Question

When we look at simple models of gravitational collapse for spherically symmetric matter distribution (such as Oppenheimer-Snyder) we always exploit the fact that the solution to the Einstein field equations just outside any spherically symmetric collapsing matter is Schwarzschild and that this is the only possible solution. This is thanks to Birkhoff's theorem. An analogous theorem exists also for charged matter.

Unfortunately, no such theorem exists for rotating matter, as the spherical symmetry is broken. This means that we can't approach the gravitational collapse of rotating matter the same way we would for spherically symmetric charged or uncharged matter collapse.

So how do theorists actually study rotating black holes? Do we need some sort of computational or numerical methods?

Answer 1

Theoretical astrophysicists study rotating black holes through a combination of the Kerr solution, computational methods, and numerical relativity simulations, with gravitational wave observations offering indirect evidence of these phenomena.

Step-by-step explanation:

Studying Rotating Black Holes

To study rotating black holes, theorists must use a combination of analytical and numerical techniques due to the lack of an analog to Birkhoff's theorem in the realm of spherical symmetry broken by rotation. Theories such as the Kerr solution of the Einstein field equations provide some analytical insights into the rotating black holes, known as Kerr black holes. However, to accurately model more complex situations, computational and numerical methods, including those used in numerical relativity, are necessary. These simulations are crucial for understanding the dynamics of gravitational collapse in rotating bodies and predicting the gravitational waves emitted during such events, which can now be detected by observatories such as LIGO and Virgo.

To model the gravitational collapse of rotating matter, astrophysicists must therefore address the complexities introduced by rotation, which can dramatically alter the collapse dynamics and the resulting spacetime structure around the collapsed object. Observations of gravitational waves provide indirect evidence supporting the existence of rotating black holes, as these waves are predicted by the general theory of relativity and can carry information about their sources, including black holes and their properties.