# How does a mass create the gravitational field of GR? [closed]

As far as I understand, and please correct me if I am wrong, but the basic idea of general relativity is that spacetime is curved by matter. What we call gravity is then not a force as per Newton but a consequence of the geometry of space time. It is assumed that there is a gravitational field produced by a mass which bends space time.

So my question is; How does a mass create the gravitational field?

## closed as unclear what you're asking by Void, Daniel Griscom, user36790, ACuriousMind♦, CuriousOneJan 5 '16 at 17:56

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• What do you mean, "how"? "How" does a charge create the electromagnetic field, in comparison? – ACuriousMind Jan 5 '16 at 14:49
• Yes, thats a related question.. How does a charge create an electromagnetic field? We can mathematically model a field and draw conclusions and test them against experiments, and see our models are correct. (better - not incorrect) But what is the interaction mechanism between mass and space that causes the curvature? Does mass cause the energy distribution in space(of space itself) to change, changing the shape of space? If so what is the mechanism behind it. If the answer is we don't know yet, thats ok. if its known - please tell me. – andy Jan 5 '16 at 16:08
• What you are eluding to is the difference between microscopic and macroscopic theories. Newtonian mechanics can explain the movements of matter, but it can't explain matter itself. For that you need quantum mechanics. General relativity explains the behavior of gravity for all known measurements, but it does not explain gravity itself. For that we will need a microscopic theory of gravity, whether it is based on QM or not. Before we can make such a theory we will need new data, since nothing in the current data set contradicts GR. – CuriousOne Jan 5 '16 at 18:04
• @CuriousOne I disagree. GR fully explain how curvature develops. It is a dynamical theory. – Timaeus Jan 5 '16 at 18:51
• @Timaeus: GR does not tell us what gravity is. It tells us how it behaves. It's a very good macroscopic theory and that is all it is. – CuriousOne Jan 5 '16 at 18:55

Briefly stated the point is, that in GR, the matter (such as a massive star or planet) serves as a non-trivial source term for the EFE, whose corresponding solution (with appropriate boundary conditions) is a non-trivial curved spacetime metric $g_{\mu\nu}$.

We can think of a "mass" as a stress energy tensor that affects the inertial path that other objects (massive or massless) take in space due to the theory of generial relativity, as described mathematically by Einstein's equation. This change in inertial path of other objects is what we call the curvature of spacetime.

We call this curvature because we are redefining what we think of as a straight line. In the absence of all forces objects will be unaccelerated and follow a "straight line" path -- and since gravity is not a force in general relativity, objects near another massive object must be following a straight line. So we redefine the straight line as a geodesic, which is curved, and say that spacetime is curved around massive objects.

Let's first look at a simpler case. How does electric charge create electromagnetic fields.

First we note that is natural to have electromagnetic fields in empty space. But they have to change in a certain way, they have to satisfy $$\vec \nabla \cdot \vec E=0,$$ $$\vec \nabla \times \vec E+\frac{\partial \vec B}{\partial t}=\vec 0,$$ $$\vec \nabla \cdot \vec B=0, \text{ and}$$ $$\vec \nabla \times \vec B-\mu_0\epsilon_0\frac{\partial \vec E}{\partial t}=\vec 0.$$

So what does charge do? It also you to connect two solutions in two region together in a way that normally they couldn't line up. For instance it is perfectly find to have zero field inside a ball. And it is perfectly fine to have a static radial field outside of a ball. But the two can't normally line up (it would violate the first equation) but when charge is present on the spherical shell between the two regions, then it can.

Similar thing happens in spacetime. It's natural to have some spacetime curvature. It has to satisfy $G_{\mu\nu}=0.$

So you could have a some curvature like Schwarzschild of parameter $M+m$ outside a big ball. And it's natural to have Schwarzschild of parameter $M$ outside a small ball and inside the big ball. But normally, in vacuum, the two solutions can't line up. But when there is some mass $m$ on the spherical shell between the two regions, then they can line up.

So what happens is when you have a layer of mass $m$ and it collapses from way outside like the original big ball of gas then it replaces the old curvature if type $M$ with new curvature of type $M+m$ and then keeps falling.

But it changed the spacetime as it fell. It changed it by allowing the curvature if type $M+m$ to reach deeper towards the center than it used to. And now that spacetime is different, and more strongly curved (becasue type $M+m$ is more strongly curved than type $M$ for the same distance from an even bigger ball).

So that's where strong curvature comes from. It comes from mass connecting two different vacuum curvature together and through its motion it allows a type of vacuum curvature to extend to regions it previously hadn't.

Just like when a shell of charge contracts it creates new fields in the region between where it started and where it contracted to. This is essential to how matter way inside the sun is related to curvature far from the sun. The gas that formed the sub used to be way out here and it warped space as it contracted. It warped it by allowing the type of curvature that was outside the ball of gas to reach in deeper towards the center. The type of curvature naturally focuses stronger as the shells where it lives get smaller.

So it was weak but of a large type when it was far (far means weak) from the center of a large (mass of the sun large) mass. As the gas contracted to form the sun, the weakness of the large type got to reach down into a region where it wasn't as weak becasue the matter and mass that allowed the large type to interface with the small type moved inwards.

• In both the answers there are statements like”We can think of a "mass" as a stress energy tensor that affects the inertial path” and..”But it changed the spacetime as it fell.”So mass ( or the stress energy tensor) affects the path ( or changes the spacetime) But it still doesn’t answer my question … What is the mechanism by which the mass (mathematically modelled as a stress energy tensor) changes the path. Ie it changes the stress energy distribution in its surroundings.. but how does it do this? – andy Jan 5 '16 at 15:14
• @andy You misread me. Mass is just the biggest contribution to most stress energy tensors. The stress energy allows two different vacuum solutions to be pasted together. The example I give tells you exactly how much mass you need to patch exactly which solutions together, and technically it is the energy (not mass) even for my example. The stress energy tensor patches together different t vacuum solutions, it didn't make spacetime curved, it was already curved in the past it just lets the curvature to change which regions get to have which type. You didn't ask how mass causes stress energy – Timaeus Jan 5 '16 at 18:50
• Yes, that is how you describe electromagnetism and gravity macroscopically. That explanation does not contain microscopic descriptions of them. For electromagnetism you have quantum field theory as the microscopic theory. For gravity, there is, at the moment, nothing. Maybe string theory will be it... that's a very small "maybe". – CuriousOne Jan 5 '16 at 18:58