Is spacetime disappearing at the center of a celestial body withmass?

If the matrix of spacetime is accelerating inwards from everywhere on
the circumference of a sphere with mass, shouldn't spacetime then
disappear at the center of the mass? If you have two individuals on
opposite sides of this planet, one on the north pole and another one
one the south pole. Both these individuals are accelerating towards
each other by 9.81 m/s2, but they don't get any closer to each other.
If spacetime didn't disappear at the center of the earth, wouldn't it
be impossible for these two individuals to accelerate towards each
other?