places after a finite time. From this, Albert Einstein concluded the existence of gravitational waves in 1916. When walking through an area of ​​space , they temporarily compress and stretch distanceswithin the space area. This can be seen as the compression and expansion of the space itself.

Since changes in the sources of the gravitational field affect the entire space without delay in Newton's theory of gravitation , it knows no gravitational waves.

On February 11, 2016, researchers from the LIGO collaboration reported on the first successful direct measurement of gravitational waves in September 2015 that were generated when two black holes collided . It is considered a milestone in the history of astronomy . In 2017 Rainer Weiss , Barry Barish and Kip Thorne were awarded the Nobel Prize in Physics for “decisive contributions to the LIGO detector and the observation of gravitational waves” .

General properties - comparison with electromagnetic waves

A ring of test particles under the influence of a gravitational wave

Generation and speed of propagation

According to the general theory of relativity, changes in the gravitational field do not act instantaneously in the whole space, as is assumed in Newtonian celestial mechanics , but spread at the speed of light (see also aberration of gravitation ). According to this, gravitational waves are generated by every system of accelerated masses (e.g. a binary star system or a planet orbiting the sun), similar to how accelerated electrical charges emit electromagnetic waves . Due to the Birkhoff theorem , a spherically symmetrically oscillating mass distribution does not emit any gravitational waves (also analogous to electrodynamics ).

Dipole and quadrupole waves

The mass is the charge of gravity. In contrast to the electrical charge , no negative mass is known and is currently only discussed in the context of hypotheses (especially as exotic matter ). So there are no dipoles of masses. However, there can be no dipole radiation without dipoles and without movements caused by external forces .

However, accelerated masses lead to quadrupole radiation , the calculation of which is based on electrical quadrupoles. Thus, the quadrupole is proportional to the mass and the square of the distance : . A mass that rotates but is not rotationally symmetrical also radiates.

Using the example of two neutron stars, each 1.4 times the solar mass, orbiting each other at a distance of 150 million km (approximately one astronomical unit , mean distance from earth to sun), the radiation can only  be calculated in the form of gravitational waves of 10 14 W. Because in this constellation, as a double star, the distance enters the radiated power with the 5th power, the radiant power of the sun (4 · 10 26  W electromagnetic radiation) would be reached in the form of gravitational waves at a distance of only 500,000 km . In this example, the power emitted in the form of gravitational waves would increase to 10 48  W until the neutron stars touched .

Radiation and calibration bosons

Gravitational waves can be described mathematically as fluctuations in the metric tensor , a second-order tensor . The multipole expansion of the gravitational field, for example, of two stars orbiting one another, contains quadrupole radiation as the lowest order .

From a quantum field theoretical perspective, the standard gravitational wave assigned to the calibration boson , the (hypothetical) graviton , is obtained as a spin- 2 particle analogous to the spin-1 photon in quantum electrodynamics . However, a consistent quantum field theoretical formulation of gravitation on all scales has not yet been achieved.

Wave type

Two-dimensional observation of gravitational waves, which are emitted by two orbiting neutron stars

Gravitational waves are analogous to electromagnetic waves, transverse waves . From the point of view of a local observer, they seem to compress and stretch space-time perpendicular to their direction of propagation. They also have two polarization states . They also have dispersion .

Mathematical description

Unlike for electromagnetic waves - which result from the linear Maxwell equations - a wave equation for gravitational waves can no longer be derived exactly . For this reason the superposition principle cannot be used either. Instead, Einstein's field equations apply to gravitational waves . In many cases, only approximate solutions can be determined for these using linear differential equations , e.g. B. the wave equation as an approximation for small amplitudes . Since the assumption of small amplitudes at the point of origin of the wave is generally not allowed, it becomes very difficult to calculate the radiation of gravitational waves, which would be necessary for predictions about the measurability of the waves and the shape of the signals.

The non-linearity of the gravitational waves makes it possible to represent them as solitary wave packets.


