Hak said:
I have a doubt about gravitation. Suppose the mass of the Sun halves in an instant, after how long does the Earth ''notice'' it?
That is, does the gravitational force also decrease instantaneously?
Instinctively I would say yes, but I don't understand why it should be so. If, for example, we attach something to a spring and give a quick tug, the object doesn't immediately feel the force; so why should it be any different for gravitation?
Can you clarify this doubt? Thank you for any intervention.
P.S. You are very free to move this thread to another Forum if you feel that I have not posted it in the more appropriate one...
As others have pointed out, it's not possible for the sun to lose half it's mass in an instant. Thus, asking what the equations of GR say in this case is like asking what Maxwell's equations say about the electric field of a disappearing charge. The answer is similiar - Maxwell's equations aren't consistent with charges just vanishing, and the equations of GR aren't consistent with mass vanishing.
To get around this, it's been suggested that you rephrase the question, though if someone has recommended exactly how, I haven't seen it.
I'll fill in this lack by suggesting how you can rephrase the question. While you can't make matter magically disappear, you can re-arrange it. Specifically, you can (in theory) blow up or explode the Sun.
The exact answer to your question will then depend on "how did I blow up the Sun"?
The easiest case to answer is if the explosion is spherically symmetrical. Note that to keep energy conserved, you'll need to include the source energy of the explosion in your calcuations. The "biggest boom" woud occur if the mass of the sun were totally converted to radiation in an instant, via a distributed, idealizazed, matter/anti-matter reaction.
There is an interesting question here - I was planning to invoke Birkhoff theorem, but when I looked at the fine print, this may not quite do the job, as it's not static. Which hapens I think because it's not a vacuum solution, either. :(.
However, I believe we can say that a spherical solution won't generate any gravitational waves, though I don't have a specific reference handy to shore up my recollection. And what I expect to happen in this case is that until the expanding wavefront of the exploding matter of the explosion reaches the observer, therre won't be any impact on the gravitation. If we imagine the "total conversion" explosion, this means there is no effect until the radiation from the explosoin reaches the observer.
IIRC - and again I don't have a specific reference - a non-spherical explosion does have the possibility of converting some of the energy of the explosion into gravitatioanl waves, so it becomes a harder problem.
A technical note - I'm assuming an asymptotically flat space-time, which is more-or-less required to talk about energy conservation in General Relativity.
