This is an interesting question.

Disclaimer: I do not have any real experience with GR. From the physics side of my education, GR requires a knowledge of differential geometry, which is not part of the standard curriculum for physics students even at the graduate level. It is mostly those students who are specializing in GR who end up studying it.

On the math side, I did take a course in differential geometry. But I never really got an intuitive feel for what a non-positive definite metric "looks like" (I can "visualize" an

*n*-manifold with a positive definite metric), nor did I ever see physics applications. So, my "explanation" is going to consist of what I understand from the math side.

Manifolds automatically come already curved. In fact, it is how the manifolds are curved that distinguishes them. The curvature is basically the shape. The only significant difference between a sphere and an oblate ellipsoid is that the curvatures are different. If I hand you a sphere, it is already curved -- that is what makes it a sphere.

So, when our universe is modelled by a Lorentzian 4-manifold, it has to come with some shape. In the physical GR model,

*mass density* is a parameter (or one of several parameters) that is part of the mathematical equations that describe the curvature.

Now the interesting question is: is there some physical quality called

*mass* that forces the otherwise flat manifold to curve? Or is does the manifold already come curved, and our experience of mass simply how we percieve this curvature? This becomes a metaphysical question, about how exactly we are going to interpret the mathematical equations to make sense of what we actually observe.

But in the end that's all we have: the mathematical models, a way of interpreting the results of calculations in terms of potential observations, and some measure of how close the potential observations match up with our actual observations. The actual ontological nature of the universe is, I suspect, beyond what science can really answer.

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Haven't you always wanted a monkey?

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