A small fornote. I realize that this is purely speculatory as I can see no probable way in which the events could take place as postulated.
On to the question.
If the sun were to suddenly cease to exist (disappear?), would the gravitational change be immediately detectable on Earth?
If yes, can this be justified within the current theories?
The bolding was mine.
No.
There have been a few threads discussing the speed of gravity that have links to sources for information on this topic. I suggest you search them out.
But, to elaborate on the answer, this was best explained to me by an electromagnetic analogy: An electric charge exerts a force on another electric charge. The direction of this force is the line between the two charges. If one of the charges is moving at a constant velocity, relative to the other, the direction of the force is, surprisingly, still the line connecting the instantaneous position of the two charges. In other words, you don’t have to correct for the finite travel time of the electromagnetic force. There is no aberration, although you would expect it. Mathematically, special relativity provides the electromagnetic field with a correction that exactly compensates for the expected aberration!
This applies in the special case of constant velocity only. If the moving charge suddenly comes to a halt, the force on the other charge continues to follow the point where the moving charge would have been if it were still moving, until the change has had time to propogate – at the speed of light.
Gravity behaves similarly, but because a gravitational field is a more complex entity than an electromagnetic field, the apparent lack of aberration extends even to accelerating masses. That is why the earth is attracted, gravitationally, to the point where the sun is at the present moment – not where it was eight minutes ago, which you would naively expect from the finite speed of gravity.
This lack of gravitational aberration is sometimes used to deduce a speed of gravity that is many times faster than the speed of light. And you don’t need to make subtle observations to base your deductions on – the fact that planetary orbits are stable for more than a few decades is proof that the aberration is non-existent or much smaller than expected.
But, getting back to the analogy, just as the force on the non-moving charge continues to follow the predicted path of the moving charge, the earth would continue to be attracted to the point where the sun would have been if it hadn’t, um, disappeared, until sufficient time had elapsed for the fact of the disappearance to propogate out – at the speed of light.
A couple of notes:
It took me a few minutes to write this, so someone may have alreaady answered. If so, I apologize.
If I screwed up the explanation it’s because I’m only parroting mathematical conclusions that I’m incompetent to make for myself. If you really want to know, see the earlier threads with the links.
Thanks!