If gravity is not a force, what makes massive objects spheroid?

Question

For most of my life, the explanation given for why celestial bodies like stars, planets, etc. are round is due to gravitational force. Simply put, if an object has enough mass, it will, in turn, have enough self-gravity to eventually turn into a spheroid, such that the object's matter is more-or-less equally spread around the center of mass, with rotation obviously deforming the shape a bit.

Now, if according to General Relativity, gravity itself is not a force, but the curving/bending of spacetime itself, then how does this bending of spacetime lead to massive objects tending towards a sphere shape?

Answer 1

The basic idea is still the same: the gravitational influence of the parts on each other tends to pull them together. The only difference is that now you don't have a force pulling them together, but rather they are following "straight lines" through a curved spacetime and tend to be clumped together. Following their natural paths through a curved spacetime brings them together and they tend to form a spheroid.

The explanation you gave,

Simply put, if an object has enough mass, it will, in turn, have enough self-gravity to eventually turn into a spheroid, such that the object's matter is more-or-less equally spread around the center of mass, with rotation obviously deforming the shape a bit.

is still just as valid as before. The only difference is that "gravity" is understood in a different manner (curved spacetime rather than a force).

Answer 2

First, even in general relativity (GR), there's nothing wrong with taking a weak-field limit where GR "looks like" Newtonian gravity, and in that limit you can think of gravity just the same way you always have in Newtonian physics. General relativity doesn't get rid of any of the successes of Newtonian gravity, and if the force picture helps you understand how stars and planets form into spheres, you shouldn't throw away that picture completely. In fact, I think it is more vivid than the picture you would get thinking directly in terms of curvature, and still essentially correct in the limit in which it applies.

Second, if you want to develop some intuition of how to think about planets/stars within the framework of GR, it's useful to remember that GR describes a two-way interaction between spacetime and matter, summarized by Wheeler:

spacetime tells matter how to move, and matter tells space-time how to curve

So if you have some matter in an arbitrary arrangement, the matter will bend spacetime. This in turn will cause the matter to move. Then, the moving matter will change the spacetime, which will affect how the matter moves, and so on. Eventually, the matter and spacetime reach an equilibrium, which we can think of as the endpoint of gravitational collapse. If the object does not collapse into a black hole, then at some point the pressure created by the matter holds the matter from collapsing further.

Here are some results which suggest the endpoint of gravitational collapse "should" be something like a rotating spherical body:

• The singularity theorems of Hawking and Penrose are built on the idea that (in the presence of "ordinary matter" that obeys various conditions of the stress energy tensor), gravity tends to focus nearby geodesics. Therefore, the curvature will tend to lead to an attractive effect where disparate matter particles are brought together. (I'm being a little vague here because the technical details require some math, and you need to be careful about what this means in general spacetimes, such as an expanding Universe, but when considering ordinary planets and stars, the intuition that spacetime curvature tends to bring matter particles closer together is basically true, and is a geometrical analogue of the Newtonian idea that gravity is an attractive force.)
• Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution outside of a non-rotating star or planet must be given by the Schwarzschild metric.

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Thanks to benrg who pointed out that in an earlier answer to this question I was implicitly appealing to a stronger version of Birchoff's theorem for rotating black holes that doesn't actually exist.

Answer 3

See Don Lincoln's Is gravity a force?. The answer is yes and no. Physics is a description of the behavior of the universe. There is more than one way to describe it.

Classical physics describes it as a force. It accelerates objects.

General relativity describes it as geometry. Objects accelerate and follow curved paths because they follow the straightest possible paths in curved spacetime.

But neither of these is the final theory of gravity. Both are good in their realms, but do not apply to all situations. E.G. G.R. does not work in the center of a black hole. We need a theory of quantum gravity. Many such theories have been proposed, but none has been shown to be correct.

One formulation of quantum gravity says gravity is caused by the exchange of virtual particles called gravitons. Since this is much like the eletromagnetic force being caused by the exchange of virtual photons, gravity is a force.

But there are variations. Some superstring theories say that particles are tiny vibrating strings. The graviton is one particular mode of vibration. At high energy, gravitons interact with particles and generate a gravitational force. The curvature of spacetime arises from gravitons vibrating an a coherent state.

Loop quantum gravity says that spacetime is quantized. There is a smallest distance and time interval. We don't know how gravity arises in this theory.

Entropic gravity tries to account for behavior that other theories cannot explain, such as the faster than expected rotation of galaxies. IGravity is not fundamental. It arises from entropy and the statistical behavior of microscopic degrees of freedom. So gravity is neither a force nor geometry.

Answer 4

The tendency of (parts of) matter is to follow geodesics (i.e. shortest paths) in the curved space(time) until the internal forces of other matter start pushing back.

If there is no force acting upon an object, it moves along a geodesic in GR. Not in straight, unaccelerated lines.

In a weak gravity regime this produces the same result as Newton's law of gravity, making it seem very force-like.

In this picture, standing on Earth is no longer understood as the Earth pulling you down. Instead the Earth warps space and you would normally follow that warped space "down" until you cannot fall any further because the Earth is in the way. So the Earth is pushing you "up", away from your geodesic preventing you from falling.

Answer 5

I don't want to be redundant of other answers, which are all very good, but instead want to focus on the premise - that "gravity isn't a force". This is like saying "bowling isn't a sport." It's not a scientifically precise statement but is rather mostly thrown around to get headlines and attention - in the same category as "everything you learned in school is a LIE."

General Relativity/spacetime curvature is a model. Currently this is the best, most precise and most predictive model we have for explaining and predicting the phenomenon we call gravity. It is not, as others have pointed out, the only possible model. It is also, most physicists are fairly certain, not complete. It could even be wrong, i.e., spacetime curvature might not be "real" because spacetime itself might not even be a fundamental property of the universe. Conversely, it is possible to model the other interactions geometrically; they just don't work as well as quantum field theory and virtual particles. The only thing we know for certain is that there's something about gravity that makes it different from the other 3.

Gravity is a "force" according to the conventional definition you learned in school - A force is a push or a pull. Gravity is a pull. Therefore it's a force by that definition.

Another definition of "force" is something that causes acceleration. Well, gravity causes massive objects to accelerate toward each other. 2 for 2 so far.

But wait!, you say. Gravitational acceleration isn't really "acceleration" either, according to [insert recent popular YouTube video here]! Well, again, what's acceleration? If acceleration is the second derivative of distance with respect to time, then gravity sure as heck results in acceleration. If you instead want to redefine "accelerating" as following a path in spacetime other than a geodesic, because that model makes better predictions applicable to your particular problem, then you have every right to say gravity doesn't cause "acceleration".

So please do not fall into the trap of thinking gravity isn't a "force" and therefore all of its observed behavior is now inexplicable or the Newtonian model is useless for thinking about the world. General Relativity would never have been accepted if it didn't reduce down to Newtonian mechanics at everyday limits. Gravity is absolutely a "force" for all intents and purposes relevant to the question, and the inverse square law works perfectly fine to explain why gravity causes extremely massive objects to tend toward spherical shapes.

Answer 6

Gravity es not a force, but there are more forces in the game, contact forces. As in the Newtonian view, in the relativistic view the particles forming the body are being diverted from its inertial path because the interaction with other particles, the difference is simply how they do. Roughly, the gravitational force in Newtonian mechanics triggers the same forces from the other particles as the curved inwards path in relativistic mechanics.