Could the universe be shrinking? It is thought the universe is expanding because of the red shift of most galaxies but if all the matter in the universe was actually falling into a massive black hole wouldn't most galaxies still be red shifted because the black hole would accelerate every galaxy and every galaxy that was nearer the black hole would be accelerating away from us and we would be accelerating away from any galaxy that was further from the black hole than us. There must be something wrong with this thought can you tell me what it is? 
 A: The red shift is in all galaxies regardless of direction.  If the galaxies were falling into a black hole the red shift would happen, but considering the fact that all of them are red shifted, and all are moving away from us, the black hole would need to have the structure of a spherical shell of enormous radius or there would need to be a large number of them farther away than we can see.
Let's consider the second possibility first.  If there was more than one, we could detect this because we would see lateral movement of galaxies as they move toward them.  This is not seen in the data.  For the first possibility, if there was possible to create a black hole as a sphere, we would not feel its effects.  This is because inside a spherical shell of mass, the sum of the gravity is zero.  So that would not work either.
A: The universe as a black hole would have observable consequences. The Schwarzschild metric
$$
ds^2~=~c^2(1~-~2m/r)dt^2~-~(1~-~2m/r)^{-1}dr^2~-~r^2d\Omega^2
$$
defines the curvature of spacetime. Here we have $m~=~GM/c^2$. The Riemann curvature tensor components to $O(c^2)$ are
$$
R_{trtr}~=~-\frac{2mc^2}{r^3},~R_{t\theta t\theta}~=~\frac{mc^2(r~-~2m)}{r^2},~R_{t\phi t\phi}~=~\frac{mc^2(r~-~2m)sin^2\theta}{r^2}.
$$
There are the components $R_{r\theta r\theta}$, $R_{r\phi r\phi}$ and $R_{\theta\phi\theta\phi}$, but these are less than the three above by a factor $1/c^2$. These enter into the geodesic deviation equation
$$
\frac{d^2x^\mu}{ds^2}~+~{R^\mu}_{\alpha\nu\beta}U^\alpha x^\nu U^\beta~=~0
$$
which determine the separation rate of two test masses separated by the vector $\bf x$ with components $x^\nu$. For test masses separated by a radial distance $x^r~=~r$. Some thought illustrates that the radial distance between the two test masses increases. Similarly the distance defined by the angles $\theta$ and $\phi$ decreases.
From a more physical perspective this is the tidal force. The Riemann tensor above determines the tidal force on an extended mass, or the acceleration between test masses. Below a diagram illustrates the motion of a spherical or ellipsoidal shell of test masses as it falls radially to a black hole. In the extreme situation this leads to the so called spagettification of any extended system of masses.
If the universe were a black hole the optical signature of this would be that a set of galaxies at antipodal regions of the sky would be redshifted. They would be accelerating away for an observer. There would also be a set of galaxies arrayed on a plane or annular region of the sky that would be more blue shifted and approaching any observer. Very clearly we do not observe the universe to be of this character.

