# New model predicts ‘yoyo’ orbits around black holes

Stars orbit black holes while jumping up and down. This is the prediction of a theoretical model developed by Leiden physicist Satish Kumar Saravanan, based on Einstein’s theory of relativity. He defends his PhD thesis on July 7th.

There are only a few certainties in life. One of them is that the sun always rises in the East and sets in the West. However, this won’t keep happening in 24-hour cycles forever. Because of friction, the Earth slightly slows its rotation every year. The law of preservation of angular momentum dictates that consequently the Moon must move away from the Earth. Think of a ballerina: if she spreads her arms, her body will rotate slower.

**Einstein**

We can describe the mechanics behind the Earth-Moon system with ‘Newtonian’ physics. If we move into more extreme territory, such as supermassive black holes with the mass of a million suns, we need Einstein’s theory of relativity. Heavenly bodies orbiting around them reach veloci ties close to the speed of light and the large black hole mass curves space dramatically. This leads to ‘relativistic’ effects which Newtonian physics cannot describe. Physicist Satish Kumar Saravanan has now for the first time done calculations for spinning bodies orbiting a black hole, starting from a full relativistic approach instead of using Newtonian formulas. He defends his PhD thesis in front of his supervisor Jan-Willem van Holten on July 7^{th} in Leiden.

**Black hole orbits**

In his theoretical study, Satish discovered different types of orbits of a rotating star around a non-rotating black hole. In a scenario where the star spins around its axis at a varying pace, its orbit will keep changing (see figure 1). We already see this in Mercury’s orbit around the Sun. Now, Satish has discovered that this irregular behavior in orbits is due to the relativistic effects of the fast rotating orbiting body.

In a more realistic scenario, the star has a spin precession, just like Earth; its tilted axis precesses like a spinning top toy. As a consequence, the star will move up and down during its orbit (see figure 2). The same actually happens with the Earth, but its velocity and the Sun’s mass are so low that this effect is negligible. In 1916, Willem de Sitter already predicted this for the Moon, but Satish has now found the same effect in systems with a rotating star around a black hole.

**eLISA**

Satish’ formulas will come in handy in 2034, when the eLISA space instrument will launch into an orbit around the Sun and measure gravitational waves from black hole systems. From these, researchers will deduce the orbits of objects around them, by using theoretical models like the one predicted by Satish. As black holes cannot be directly observed, this is a very useful tool for scientists.

*Figure 1: In a scenario where the star spins around its axis at a varying pace, its orbit will keep changing. *

*Figure 2: In a more realistic scenario, the star has a spin precession, just like Earth; its tilted axis precesses like a spinning top toy. As a consequence, the star will move up and down during its orbit. *