Gravitational wave spectrum (overview)
Designation of the frequency range frequency wavelength Detection
beyond the Hubble frequency band 0 Hz 10 -18  Hz 3 · 10 26  m Verification of inflationary / primordial cosmological models
Extremely Low Frequency (Hubble Band) 10 -18  Hz 10 -14  Hz 3 · 10 22  m 3 · 10 26  m Experiments with cosmic background radiation
Ultra Low Frequency (ULF) 10 -14  Hz 3 · 10 −10  Hz 10 18  m 3 · 10 22  m Astrometry of the proper motion of quasars , Milanković cycles
Very Low Frequency (VLF) 3 · 10 −10  Hz 10 −7  Hz 3 · 10 15  m 10 18  m Pulsar timing arrays
Low Frequency (Millihertz band) 10 −7  Hz 10 −1  Hz 3 · 10 9  m 3 · 10 15  m Space-based laser interferometry, arm length> 60,000 km
Medium frequency band 10 −1  Hz 10 1  Hz 3 · 10 7  m 3 · 10 9  m Space-based laser interferometry, arm length 1,000–60,000 km
High frequency band (audio) 10 1  Hz 10 5  Hz 3 · 10 3  m 3 · 10 7  m Low temperature resonators, earth-based laser interferometry
Very high frequency band 10 5  Hz 10 12  Hz 3 · 10 −4  m 3 · 10 3  m Microwave resonator / waveguide detectors, laser interferometry and Gaussian beam detector
Ultra high frequency band 10 12  Hz 0 m 3 · 10 −4  m Terahertz resonators, optical resonators and magnetic field conversion detector

Thus the gravitational wave spectrum differs from the spectrum of visible light. Since on the one hand only emitting objects can be recorded with telescopes and on the other hand approx. 99 percent of all matter does not emit any radiation, gravitational waves open up a possibility for the detection of dark matter .

Sources of gravitational waves

Sources of gravitational waves with frequency and suitable detectors

In general, accelerated masses generate gravitational waves, or more generally: any change in the distribution of mass and / or energy in the universe in which at least the quadrupole moment varies over time. The strength of the gravitational waves depends on the moving mass and, to an even greater extent, on its change in speed (amount and direction). They are strongest and therefore most likely to be observed in the case of very massive, very strongly accelerated astronomical objects. these are

  • objects quickly circling each other
  • fast rotating objects that are not rotationally symmetrical,
  • Objects that rapidly collapse or expand asymmetrically (not spherically symmetrically).

Compact objects that circle and merge with each other

Orbiting objects emit gravitational waves. The orbit of the earth around the sun generates gravitational waves with a power of almost 200 W, which is why the influence of this effect on the earth's orbit cannot be measured. It would take about 10 18 (one trillion ) years to radiate only a millionth of the kinetic energy of this movement .

  • Planck performance
  • Quadrupole moment , same here
  • Moment of inertia
  • moved point mass, here: mass of the earth
  • Radius of the orbit, here: 1  AU

For an effect worth mentioning, the objects must have masses of stars, but must be much more compact than ordinary stars and move very closely and therefore very quickly around one another. Suitable: neutron stars or black holes. This effect was indirectly demonstrated for the first time with the double pulsar PSR 1913 + 16 . The measurements fit exactly with the predictions of general relativity. Due to the radiated gravitational waves, the two neutron stars in this system approach each other by 3.5 m and will merge in approx. 300 million years.

Shortly before such objects merge, the orbital speed and thus the frequency and strength of the gravitational waves increases dramatically. The first directly detected gravitational wave signal GW150914 came from the last hundredths of a second before two black holes merged. In the event GW170817 , two neutron stars merged.


Pulsars are neutron stars that have a strong magnetic field and rotate around their own axis at up to 500 revolutions per second. If these pulsars show asymmetries in their mass distribution (e.g. due to a small elevation on their surface), they cause a gravitational wave that is constant in frequency and amplitude. No such sources have yet been discovered.


