My cursory studies of general relativity had introduced me to the concept of how gravity is associated with the warping of spacetime and that the presence of matter in space warps space and this warping is observed as gravity. And this left me with the belief that you have to have matter to have mass and thus gravity. And only when you have matter do you have mass.
But now I'm reading Kip Thorne's The Science of Interstellar, and in Thorne's description of black holes he says".. matter as we know it gets stretched and squeezed out of existence." and "all that is left is warped space and time"
So according to Thorne (and others) black holes contain no matter, yet they have mass and exert gravitational forces. So my initial belief must therefore be wrong.
How can mass exist without matter?
Black holes are created from collapsing stars that once contained very large quantities of matter. Through the process of collapse and formation of the black hole, mass is conserved, but matter is not? Where did the matter go?
Best Answer
Treating only
and not the context, it is important to understand the usual relativistic definition of mass as the norm of the energy-momentum four-vector $$ \left( m c^2 \right)^2 = \left|\mathbf{p}\right|^2 = E^2 - \vec{p}^2 c^2\,.$$
In this context any system of photons not all pointing in the same direction has mass without having any "matter" in a conventional understanding.