# Mass and Expanding Space

1) space is expanding at an increasing rate, therefore things are getting farther from each other and therefore increasing in velocity.

2) the faster an object moves relative to another, the more mass it has

3) supermassive objects can turn into neutron stars, black holes, etc. Therefore, will this effect of space expanding cause this to happen to objects?

A sub question is if two objects are now traveling towards one another, given enough time under the effect of expanding space, will they travel towards one another but never reach one another, or will they eventually appear to reverse directions from one another because space is expending so fast? Does it depend on the reference point?

(1) Velocity relative to what? Their speed relative to each other increases, but their velocity relative to space itself, as it were, doesn't change.

(2) The faster an object moves through space, the higher its energy. However, the objects aren't changing their velocity through space, that remains constant as we said in 1.

(3) No, as their energy doesn't increase.

(4) If they are moving towards each other through space but space is expanding fast enough, they will appear to be moving away from each other, yes. I don't believe this depends on the reference point; the distance will be different in different reference frames, but in all reference frames its change will be with the same sign.

GR defines velocities in non-expanding space. But the problem with expanding space is, that we do not have in GR a definition of velocity in expanding space.

What you are referring to, is that two objects (galaxies) are receding from each other because space itself is expanding between them. Though, the galaxies might actually even be moving locally towards each other through space, they are still receding from each other because space itself is expanding between them. This is because these galaxies might actually be moving in their own galaxy cluster towards each other, that is, their speed vectors show a direction towards each other. If you would locally measure the speed of one galaxy (A) compared to another (third) galaxy close to it, you could see that the galaxy is moving in the direction of the other (B) galaxy. This is if you view it from the local frame. So you would see that A is moving towards B when viewed from A's frame. But when you look at A and B from outside the whole galaxy cluster (that involved both A and B), then you would see them receding. You would see the whole galaxy cluster expanding. Every galaxy in the cluster is receding from the other one (in this example). This happens because the whole space that the cluster is in, is expanding.

You are right that when an object moves through space, as it accelerates, it gains more energy (momentum). But since in your case, the objects are not moving through space faster and faster, they do not gain more momentum. It is space itself that expands, causing them to be further from each other. There is no acceleration through space, because in their local (in the galaxy itself) frame they are not accelerating. As per GR, they are not accelerating.

Space between them is expanding, and the expansion is accelerating, but as per GR, this is not the definition of acceleration of an object. Because of this, they will not gain energy, and their stress-energy will not become bigger. They will not become black holes.

• Thank you for your reply. What is the definition of acceleration in general relativity? – Meuchedet Aug 21 '18 at 18:09
• Also, based on what you said, if an asteroid was accelerating into the Sun it would not gain mass due to it's acceleration? If it would, then let's say that a long time from now when space is accelerating so fast i.e. so fast that and asteroid flying towards the Sun, wouldn't be able to reach the Sun, what would be the effect on the asteroid's mass in such a case? Same thing as the galaxies? – Meuchedet Aug 21 '18 at 18:20
• Distance matters in terms of its relative effects on the masses. The Sun, with an incoming asteroid, inside the solar system, is inside the gravitational zone of the Sun. There, expanding space is not dominant, space is not expanding, due to gravity of the Sun. Space is not expanding inside the Milky Way either, at least the expansion is not dominant. The areas where the expansion of space is dominant is the inter-galactic vacuum of space, and the vacuum of space between galaxy clusters, the voids. – Árpád Szendrei Aug 21 '18 at 19:19
• If the asteroid is flying towards the Sun from another galaxy, the expanding space between the two galaxies might make the asteroid recede from the Sun. But in the local frame of the asteroid, the asteroid would gain energy from accelerating. This acceleration needs energy. What would accelerate the asteroid to speeds even faster? This acceleration cannot continue unless the asteroid would have infinite energy resources. Thus, the asteroid will stop accelerating and continue moving with constant speed through space. – Árpád Szendrei Aug 21 '18 at 19:21
• As space expansion would cause the asteroid to recede from the Sun (and the Milky Way), after a while the asteroid would never be able to reach the Milky Way and the Sun. Still, the asteroid might be locally accelerating for a short time, and gaining energy. – Árpád Szendrei Aug 21 '18 at 19:23