Supernovae are exploding stars. They arise during the thermonuclear explosion of a white dwarf ( supernova type Ia ) or during the gravitational collapse of a very massive star (supernova type Ib, Ic, II). In this explosion, a considerable part of the star's mass can be thrown away at great speed (up to 10% of the speed of light). When this explosion occurs asymmetrically, gravitational radiation is generated.

Gravitational wave background radiation

Many models of the universe predict strong gravitational waves that arose shortly after the Big Bang . Due to the cosmic expansion, their frequency would meanwhile be very small. With detection of these gravitational waves one could look much further into the past of the universe than is possible with the cosmic microwave background radiation . The eLISA detector, originally planned for 2019 , may be able to detect this. After NASA left, the future of the project was uncertain. The follow-up project NGO (New Gravitational Wave Observatory) was postponed in 2012 by the European Space Agency ESA in favor of the JUICE mission , the aim of which is to explore the moons of Jupiter. In 2013 the project was included in the further planning of the ESA as an L3 mission under the topic "The Gravitational Universe". The start is planned for 2034.

Experimental evidence

The effects of gravitational waves are so small that it will not be possible for the foreseeable future to detect artificially generated gravitational waves, so that they can only be detected with astronomical events.

signal modeled unmodeled
continuously pulsar Background
transient Fusion of
compact objects

When searching for gravitational waves, a distinction is made between (quasi-) continuous and short-term ( transient ) events as well as between modeled events (predicted by theoretical calculations) and unmodeled events.

Direct evidence

First try

In 1958, Joseph Weber tried at the University of Maryland to detect gravitational waves with the help of resonance detectors : A massive aluminum cylinder (length 1.8 m, diameter 1 m, mass 3.3 t) was suspended from wires without vibration. To reduce disturbances (air molecules, own heat oscillations), the cylinder was cooled in a vacuum . Piezo crystals attached to the outside were able to detect relative changes in length of the cylinder of 1:10 16 , i. H. 1/100 of an atomic nucleus diameter. In order to be able to differentiate between local disturbances, a similar apparatus was set up 1000 km away; Simultaneous vibration phenomena on both cylinders would indicate gravitational waves. A vibration observed in the late 1960s could have been triggered by gravitational waves from the center of the Milky Way . More advanced detectors later consisted of niobium cylinders that were cooled down to a few Kelvin ; the sensitivity was increased to 1:10 19 . Five of these detectors in Geneva , Louisiana , Western Australia , Maryland and Stanford were interconnected.

These methods have not yet been able to provide clear evidence. A disadvantage of this technology is that the cylinders are only sufficiently sensitive in a very narrow range of their resonance frequency and only for very strong gravitational waves. For this reason, other ways of detecting these waves were turned to.


Schematic representation of an interferometer

Today, Michelson interferometers are used to observe waves traveling through them in real time by changing the local changes in the space-time properties of the sensitive interference between two laser beams . Current experiments of this kind such as GEO600 (Germany / Great Britain), VIRGO (Italy), TAMA 300 (Japan) and LIGO (USA) use light beams that travel back and forth in long tunnels. A difference in the length of the running distance, as it would be caused by a passing gravitational wave, could be detected by interference with a control light beam. In order to detect a gravitational wave directly in this way, minimal changes in length in relation to the total length of the measuring apparatus - about 1 / 10,000 of the diameter of a proton  - must be determined. More precise measurements at greater distances should be made between satellites . The LISA experiment planned for this purpose was abandoned by NASA in 2011 for cost reasons, but it may be implemented on a smaller scale by ESA . In July 2014, the University of Tokyo presented its KAGRA (Kamioka Gravitational Wave Detector) project in Hiba, which has been carrying out its first observations since February 2020. The experimental setup is similar to the one previously used in the USA and Europe, but is 10 times more sensitive, corresponding to 1000 times the volume.

The simulation shows two black holes orbiting each other and finally merging. This creates gravitational waves with increasing frequency that are radiated outwards.

