# Time Delays in General Relativity

If gravity propagates at, or less than, the speed of light, and is therefore not instantaneous, does that introduce time delays to gravity? For example: suppose that we, the observer, sit within the future light cone of a massive star, and that the light from that star is due to reach Earth for the first time in 100 years time. Is it theoretically possible that we might we feel a sudden (possibly small but theoretically detectable) gravitational ‘tug’ in 100 years time?

Further: Is it possible that, whilst we might currently sit outside of the future light cone of some a star (for example) - over time, due to expansion of the universe - the future light cone of that star could expands to encompass us – thereby enabling us to observe and be influenced by that previously unobservable and undetectable object?
(Note this is in reference to the expansion of the universe, as opposed to the light simply not having reached us yet)

Apologies if I may be confusing 2 topics here. I only follow popular science at present….

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–  Qmechanic Jan 15 at 15:36

Yes, although there are a couple of points in your question that I would take issue with (in a minor way). Changes in the curvature of spacetime do indeed propagate at the speed of light, so a change to the matter distribution at some distance $d$ won't affect us until a time of approximately $d/c$ has passed.

But we won't feel a tug. In fact we won't feel anything at all, just as an astronaut in free fall doesn't feel any gravitational force. Well, not unless the propagating change in the curvature exerts a tidal force - we would feel that.

Also, a star can't just pop into existance. The star formed from a dust cloud, but if both were roughly spherically symmetric the formation of the star from the dust cloud wouldn't affect the spacetime curvature at our location at all. When the star eventually blows up into a supernova that that too won't affect us, as long as the supernova debris is roughly spherically symmetric. It's only deviations from spherical symmetry that would (eventually) change the spacetime curvature in our location.

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Thanks John

I’m still slightly uncomfortable with the notion that we wouldn’t be able to detect (theoretically) the change in curvature. This is possibly due to the stubbornness of my own preconceptions, so bear with me!

Consider that the gravitational influence from an incredibly massive galaxy is due to reach is in 100 years time. Ok - granted the gravitational influence trails off as the inverse square of the distance between us and the galaxy - so it may be an infinitesimally small change in our local curvature, but wouldn’t there still be a change? Or are you stating that it would simply not exert any change whatsoever in our local curvature?

In reference to your point about an astronaut in free fall: Do you mean that the reason we wouldn’t be able to detect a change in the local curvature, is because the earth is in free fall around the sun? If so, could you please expand on that point?

In reference to your point about the star not popping into existence: I agree that the mass was always there, albeit the matter may have been structured differently (in your example: a proto-star vs a fully formed star). I was trying to describe a scenario whereby the object had been in existence for some time, but the light had simply not had a chance to reach us yet (and so no information could have reached us: gravitational or otherwise) However that leads me down a different route: What if new mass is created (converted from energy), 10 light years away.
Wouldn’t we feel THAT, in 10 years time? …. I’m possibly clutching at straws now!

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