Gravity can be repulsive!

OK, so to recap (correct me if I’m wrong):

  1. Gravity is attractive for ordinary matter.
  2. LambdaCDM implies that repulsive gravity must exist.
  3. This repulsive gravity must be generated by some unknown exotic matter which violates the SEC and we call dark energy, which would explain point 2.
  4. We have no idea what DE is nor what it properties are, such that it can violate the SEC.
  5. The logical next step would be to look and test for possible candidates of matter/energy that can violate the SEC, which seems to be what Villata was doing - he proposed that antimatter violated the SEC and can explain point 2. These kinds of hypotheses can then be tested in the lab.

I would add the following corrections:
-) The fact that the expansion of the universe is accelerating (not necessarily LambdaCDM) gives rise to the hypothesis that gravity can be repulsive
-) Dark energy is a general, catch-all term for a form of energy that permeates the universe and causes the accelerating expansion of the universe
-) The cosmological constant, Lambda, is a specific model for dark energy
-) LambdaCDM proposes that Lambda IS dark energy

Further, I would be careful when saying

For example, gravitational waves is gravity that is created by ordinary matter, yet when it hits LIGO it causes changes in the lengths of the arms in an oscillatory fashion; this looks neither attractive or repulsive to me. Another example: in addition to its usual attractive gravity, a spinning star generates gravity that causes other objects to spin along with it. Again, this looks neither attractive or repulsive to me.

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OK, but you can surely agree that gravity is non-repulsive for ordinary matter?

Now you’re getting all physicist-superior. Not cool.

I don’t think I am. I wanted to make sure I am answering your question properly, so I wanted to see what exactly you are asking for. Never did I say that physicists>>other scientists.

All evidence points to this at the moment. Or rather, I have not seen evidence to the contrary. I would also point out that the word “ordinary” in “ordinary matter” is human-centric. If LambdaCDM is correct, there are much more of this “exotic” matter than “ordinary” matter.

Going back to the question of gravitational waves being neither clearly attractive nor repulsive, is there a rigorous definition (other than the SEC itself) for what it means for gravity to be “attractive” or “repulsive” anyway?

First of, the SEC is not a definition for attraction/repulsion, it’s just a property of the matter.

In general relativity, attraction/repulsion can be rigorously defined in terms of the geodesic motion of test particles. Suppose a central object; if the geodesics all get “sucked” into the central object, then it’s attractive, if the geodesics get repelled, then it’s repulsive.

For the other forces, attraction/repulsion can be rigorously defined in terms of the energy-momentum flux being positive or negative (I learned this in Matt Schwartz’s class).

Assume I’m not a physicist and I don’t know how to write the equations you asked for (apparently) gravity in general relativity. Assume that when I clearly don’t know what you are saying you should reply in the best layman’s terms you can manage. You’re coming off as showing how much you know without explaining what you know, whether or not you intend to.

I don’t need you to write equations of gravity in general relativity. I just wanted to make sure that we are talking about the same things, so I need you to write what you mean when you ask, for example, whether the strength of repulsive gravity is a high-order polynomial power of distance. This:

to me sounds like you are asking whether that the gravitational force is:

F = F_r(r) + \frac{GMm}{r^2} \; ,

where F_r(r) is the repulsive part of gravity, and that F_r(r) is a “high-degree polynomial function of distance”.

If so, the answer is no. But I don’t want to presume that this is indeed what you are asking, which is why, if I were to answer the question

I need to know what is the equation that you are talking about that is a high-degree polynomial function of distance.

OK. Don’t know how to do equations in a nice pretty way, but it would be something like F sub r = (G sub r)(Mm)(r^x), where x is an integer greater than 2. (G sub r would be the repulsive gravitational constant.)

OK, I now understand what you are asking. Knowing this I can now answer your question on whether dark energy is…

The answer is no, for two main reasons:

  1. The gravitational interaction is not split to a “repulsive” part and an “attractive” part
  2. The equation F=GMm/r^2 is only valid in very specific conditions (Newtonian limit, i.e., very weak gravity, and only for point particles) – these conditions are not the situations for dark energy

There are also further technical issues. For example, defining the repulsive gravitational constant as you do, G_r, will introduce length scales, as this means G_r will have an extra unit of [length]^(x-2) to keep the units of Force to be Newton. This is not a problem per say, but is an issue nonetheless that needs to be addressed in the theory.

Right. After rereading the relevant sections in Chapter 4 of Carroll’s GR textbook (2004): in the situation you described where the test particles are initially at rest and follow the geodesics \theta, then their evolution is described by
\frac{d\theta}{d\tau} = -4 \pi G (\rho + p_x + p_y + p_z) (eq. 4.86, p. 168), where \rho = energy density and p = pressure components of the energy momentum tensor. If the quantity in the parentheses is positive, then gravity is attractive. And this is exactly what the SEC posits: one of its conditions is \rho + 3 p \geq 0 (p. 175, assuming the case of a perfect fluid where p_i = p). Thus, while the SEC doesn’t strictly define attraction or repulsion, it seems mathematically equivalent to a test of whether a source object results in attractive or repulsive gravity.

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I think you get the idea. There is still one caveat: Carroll is talking about the Raychauduri equation, which tells you whether two geodesics converges or diverges. This is almost, but not quite the same as the question of whether an object (say, a blob in space, not necessarily spherically symmetric) generates a spacetime whose geodesics (initialized with “0 velocity” in an appropriate way) all point toward the blob (attraction) or is repelled by the blob (repulsion). There are super fine-tuned, edge-cases in which I can have geodesics move away from the blob (repulsion) but still at certain points, converge with each other. For most cases, however, using the concept of attraction/repulsion in the Raychauduri sense is good enough. This is doubly true for spherically symmetric situations, as is the case of Dark Energy in cosmology.

Keep in mind, however, that the energy condition is not defined so that attraction/repulsion in the Raychouduri sense is obtained, but rather is motivated by considerations such as making sure that the object has positive mass-energy in its rest frame. In this sense, I would claim that their relevance to attraction/repulsion (in the Raychauduri sense) is a symptom of the energy conditions, but is not their defining trait.


I don’t make posts to appear smart. I make posts to have people tell me I’m dumb so that I have something else to consider. So yes, I want you to comment.


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