Gravitational waves allow us to test the General Theory of Relativity

Based on the latest research results from the LIGO / Virgo gravitational wave observatories, scientists conducted tests of General Relativity (GRT). Nine different methods were used to verify the consistency of Einstein’s theory with the observational data. No discrepancies were found. Polish scientists from the Polgraw group, including scientists from NCBJ, participated in the research.

The General Theory of Relativity, proposed over 100 years ago by Albert Einstein, is now the widely accepted theory of gravity. It is extremely elegant and conceptually simple, although the calculations made on its basis are not simple. The theory correctly describes the known astronomical phenomena driven by gravity, and is also the basis for the construction of cosmological scenarios. As research and observation progresses, along with the collection of larger, more and more accurate and more and more well-ordered data sets, the area of ​​phenomena available to us is constantly expanding. „In science, we do not treat any theory as a dogma” – explains Prof. Marek Biesiada from the NCBJ Astrophysics Department. „That is why we put the theories to the test, constantly checking their predictions. So far, GRT has been confirmed by very precise observations in the solar system and binary pulsar systems. Gravitational waves emitted by merging black holes provide another way to test the theory of relativity. It is a highly curved spacetime regime, previously poorly available for testing. "

There are at least two reasons for us to check whether the GRT requires modification or replacement with a new theory. The first is the cosmological problems known as dark matter and dark energy. The problem with dark matter is that galaxies and their clusters are attracting more than they should if all matter we know is included. The problem with dark energy is that the universe is accelerating its expansion, rather than slowing down as GRT seems to predict. While the working names dark matter and dark energy suggest an unknown material response, the possibility remains that the GRT needs modification. The second premise is the necessity of singularities, resulting from the GRT, i. e. areas where the stories of all particles and photons end. This problem seems to be related to the quantum theory of gravity, which could not be created in a satisfactory form. Here, too, the gravitational waves emitted by the confluent black holes can provide clues.

Research collaboration between LIGO and Virgo posted this week a summary of the analyzes of the data collected by them in terms of their compliance with the predictions of the GDA. The analyzes were grouped into 9 main groups constituting tests of the theory.

The first test concerned the compliance of the recorded base signal (noise) with the detector noise known from laboratory tests. From GRT we know how the signal from two compact objects should look like in gravitational wave detectors. However, what we use to describe a signal is a theory – how all science is some kind of approximation, the best we have, describing the world until we find a better one. If GRT did not describe such signals well enough, we would have theoretical prediction plus an additional component that arises from the effects that are not taken into account. To see if such an additional component was present, it had to be checked that, after subtracting the predicted signal, the remainder would have a normal noise characteristic in the detector. The conducted test confirmed the validity of the GRT.

A waveform compliance test was also carried out before and after the merging of two objects. The sources of gravitational waves that we observe are the following systems: two neutron stars; two black holes; black hole – neutron star system. The fusion event of these objects takes place in 3 main phases: the moment just before the collision, the moment of fusion and the stabilization phase. GRT predicts that the pre-impact and post-collision phases should generate similar waves. The GRT predictions are consistent with the observations for the analyzed sample. The next two tests concerned the behavior of the objects in the first phase of merging, when the celestial bodies circle one another.

Circumventing compact objects, such as black holes and neutron stars, approaching each other due to the loss of energy emitted in the form of gravitational waves, can be approximated by slowly moving a weak-field approximation – this is known as the post-Newtonian GRT approximation. This approach is described by several parameters, the determination of which on this basis can be compared with the parameters obtained by GRT. The newest observations, along with the existing ones, make it possible to very well define the limitations of these parameters. These results are statistically consistent with the GRT predictions.

The first phase, before the merging of the objects, also allows to check if the observed signal is consistent with the predictions of the merging of two rotating black holes (Kerr black holes). If any of the components (or both) rotates – the resulting object will be flattened at the poles and widened at the equator. Scientists are able to extract this information from observational data, thanks to which it can be determined that the source of gravitational waves is not any exotic, unforeseen by the GRT, objects.

A similar approach was used to determine the parameters of the event during and after the convergence of the objects. The duration of the fusion and stabilization of the new object is much shorter than the approach phase, so the observed signal is much stronger than the visible noise. The parameters estimated on this basis give values ​​statistically consistent with the predictions of GRT.

