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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?

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    $\begingroup$ You can use Newtonian theory of gravity to account for almost everything, outside of things like very strong gravity, deflection of light, or time dilation. So in that context gravity is a force, and causes the planet to form a spheroid as you've understood $\endgroup$
    – RC_23
    May 7 at 1:10
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    $\begingroup$ Remember everything is a model $\endgroup$ May 7 at 1:12
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    $\begingroup$ It’s the centrifugal force discussion all over again ;) $\endgroup$
    – Michael
    May 7 at 12:57
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    $\begingroup$ From a logical standpoint, a "new" theory such as general relativity does not efface an old theory such as Newtonian gravity. Instead, the new theory generalizes the old. In ordinary situations the new theory applies and the old theory still applies, so in those situations you may still think of gravity as a force. It is only in the extraordinary situations where the old theory breaks down that the new theory comes to the fore; and yes, in those situations, you should probably avoid thinking of gravity as a "force". $\endgroup$
    – Lee Mosher
    May 7 at 13:31
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    $\begingroup$ @stackoverblown are they not? Spheroid implies that they are imperfect sphere-shaped, such as our own planet Earth. $\endgroup$ May 7 at 19:10

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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).

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    $\begingroup$ Does the concept of following straight lines imply acceleration or a locking force? If I exist on a straight line I would expect that if I were accelerated in the x+ direction absent any other force I would continue travelling in the x+ direction; ergo I could lift dirt up and it should keep going up -- except that (I just got it) it doesn't keep going "up" because the path of x+ curves back around to being "down" (vs a reversal of the direction of travel which I was intuitively thinking) $\endgroup$
    – Sidney
    May 7 at 15:26
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    $\begingroup$ @Sidney What I meant by "straight lines" is actually what we call a geodesic, which is inertial motion in the general relativistic sense, i.e., motion in the absence of any forces (and gravity is to considered a force) $\endgroup$ May 7 at 15:33
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    $\begingroup$ I would add (perhaps stating the obvious) that 'downhill' is a lower potential energy state. The tendency to form a spheroid is resisted (or assisted) by material strength, frictional, adhesion, magnetic and electrostatic forces between objects and particles, etc. Thus not all objects (especially not smaller objects with low self-gravity) form spheroids, however very large, dense objects and clumps will tend to. Chunks of rock will resist; liquids and dust clumps not so much. $\endgroup$ May 8 at 23:09
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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.

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.

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  • $\begingroup$ The exterior geometry of a rotating body isn't Kerr; there isn't any rotational analog of Birkhoff's theorem. I suppose Kerr is a good approximation beyond some point, but so is Schwarzschild. I also don't really understand how this is supposed to guarantee a roughly-spherical shape. $\endgroup$
    – benrg
    May 7 at 16:19
  • $\begingroup$ @benrg I didn't actually appreciate that the exterior solution of a rotating star was an open problem, thanks for pointing that out. I cleaned up the answer to restrict myself to Birkhoff's theorem to avoid over-generalizing. $\endgroup$
    – Andrew
    May 7 at 21:50
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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.

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  • $\begingroup$ From your answer it seems like the definition of "force" is somewhat arbitrary. We say Einsteinian gravity is not a force because it is caused by spacetime curvature and not a Newtonian mechanism. But then you say that electromagnetism IS a force because it is caused by an exchange of a particle. EM is also not described by a Newtonian model, just like gravity. So why are EM and the other two fundamental interactions considered forces but not gravity? This confusion seems to be the deeper source of OP's question. $\endgroup$
    – Hrach
    May 7 at 15:34
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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.

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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.

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  • $\begingroup$ Gravity is not necessarily a "pull" as you say. We generally say it's neither (see: astronomy.stackexchange.com/questions/12408/…). $\endgroup$
    – AtesComp
    May 15 at 18:43
  • $\begingroup$ @atescomp well are we talking about dictionary definitions or physics? I don't see how there's a physically or mathematically meaningful distinction there. I don't think it's useful to take a mathematical model - which is all GR is - and use it to make linguistic arguments. That's really the point of my answer and IMO the flaw in the premise of the OP. $\endgroup$ May 16 at 3:04
  • $\begingroup$ Your response included the push/pull language. No one knows what causes gravity, just its effect. There is nothing intrinsically known about matter to cause two bodies to come together--is it some external process effecting the objects? Internal? Geodesic? A pull or push characteristic is simply unknown. If it is intrinsic to matter, it can be both. If it is a product of curved space-time, it's neither. There are other models as well that equally explain it...quantum vacuum, de Broglie standing wave, etc. Even Newton was concerned over this. So, a flaw in your linguistic argument. $\endgroup$
    – AtesComp
    May 17 at 13:54
  • $\begingroup$ I'm not the one making the linguistic argument! Y'all are. "Push or pull" is a common definition of force we're taught in school. That's the only reason I cited it. And the definition fits. "Curved spacetime" is another definition that emerged from GR. And that definition fits too. There are probably infinite ways to define gravity linguistically that all fit with observation. What matters is the math. Anything beyond that is philosophical and frankly a distraction IMHO. $\endgroup$ May 17 at 14:35
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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.

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