Notes on Relativity and Cosmology - Physics Department, UCSB

252 CHAPTER 9. BLACK HOLES
the first picture I showed you (above) of the black hole spacetime and also on
the diagrams below. Note that they do not move at all outward toward larger
values of r. These are the horizons of the black hole.
Another thing we can see from these diagrams is the symmetry we discussed.
The symmetry of the 2-D black hole spacetime is the same as the boost symmetry
of the larger 3D Minkowski space. Inside the black hole, this symmetry
moves events in a spacelike direction. We can also see from this picture that,
inside the black hole, the spacetime does change with time.
9.4 Stretching and Squishing: Tidal effects in
General Relativity
We have now seen several manifestations of what are called ‘tidal effects’ in
general relativity, where gravity by itself causes the stretching or squashing of
an object. We discussed these a lot in homework problems 1 and 2, but even
earlier our most basic observation in general relativity was that gravity causes
freely falling observers to accelerate relative to each other. That is to say that,
on a spacetime diagram, freely falling worldlines may bend toward each other or
bend away. In problem 1 and 2 I asked how you thought this effects the ocean
around the earth as the earth falls freely around the moon. The answer was