[nchagnet]

This is already sort of the case. Of course it's not as immediate a comparison, but in the same way that charge sources the divergence of the electric field (Maxwell's equations), mass-energy are sources of the Einstein equations involving the curvature. It's the same reasoning and something we generally already consider.

[floxy]

But I want to go the other way. In general relativity space-time curves because of mass. But what is mass? Just a given. But maybe mass comes about as distortion of space-time.

[nchagnet]

This is what I was trying to convey: this is already how we think about it.

In general relativity, mass is not more fundamental than the gravitational field and its curvature. While we generally speak of spacetime curving because of mass, this doesn't mean this is a one way relation. The stress energy tensor is equal to the Einstein tensor (roughly curvature), so the relationship is already two-way.

It's a cool thing to think about of course, just wanted to clarify.

[floxy]

Interesting, I've never heard that before. Do you know of a lay-man's article / book that goes more in-depth into treating mass as a curvature of space-time?

[nchagnet]

Sadly no, most examples I'm familiar with are within research articles. A typical thing done within such articles is to consider a spacetime geometry, calculate its Einstein tensor and map it to some ansatz like that of a perfect relativistic fluid. It's a neat way to interpret the geometry in question as an energy/matter content.

Hope that helps point you in the correct direction!