Bending of Spacetime: Time Delay?

[TheoEndre]

I am still new to the theory of relativity (both SR and GR), but I've read few books which gave me an insight about the subject (not a mathematical insight though). There's a question that I really would like to know the answer of: Is there a time delay for the bending of spacetime to occur? Now, I don't know if this is actually something that I would know if I studied more about relativity, but I am really curious to know the answer.
What I am questioning here is illustrated in this hypothetical example: Suppose an object A is moving in a constant velocity in space with no gravitational field to affect it, then suddenly (let's just skip the how) an object B with a mass vastly greater than object A appeared near A. Will the spacetime around B change instantly such that A follows the curvature at the instance object B shows up, or will there be a delay before the spacetime around B starts bending?

 

[Dale]

then suddenly (let's just skip the how) an object B with a mass vastly greater than object A appeared near A

You cannot skip the how. The conservation of energy and momentum must be respected in GR, it is built into the framework and cannot be violated, and in this question it makes a difference.

Did the object coalesce as a collapse of a spherical distribution of matter? Did it arrive intact at a high velocity from somewhere else and use a rocket to stop? Did it arrive at high velocity and is simply flying by? All of these will have different descriptions.

 

[phinds]

As Dale has pointed out, the question is meaningless because you've used magical hand-waving to posit a situation that violates the laws of physics and yet you want to use those same laws of physics to answer a question about the impossible situation (this assumes you want the new object's appearance to instantaneous, otherwise answer Dale's question).

Perhaps the heart of your question is intended to be whether or not the effects of "gravity" are instantaneous and for that the answer is no. Gravitational waves travel at c. That is, if there are perturbations in a gravity field, those perturbations ripple through space-time at c (although in most cases they are too week to detect - Google LIGO)

 

[martinbn]

Although the question is imprecise to the point that it doesn't make sense, the answer is that it will not be instantaneous.

To talk about it meaningfully you need to learn a bit about the initial value problem in GR and what domain of dependence is. No way you can avoid math for this. What you can do is look how the finite speed of propagation for the wave equation is explained. You can do that with just a bit of calculus. And then take it for granted that in the case of GR it is similar.

 

[FactChecker]

Ignoring any complications of your question, the answer is that it does take time for the distortions to go long distances. The sources of gravity waves that have been detected by LIGO are (roughly) located using the time difference that they are observed at different Earth locations. When there are more detectors on Earth, the locations can be determined with more precision. The gravity waves arrive at the same time as light or radiation from the event does.

EDIT: This post may be wrong or at least give the wrong impression. The reference given by @jbriggs444 distinguishes between two situations, one with a delay and one that is instantanious.

 

[FactChecker]

I always thought that the traveling Sun's gravitational effect on the Earth is as though the position of the Sun is where it was 8 min, 20 sec ago (the same time it takes light to get here). But I don't know if I based that on anything valid. Is that wrong?

 

[David Lewis]

You're correct. My understanding is we only see where an astronomical object was. Likewise its gravitational effects coincide with its apparent position.

 

[jbriggs444]

I always thought that the traveling Sun's gravitational effect on the Earth is as though the position of the Sun is where it was 8 min, 20 sec ago (the same time it takes light to get here). But I don't know if I based that on anything valid. Is that wrong?

The Sun's gravitational effect on the Earth is as if the Sun is where it is now. If the position were old then you'd have unstable planetary orbits.

https://en.wikipedia.org/wiki/Speed_of_gravity#Background

 

[TheoEndre]

Thank you everybody so much for your replies. Even though my question was meaningless (at least, from the perspective of physical laws), I got what I was looking for.

 

[Nugatory]

You're correct. My understanding is we only see where an astronomical object was. Likewise its gravitational effects coincide with its apparent position.

True for light, not true for gravity. This is one of the ways of stating the incompatibility between Newtonian gravity and special relativity.

 

[David Lewis]

The Sun's gravitational effect on the Earth is as if the Sun is where it is now.

Thank you. So the Sun's effective center of mass would be offset from its apparent position in the sky, and tides, for example, would respond to where the Sun is, not where it appears to be?

 

[PeterDonis]

Is there a time delay for the bending of spacetime to occur?

The "bending of spacetime" is not a process. Spacetime does not "change". It just is. It is a 4-dimensional geometry which can be curved.

Situations where it is natural for us to think of spacetime "changing" are really just situations where the geometry of spacetime is more complicated because there is a more complicated configuration of objects: instead of just one object there are multiple objects whose trajectories have more complex relationships.

 

[PeterDonis]

The Sun's gravitational effect on the Earth is as if the Sun is where it is now.

Not quite. Gravity is still causal: all of the aspects of spacetime curvature at a particular event are entirely determined by the configuration of stress-energy in the past light cone of that event. So the effects of the Sun's gravity on the Earth now are entirely determined by how the Sun was 500 seconds ago. But those effects are also more than just the Newtonian force; there are velocity-dependent terms in the interaction that cancel out almost all of the effects of aberration that would be expected for a pure Newtonian force with a finite propagation speed. The leftover, non-canceled effects of aberration show up as small corrections like the perihelion shift of orbits.

Carlip's classic paper on aberration and the speed of gravity goes into this issue in detail:

https://arxiv.org/abs/gr-qc/9909087

 

[PeterDonis]

So the Sun's effective center of mass would be offset from its apparent position in the sky

No. See my response to @jbriggs444 in post #13 just now.

tides, for example, would respond to where the Sun is, not where it appears to be?

Almost, but not quite. See post #13.

 

[timmdeeg]

Jet another way to interpret the OP could be to ask if the gravitational field of a body with proper acceleration remains spherical symmetric.