First evidence

LIGO measurement of gravitational waves

On February 11, 2016, scientists announced the first direct detection of gravitational waves from the ongoing LIGO experiment. The event was observed on September 14, 2015 almost simultaneously with a 7 ms difference in the two LIGO observatories in the USA. Extensive statistical analyzes were carried out. One of the findings is that the result with more than five times the standard deviation is significant and unambiguous. The measurable event lasted 0.2 seconds. The shape of the signal was of a characteristic shape, like a wavelet , which confirmed predictions from numerical simulations of the collision of two black holes. It was a sine wave of 10 to 15 cycles, the amplitude of which increased to a maximum and then subsided at a constant frequency. The signal frequency before the collision was proportional to the monotonically increasing orbital frequency of the two black holes approaching each other and (most recently at almost the speed of light) orbiting each other, so that the frequency rose to a constant value. The amplitude was proportional to the orbital velocity of the black holes until the collision. The event took place 1.3 billion light years (410 megaparsecs ) apart  . Two black holes of around 29 and 36 solar masses orbited each other and merged to form a black hole of 62 solar masses, 3 solar masses of energy were radiated in the form of gravitational waves. The event was named GW150914 . Before that, it was not even known with certainty whether stellar black holes existed with 20 or more solar masses. The signal was so intense (contrary to expectations it could also be seen "with the naked eye" in the data) that it was also possible to test whether deviations from the general theory of relativity existed, which was not the case. The detection of another gravitational wave event on December 26, 2015, named GW151226 , was announced on June 15, 2016. Here, too, two black holes, one of 8 and one of 14 solar masses, merged to form a black hole of 21 solar masses, whereby 1 solar mass of energy was radiated. The next gravitational wave event detected by LIGO was GW170104 on January 4th, 2017. The black holes with 20 and 30 solar masses were about 3 billion light years away, the released energy corresponded to about 2 solar masses. In August 2017, such a wave (GW170814) was detected for the first time with three detectors (apart from the two Ligo and the Italian Virgo detector), so that the direction of the triggering event could be assigned to the constellation Eridanus using methods corresponding to classic triangulation .

A different signal, GW170817 , was registered on August 17, 2017 by the same three detectors (two Ligo and Virgo). It is interpreted as the merging of two neutron stars that had previously orbited each other on increasingly narrowing spiral orbits. With a duration of around 100 seconds, the signal was much longer than the previously observed signals from the merging of black holes. The two objects were likely in the mass range between 1.1 and 1.6 solar masses (the total mass was about 2.7 solar masses). At almost the same time, the Fermi Gamma-ray Space Telescope (FGST) registered a short gamma-ray flash (GRB 170817A), which is assigned to the same event. Since the gamma-ray burst occurred only 1.7 seconds after the end of the gravitational signal, it has been proven that the speed of gravitational waves differs from that of light by at most a tiny amount. This excludes certain theories of gravitation that are alternative to general relativity. Thanks to the good directional resolution of the FGST, the source could also be optically identified and observed, initially from the Las Campanas Observatory in Chile. It is located in the galaxy NGC 4993, 130 million light years away. Observations in the infrared, ultraviolet and X-ray range followed (the afterglow is known as the kilonova ). In the aftermath of the collision, heavy elements such as gold, platinum and uranium were identified, and many questions remain about their formation. The observation also provides new insights into the structure of neutron stars. GW170817 was the first simultaneous observation of an electromagnetic and a gravitational signal from the same source and thus opened a new chapter in observational astronomy. It also enables the Hubble constant to be determined independently by observing gravitational waves. The obtained value of H = 70.0 agrees well with the value from redshifts. Furthermore, there were new bounds for a possible violation of the Lorentz invariance . It was the gravitational wave signal with the closest source so far (about 70 times the distance from the Andromeda Galaxy), and the observation also provided the first connection between the previously puzzling gamma-ray bursts and the merging of neutron stars.

