Unless Einstein is wrong, a black hole is defined by three properties: mass, spin, and electrical charge. The charge on a black hole should be close to zero because the matter absorbed by a black hole is electrically neutral. The mass of a black hole determines the size of its event horizon and can be measured in a number of ways, from the brightness of the material around it to the orbital motion of neighboring stars. The spin of a black hole is much more difficult to study.
How X-rays from a black hole tell us its spin. Photo credit: NASA / JPL-Caltech
The spin of a black hole is basically its rotation. Just as stars and planets rotate around their axes, so do black holes. The difference is that black holes do not have a physical surface like stars and planets. Black Hole Spin, like mass, is a space-time property. Spin determines how the space around a black hole warps. To measure the spin of a black hole, you need to study how nearby matter behaves.
The spin of some supermassive black holes was measured. With a couple of black holes active, we can examine the x-rays emitted by their accretion disks. X-ray light from the disk receives a boost of energy from the rotation, and by measuring this lift we can determine the spin. Another option is to take a direct picture of the black hole, as we did with the one in the center of M87. The ring of light we see is brighter on the side that turns towards us.
One side is lighter because of the spin of the black hole. Photo credit: EHT Collaboration
But we don't know the spin of the next supermassive black hole, the one in our own galaxy. Our black hole is not very active and much smaller than the one in M87. We cannot measure its spin by observing light in its vicinity. However, a new paper in Astrophysical Journal Letters argues that there is another way to measure spin.
Your method uses a property called frame dragging. When a mass rotates, it slightly rotates space around it. We know it's real because we measured the frame drag effect of the earth's rotation. The spin of a black hole creates the same type of frame dragging. By measuring, we can determine the spin of the black hole. We can't put a probe into orbit around the black hole like we did with Earth, but we can use the next best thing.
The S star cluster orbits the black hole in our galaxy. Photo credit: NCSA, UCLA / Keck
Hundreds of stars orbit the black hole in the center of our galaxy. About forty of them, known as S-stars, have orbits in close proximity to the black hole. Over time, their orbits are shifted by the frame drag effect. If we can measure these displacements, then we can measure the spin – the bigger the spin, the larger the orbit shift.
In this new work, the team examined the orbits of the S-stars and found no shift in image drag. Given how well we know the orbits of these stars, we know that the black hole at the center of our galaxy has to spin slowly. The team found that his spin can't be more than 0.1 on a scale of 0 to 1, which means he's spinning less than 10% of the maximum possible spin for a black hole. In contrast, the spin of the black hole of M87 is at least 0.4.
Reference: Fragione, Giacomo and Abraham Loeb. "An upper limit for the spin of SgrA * based on star orbits in its vicinity." The Astrophysical Journal Letters 901.2 (2020): L32.
Reference: Nemmen, Rodrigo. "The spin of M87 *." The Astrophysical Journal Letters 880.2 (2019): L26.