# Tests of General Relativity

The galactic center with its supermassive Black Hole Sgr A* and its extreme gravitational potential offers a unique possibility to study effects of general relativity. We use the stars in close orbits around the black hole, especially S2, to find deviations from Newtonian gravity and test General Relativity in different ways.

## Measurement of gravitational redshift in the Galactic centre

Sagittarius A* (SgrA*), the massive black hole in the center of our galaxy is at a distance of 26'000 lightyears from Earth the closest of its kind and with an apparent Schwarzschild radius of 53µm the largest in the sky. It is surrounded by a cluster of high velocity stars called the S-stars whose trajectories are governed by the gravitational field of the black hole. We used the Very Large Telescope (VLT) instruments GRAVITY and SINFONI to follow the short (16y) orbit star S2/S-02 during its recent pericenter passage in may 2018, collecting astrometric and spectroscopic data, respectively. These joint data allowed for the first time a robust detection of the combined gravitational redshift and transverse Doppler effect on S2/S-02.

Gravitational redshift is one of the three classical tests of General Relativity. Einstein's theory predicts that due to gravitational time dilation a light beam gets stretched to longer wavelengths by a gravitational field. The change in the wavelength of light from S2/S-02 is inconsistent with Newtonian predictions and in excellent agreement with Einstein’s theory of general relativity. On a technological level, the success of this measurement with GRAVITY/VLT opens the door to an entirely new type of laboratory to probe and test the General Theory of Relativity: the Galactic Centre.

GRAVITY Collaboration, 2018A&A...615L..15G

**Einstein Equivalence Principle**

One of the cornerstones of general relativity is the Einstein Equivalence Principle. It consists of three parts: the weak equivalence principle, the local Lorentz invariance and the local position invariance. In Amorim et al 2019 we use the orbit of S2 to test the local position invariance (LPI), which states that the results of a non-gravitational experiment are independent of the position in spacetime.

The star S2 experiences very strong changes in gravitational potential on its eccentric orbit around the supermassive black hole Sgr A*. In the three years leading up to the pericenter passage of S2, the gravitational potential experienced by the star changes by four orders of magnitude, which makes it a unique probe and allows to test the LPI. This is possible by observing the redshift from two different atomic lines, Hydrogen and Helium. During the pericenter passage we did not detect a different behavior of the two absorption lines, which allows us to put a limit on violations of the LPI to below 5%. While current tests on Earth are much more restrictive on that limit, our test in the galactic centre laboratory, using stellar spectra and a supermassive black hole, charts a completely untested potential regime.

In an outlook we also show that with the next generation class of telescopes, such as the ELT, much more restrictive tests of the LPI and also the weak equivalence principle will be possible.

Amorim et al, (2019) PhysRevLett.122.101102

## What stellar orbit is needed to measure the spin of Sgr A* from astrometric data?

The spin of a black hole causes the entire spacetime in its vicinity to be dragged along with the black hole rotation. This frame-dragging, or Lens-Thirring effect is, however, a subtle quantity that affects the spacetime only in the immediate vicinity of the source of gravity. Therefore, in order to measure the spin of a black hole with stellar orbits, a star must have a trajectory that passes sufficiently close to the black hole. In the case of the Galactic centre massive black hole, Sgr A*, observed with GRAVITY/VLT, a star requires a certain combination of semi-major axis, aorb, and eccentricity, e, to enable a spin measurement based on a number of N observations within T years.

Spin measurement enabling stars are then expected on oribts with semimajor axes of a several hundred Schwarzschild radii. Using the current distributions of eccentricities and semimajor axes in the inner region of the Galactic centre, the estimated number of stars satisfying this conditions is about 0.12 for a 10y observing campain. Including radial velocity measurements with precision 50 km/s helps as this provides stronger constraints on the parameters and increases the number of expected stars by a factor of 2.

Waisberg et al. (2018) 2018MNRAS.476.3600W