Gravitational Length Contraction

[nigelscott]

I understand the concepts of time dilation and length contraction in SR. I also understand the concept of time dilation in a gravitational field. But what about length contraction in a gravitational field? Is there such a thing and can it be derived from the Schwarzschild metric?

 

[Agerhell]

I believe that in the Schwarzschild solution expressed in Schwarzschild coordinates the speed of light is anisotropic and that in order to explain this a "gravitational length contraction" in the radial direction is sometimes thought of.

 

[pervect]

A lot of lay people seem to think that gravitational length contraction should exist for reasons that are unclear, but I don't think I've ever seen a textbook or paper discussing the concept specifically. (It's possible I could have missed a paper on the topic, of course.)

Going from analogy with time dilation, though, I'd guess one could define it as the ratio between proper distance and changes in coordinates.

The value of this ratio will be dependent on the coordinates used of course, just as in the case of time dilation. So I don't see any coordinate-independent significance to the term.

 

[1977ub]

Recent thread relating to space being warped in the presence of mass.

https://www.physicsforums.com/showthread.php?t=679754

 

[sardar]

I can confirm that there is indeed a phenomenon known as gravitational length contraction, which is a consequence of the theory of general relativity. This theory explains how gravity affects the fabric of space-time, and one of its predictions is that objects near massive bodies, such as planets or stars, experience a contraction in their length.

This phenomenon can be derived from the Schwarzschild metric, which is a mathematical solution to Einstein's field equations that describes the curvature of space-time around a spherically symmetric mass. In this metric, there is a term known as the "gravitational time dilation factor," which is responsible for both time dilation and length contraction in a gravitational field.

To understand how this works, imagine two objects of equal length placed at different distances from a massive body. The object closer to the body will experience a stronger gravitational force, and therefore its gravitational time dilation factor will be larger. This means that time will pass slower for this object compared to the one farther away. As a result, the length of the object will appear to be contracted when viewed from the perspective of the other object.

This effect becomes more significant as the distance from the massive body decreases. In the case of a black hole, where the gravitational pull is extremely strong, the length contraction can be extreme, leading to the phenomenon known as spaghettification, where an object is stretched and compressed in different directions due to the intense gravitational forces.

In summary, gravitational length contraction is a real phenomenon that can be derived from the Schwarzschild metric in general relativity. It is a consequence of the curvature of space-time caused by massive bodies and is an essential aspect of our understanding of gravity.