Black holes are objects so massive that nothing can escape from their gravitational pull. Suppose we have an sphere of mass $ M $, which we compress indefinitely. At what point will it become a black hole? From the special theory of relativity we know that the highest speed attainable is the speed of light $ c $. Hence, the criterion is that the escape velocity be greater then the speed of light.

$ \frac{G M}{R} > \frac{1}{2} c^2 $

$ R < R_s = \frac{2 G M}{c^2} $

where $ G $ is the universal constant of gravity. The critical radius is called Schwartzschild radius.

Once something has collapsed into a black hole, all of its previous attributes and properties disappear, except for three conserved quantities: mass, angular momentum and electric charge. For simplicity, we will consider a non rotating, neutral black hole, whose only property is mass. Since this is the only dimensional parameter, many attributes of such black holes can be obtained just with dimensional analysis.

All items (6)