Testing Einstein’s equivalence principle near a supermassive black hole

Image of the Galactic Centre.
Credit: European Southern Observatory (ESO).

The GRAVITY Collaboration, a team of researchers at several renowned institutes including the Max Planck Institute, LESIA Paris Observatory and the European Southern Observatory, has recently tested part of the Einstein Equivalence Principle, namely the local positon invariance (LPI), near the galactic center supermassive black hole. Their study, published on Physics Review Letters (PRL), investigated the dependency of different atomic transitions on the gravitational potential in order to give an upper limit on LPI violations.

“General relativity and in general all metric theories of gravity are based on the  of inertial mass and gravitational mass, formalized in the Einstein ,” Maryam Habibi, one of the researchers who carried out the study, told Phys.org. “General relativity is the best theory of gravity that we have, however, there are still many unanswered puzzles that are closely tied to our incomplete understanding of gravity.”

The equivalence principle, a crucial part of Einstein’s general relativity theory, states that the  experienced in any small region of space-time is the same as the pseudo-force experienced by an observer in an accelerated frame of reference. Testing this principle is of key importance, as it could lead to interesting observations and broaden our current understanding of gravity.

“Einstein’s equivalence principle consists of three main principles,” Habibi explained. “One of them, called the local position invariance (LPI), states that non-gravitational measurements should be independent of the location in space time (characterized by gravitational potential) where they are carried out. The main part of our study focuses on testing the LPI principle.”

Past observations suggest that most, if not all, massive galaxies contain a supermassive black hole, which is typically located at the center of a galaxy. The mass of the Milky Way’s  supermassive black hole is 4 million times greater than that of the sun. It thus generates the strongest gravitational field in the galaxy, which makes it the ideal place to hunt for unexplored phenomena and test general relativity principles.

Star S2, one of the brightest stars in the Milky Way’s innermost region, has its closest encounter with the galactic center supermassive black hole at a distance of 16.3 light hours. In other words, the star takes 16 years to make a complete orbit around the black hole, which in astronomical time scales is extremely short. S2 moves in and out of the black hole’s gravitational field, hence the GRAVITY collaboration team decided to use it to test part of Einstein’s equivalence principle.

“As it was predicted, and we showed in a previous study published in June 2018, during the closest approach of the star S2 to the black hole we observe the ‘gravitational redshift’ in the light of the star,” Habibi explained. “Gravitational redshift occurs because intense gravity on the star’s surface slows the vibration of light waves, stretching them and making the star appear redder than normal from Earth.”

To test Einstein’s LPI principle, the researchers used two different types of atoms in S2’s stellar atmosphere: hydrogen and helium atoms. The LPI principle states that the gravitational redshift seen in a star that is flying in and out of a strong gravitational field only depends on the  and does not rely on other parameters, such as the internal structure of the atom.

“We measured the frequency change of light from these atoms moving through a varying potential,” Habibi said. “The vibration of light waves was measured by fitting the line-of-sight velocity of the S2’s spectrum using the Hydrogen and Helium spectral lines separately. By measuring the difference in frequency change for both atoms we were able to give an upper limit on the LPI violation during the pericenter passage. If there was an obvious violation of LPI, we should have measured very different vibration of light waves, from the helium and hydrogen lines.”

The equivalence principle and general relativity at large are merely theories, thus they need to be tested in order to ascertain their validity. So far, most researchers have carried out tests on Earth and in the solar system.

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