In 2017, a merger of black holes was detected for the fifth time under the designation GW170608. A total of ten gravitational waves from the merging of black holes and one more from the merging of two neutron stars had been detected by 2018. In order to significantly increase the number of such events detected annually from 2019, the sensitivity of the LIGO and VIRGO detectors was technically improved based on the model of the GEO600 detector using squeezed light .

Indirect evidence

Russell Hulse and Joseph Taylor from Princeton University succeeded in indirectly detecting gravitational waves . The two physicists were able to multi-year observation of the 1974 discovered double pulsars 1913 + 16 PSR prove that the orbits of the system are getting closer to each other orbiting masses over time and the system therefore loses energy. The observed energy losses corresponded with an accuracy of one percent to the radiation from gravitational waves expected from theoretical considerations. Hulse and Taylor were awarded the 1993 Nobel Prize in Physics for their discovery .

In the case of the binary (double) black hole in quasar OJ 287 , the same effect could be observed many times more strongly in September 2007.

The white dwarfs J065133.338 and 284423.37 (with about 0.26 and about 0.5 solar masses) orbit each other in about 12.75 minutes on a very narrow orbit. The system has been monitored since April 2011. Their orbital time decreases by 310 microseconds per year. The decrease is in very good agreement with the prediction of general relativity and will accelerate more and more.

In the binary star system consisting of the pulsar PSR J0348 + 0432 ( neutron star with about 2.0 solar masses and about 20 km diameter) and a white dwarf (about 0.17 solar masses and about R = 0.065  R , which corresponds to a diameter of 90,000 km) the two stars orbit each other in about 2.46 hours on a very narrow orbit, their distance is about 830,000 km. The masses were determined by measuring the changes in the light curve of the white dwarf on the Very Large Telescope , and the period of rotation was measured with the help of the radio telescopes in Effelsberg and Arecibo since April 2011. Their orbital period decreases by 8.6 microseconds per year, which is in very good agreement with the prediction of gravitational wave radiation in general relativity.

On March 17, 2014, US scientists from the Harvard-Smithsonian Center for Astrophysics published results according to which they observed a signal for the first time that was related to the influence of gravitational waves using the BICEP 2 telescope to measure the cosmic microwave background radiation at the Amundsen-Scott South Pole Station would indicate cosmic inflation shortly after the Big Bang around 14 billion years ago. However, this statement did not stand up to an extended analysis that also includes the measurement results of the Planck space telescope . According to this, the galactic dust contributes so much to the observed polarization that an effect of any gravitational waves next to it could not be detected with the measurement setup at that time (for more details see under BICEP ).


The German post office brought in 2017 a stamp gravitational waves to 0.70 € out.



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  • Rüdiger Vaas: Signals from gravity. Gravitational Waves: From Einstein's Insights to the New Era of Astrophysics. Franckh-Kosmos-Verlag, Stuttgart 2017. ISBN 978-3-440-15957-6 , incl. 4th signal and Nobel Prize in Physics 2017.
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  • Lucien F. Trueb: The Difficult Search for Gravitational Waves. Naturwissenschaftliche Rundschau 58 (11), pp. 573-580 (2005), ISSN  0028-1050 .
  • Peter Aufmuth: On the threshold of gravitational wave astronomy. Stars and Space 46 (1), pp. 26-32 (2007), ISSN  0039-1263 .
  • Stanislav Babak, Michael Jasiulek, Bernard F. Protection: Fishing for gravitational waves . Research report at the Max Planck Institute for Gravitational Physics, 2013.
  • Uwe Reichert: A new era in astrophysics. The age of gravitational wave astronomy has begun. Stars and Space 55 (4), pp. 24-35 (2016), ISSN  0039-1263 .

Web links

Wiktionary: Gravitational wave  - explanations of meanings, word origins, synonyms, translations
Commons : Gravitational Waves  - Collection of Images, Videos, and Audio Files

Individual evidence

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