Another is the gravitational wave propagation test. According to the GRT predictions, gravitational waves are not dispersed, so the speed of their propagation does not depend on their frequency. GRT can be modified such that this property is not retained. In such a situation, waves originating directly from the merging of objects, with a higher frequency, would reach the observer faster than waves with a lower frequency – originating from the initial phase. No evidence of the dispersion of gravitational waves was found, which is in line with the predictions of GRT.

The lack of the observed dispersion allows us to limit the models of particle physics, which assume that the gravitons of the particles responsible for the gravitational interactions – have mass (the so-called heavy graviton model). In an GRT, gravitons should be massless and travel at the speed of light. However, heavy graviton models predict the existence of dispersion to some extent, so observations may give a limit to the mass of gravitons. In these tests, the mass of gravitons (if any) was determined to be less than 1.3*10^–23 eV/c².

The eighth test concerns the polarization of gravitational waves. Under GRT, gravitational waves can only have two types of polarization: plus-type or X-type. A more general theory can lead to up to six unique types of wave polarization. The data of both LIGO detectors and the Virgo detector were analyzed in terms of polarization, which the GRT does not take into account. The tests did not show any possible polarities other than those predicted by the GRT.

There are alternative theories to the existence of black holes. Such objects are called black hole mimics due to the fact that they have similar parameters to black holes, but they are not black holes in the sense of the GRT. One of the most distinctive features of black holes is the event horizon, an area from which nothing can escape – not even light. In the case of facial expressions, such a surface would have either partial or full reflectivity, which would cause some kind of echo in the signal from the third phase of fusing of objects. The analyzes did not show the existence of this type of echoes, which is in line with the predictions of the GRT.

Putting themselves in the position of opponents of the GRT, scientists conducted 9 tests that could prove the General Theory of Relativity in error. No evidence of non-compliance was found. The tests will certainly be continued, because this is the essence of scientific research. Any inconsistencies that may occur between the observations and the predictions of the GRT may result in the knowledge of new phenomena in the future.

„These are not all the tests that can be subjected to the theory of gravity thanks to the study of gravitational waves” – explains Dr Adam Zadrożny from the NCBJ Astrophysics Department, member of the Polish research group Polgraw. „A very interesting example was the measurement of the Hubble constant for the observations of gravitational waves GW170817 and the optical flare AT 2017gfo, which were the result of the same event. This was reported in the 2017 journal Nature (vol. 551, pp. 85–88). Measurement of the Hubble constant using data from gravitational wave detectors was consistent with results obtained by other methods. It is also worth adding that Prof. Andrzej Królak (IM PAN and NCBJ) together with Prof. Bernard F. Schutz (Cardiff University), in their work in the 1980 s, gave the basis for many methods of data analysis from interferometric detectors such as LIGO and Virgo. "

Poland has been part of the Virgo project since 2008. Polish participants of the project form the Polgraw group led by Prof. Andrzej Królak (IM PAN, NCBJ). The group participates both in the scientific research of the LIGO-Virgo-KAGRA (LVK) consortium and in the construction of the Virgo detector. Scientific research conducted by the Polgraw group as part of the LVK includes, among others, data analysis, development of statistical methods, modeling of gravitational wave sources and analysis of electromagnetic wave emissions accompanying the emission of gravitational waves. The Polgraw group consists of 12 institutions, including the Institute of Mathematics of the Polish Academy of Sciences, CAMK (Warsaw), Astronomical Observatory of the University of Warsaw, University of Zielona Góra, University of Białystok, NCBJ, University of Wrocław, CAMK (Toruń), Astronomical Observatory of the Jagiellonian University, AGH, ACK Cyfronet AGH, Centrum Theoretical Physics of the Polish Academy of Sciences. The LVK consortium includes NCBJ Prof. Andrzej Królak, dr Orest Dorosh, dr Adam Zadrożny and mgr Margherita Grespan. The work carried out at NCBJ concerns methods of detecting signals from rotating neutron stars, infrastructure enabling rapid detection of gravitational signals, and new methods of signal analysis and localization based on neural networks.