What does the term zero volume mean?

Answer 1

Volume = mass / density; there zero volume means the mass is zero. You can divide zero, but you cannot divide by zero. A gravitational singularity, associated with a black hole, is said to be thought of a zero volume and infinity density.

Note: The massless condition of a gravitational singularity is expected to experience the same gravitational acceleration as other black hole mass with near zero volume (which provides empirical evidence for the equivalence principle) because they do have relativistic mass.

Mass in special relativity incorporates the general understandings from the concept of mass-energy equivalence. Added to this concept is an additional complication resulting from the fact that "mass" is defined in two different ways in special relativity: one way defines mass ("rest mass" or "invariant mass") as an invariant quantity which is the same for all observers in all reference frames; in the other definition, the measure of mass ("relativistic mass") is dependent on the velocity of the observer. Thus, perpendicular components of forces acting on massless particles simply change their direction of motion, the angle change in radians being GM/rc2 with gravitational lensing, a result predicted by general relativity. The behavior of massless particles is understood by virtue of special relativity. For example, these particles must always move at the speed of light. In this context, they are sometimes called luxons to distinguish them from bradyons and tachyons.