Black hole mass

Question

It has been taught to us that since the black holes have finite mass, their gravitational force is also finite, which totally fits. The Black hole anyhow has a singularity at it's center which is infinitely dense. So if, there's a region inside the black hole having infinite density, how can the total mass of the Black hole be accurately determined?

Answer 1

The mass of a black hole can be determined in the same way as we determine the mass of any other astronomical object - by observing how it deflects the paths of other objects that pass close to it. These might be objects in closed elliptic orbits (like satellites around planets) or objects in hyperbolic trajectories that are just passing through.

For example, the orbits of several stars orbiting the compact radio source Sagittarius A* at the centre of the Milky Way have been observed over several years, and this gave an estimated mass for Sagittarius A* of 4.31±0.38 million solar masses (see Wikipedia's article on Sagittarius A*). Together with a maximum size estimate for Sagittarius A* (deduced from radio telescope observations), this mass estimate established beyond doubt that Sagittarius A* must be is probably a supermassive black hole.

We are not sure precisely what lies at the centre of a black hole - the prediction of a singularity is probably an indication that current physics just does not have an adequate model of what happens in such an extreme environment. But whatever the exact structure is, it does not affect what happens outside of the event horizon.