When testing Einstein's theory of general relativity, small modeling errors add up fast

"Testing general relativity with catalogs of gravitational wave events is a very new area of research," says Christopher J. Moore, a lecturer at the School of Physics and Astronomy & Institute for Gravitational Wave Astronomy at the University of Birmingham in the United Kingdom and the lead author of the study. "This is one of the first studies to look in detail at the importance of theoretical model errors in this new type of test. While it is well known that errors in theoretical models need to be treated carefully when you are trying to test a theory, we were surprised by how quickly small model errors can accumulate when you start combining events together in catalogs."

In 1916, Einstein published his theory of general relativity, which explains how massive celestial objects warp the interconnected fabric of space and time, resulting in gravity. The theory predicts that violent outer space incidents such as black hole collisions disrupt space-time so severely that they produce ripples called gravitational waves, which zoom through space at the speed of light. Instruments such as LIGO and Virgo have now detected gravitational wave signals from dozens of merging black holes, which researchers have been using to put Einstein's theory to the test. So far, it has always passed. To push the theory even further, physicists are now testing it on catalogs of multiple grouped gravitational wave events.

"When I got interested in gravitational wave research, one of the main attractions was the possibility to do new and more stringent tests of general relativity," says Riccardo Buscicchio, a PhD student at the School of Physics and Astronomy & Institute for Gravitational Wave Astronomy and a co-author of the study. "The theory is fantastic and has already passed a hugely impressive array of other tests. But we know from other areas of physics that it can't be completely correct. Trying to find exactly where it fails is one of the most important questions in physics."

However, while larger gravitational wave catalogs could bring scientists closer to the answer in the near future, they also amplify the potential for errors. Since waveform models inevitably involve some approximations, simplifications, and modeling errors, models with a high degree of accuracy for individual events could prove misleading when applied to large catalogs.

To determine how waveform errors grow as catalog size increases, Moore and colleagues used simplified, linearized mock catalogs to perform large numbers of test calculations, which involved drawing signal-to-noise ratios, mismatch, and model error alignment angles for each gravitational wave event. The researchers found that the rate at which modeling errors accumulate depends on whether or not modeling errors tend to average out across many different catalog events, whether deviations have the same value for each event, and the distribution of waveform modeling errors across events.

"The next step will be for us to find ways to target these specific cases using more realistic but also more computationally expensive models," says Moore. "If we are ever to have confidence in the results of such tests, we must first have as a good an understanding as possible of the errors in our models."

This work was supported by a European Union H2020 ERC Starting Grant, the Leverhulme Trust, and the Royal Society.