The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Landmark Science)

by Roger Penrose

The above considerations are ‘local’. However, if one is allowed to make (not quite local) measurements of sufficient precision, one may, in principle, ascertain a difference between a ‘true’ gravitational field and a pure acceleration. In Fig. 5.25 I have shown, a little exaggerated, how an initially stationary spherical arrangement of particles, falling freely under the earth’s gravity, would begin to be affected by the non-uniformity of the (Newtonian) gravitational field. The field is non-uniform on two accounts. First, because the centre of the earth lies some finite distance away, particles nearer to the earth’s surface will accelerate downwards faster than those which are higher up (recall Newton’s inverse square law). Second, for the same reason, there will be slight differences in the direction of this acceleration, for different horizontal displacements of the particles. Because of this non-uniformity, the spherical shape begins to distort slightly–into an ‘ellipsoid’. It lengthens in the direction of the earth’s centre (and also in the opposite direction), since the parts nearer to the centre experience a slightly greater acceleration than do the parts more distant; it narrows in the horizontal directions, owing to the fact that the accelerations there act slightly inwards, in the direction of the earth’s centre.

Basically how black holes operate