The question is currently a fallacy in our understanding of physics, we have no concept of the effects of such an event as our model of quantum physics does not account for the disappearance of mass (at least not at any level that could induce a significant gravitational field). With this said we can only imagine the effects of the sun quickly moving away from us or of the sun exploding which would not immediately alter our perception of its mass as a single point of gravity. Quiet quickly tho we would be consumed by the resulting supernova, the period of time between the light from the explosion arriving and the resulting expansion of mass, that would lead to the dispersion of a central mass for our solar system would very small if not non existent.
In some circumstances it could even be reversed as noted in the crab nebula when matter has been recorded moving faster then the speed of light as a result of a supernova, at which point we would literally be destroyed before we knew it.
However, in the case of our sun this should not be the case as our sun lacks the mass to go supernova in the first place much less propel matter at supersolar speeds. So in that infinitesimal moment between the light going out and the blast ripping the earth apart as the sun is destroyed (rather than going supernova) there could possibly be a moment when we could decide if the magnetic field being emitted by the concentrated mass of the sun disappeared before the light went out or the other way around.
but again to the initial question, it will currently be impossible to formulate any answer that could be accurate given we lack the proper models, language, or principles to define such an event much less convey it to another person via text.
It is also interesting to note that in Einstine's theory of relativity, which is currently used in our understanding of celestial mechanics, G is defined using c or the speed of light. not sure what effects this could have on any hypothesis that might exist outside our current understanding.
I am currently looking for any information about the maximum rate of change of a magnetic field.
and this is the best i have come up with
Dr. Jesse L. Greenstein of the California Institute of Technology wrote:
The detection of gravitational waves bears directly on the question of whether there is any such thing as a "gravitational field," which can act as an independent entity. … this fundamental field hypothesis has been generally accepted without observational support. Such credulity among scientists occurs only in relation to the deepest and most fundamental hypotheses for which they lack the facility to think differently in a comparably detailed and consistent way. In the nineteenth century a similar attitude led to a general acceptance of the ether ….[SUP]
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