# Does a massive object contract space-time or expand it?

Before asking, I must say that I am not a physicist of any sort, but I do have a strong interest in Relativity that has led me to question my layman’s understanding. So please stay with me on this “thought experiment” despite my lack of formality.

At center is the so-called rubber sheet analogy for how massive objects such as the Earth warp space-time. Similar to how a bowling ball is placed onto a trampoline, the surface will warp and anything on a straight path that crosses this warped surface will have its trajectory altered by the curvature of space-time. Light does this when it curves around the gravity of the sun.

Given a few things I’ve heard, I wonder if the expansion of space-time by massive objects is actually true. Is the space warped outwardly because of a “bowling ball” on a tense surface, or does the “bowing ball” actually make space-time more dense? I ask because there are three things I’ve considered. I will cover two of them first.

Considering it factual that:

1. An object free-falling toward a massive body without resistance will accelerate proportionally given its distance.

2. The closer one is to a massive object, the slower time moves.

My thoughts are that the reason an object in free fall will accelerate toward something more massive, is because it crosses to regions of evermore condensed space-time.

My third thought is that less time passes but more “distance” is covered.

That said, I also considered how a gravitational wave might interact with a gravity well. If as Einstein said was true, then all gravity should propagate equal to the speed of light. However, if one considers that a gravity wave both contracts and expands space-time as it propagates, then is this not a wave that may potentially move faster than light in its locality?

My suggestion here is that massive bodies gravitationally attract space instead of expanding it, and this eventually could be seen in the data with the likes of LIGO and future experiments. I’m not betting my life on it, but I’d like to offer a suggestion to people way smarter than me.

Does mass contract or expand space time?

• – StephenG Mar 29 '18 at 4:40
• I've suggested this is a duplicate of a question asking for a better analogy for gravity than the (awful) rubber sheet one. I get the impression a lot of your problems stem from the confusions that concept creates. – StephenG Mar 29 '18 at 4:41

You need to be careful about statements like spacetime is contracting or expanding or indeed doing anything else. Spacetime isn't a thing. It is a mathematical object that we use to describe the motion of things. So it is meaningless to ask whether spacetime contracts.

However what we can do is take a sphere of test particles and see how it changes as it moves through spacetime.

Imagine taking a large number of particles that are too small to exert any significant gravitational force on each other and arranging them in a sphere. If these particles are floating in space far from any other matter then they will just stay as a sphere - the radius and volume of the sphere won't change. But if we now let our sphere move into some gravitational field then it will change in shape and/or volume. So while it doesn't make sense to ask if spacetime expands or contracts it does make sense to ask if our sphere expands or contracts and how that sphere changes does tell us about the curvature of the spacetime.

It turns out that the volume of the sphere is related to an important properties of the spacetime geometry called the Ricci tensor and Ricci scalar aka scalar curvature. Basically an increasingly positive Ricci scalar means the sphere is contracting and an increasing negative Ricci scalar means the sphere is expanding.

The shape of the sphere is related to another property called the Weyl tensor. This tells about tidal forces acting on our sphere.

To make this concrete take your example of the sphere falling towards a massive body - possibly a black hole or possibly just any massive object. When we calculate the spacetime curvature we find that the Ricci tensor and scalar are both zero so the ball stays the same volume. It neither contracts nor expands. However the Weyl tensor is not zero so the ball experiences tidal forces. In fact the ball gets stretched along the line towards the massive object and compressed at right angles to this line. This process is what s commonly known as spaghettification.

So for a massive object if we were going ignore the imprecision and use the metaphor of spacetime spacetime expanding or contracting we would have to say that spacetime is neither expanding nor contracting near the massive object, but it is changing shape.

There are examples where the volume of our sphere does change and the most obvious is an expanding universe. In an expanding universe like ours we find the volume of the sphere increases with time, which is why we talk about the universe expanding. In a hypothetical contracting universe we would find the volume of the sphere decreases with time.

Does mass contract or expand space time?

No.

My suggestion here is that massive bodies gravitationally attract space instead of expanding it,

No, not that either.

Mass causes curvature of spacetime in general relativity.