Relativistic Stars and the Schwarzschild Solution

The Singularity at r = 0
• The Schwarzschild solution and its Kruskal extension
appear to have a true singularity at r = 0. This
singularity is however hidden behind a horizon
(Penrose suggested the „Cosmic Censorship“ hypoth).
• To see that this is a true singularity, one must look at
quantities that are independent of the choice of
coordinates (Ricci scalar is not a suitable quantity,
since R = 0 !). One such important quantity is the
Kretschmann invariant, which is given by
R abcd R abcd = 48 r g ²/r 6