Deepak K Kapur said:
Does it mean Gravity is classical and not quantum mechanical?
We only have (successful) classical models for gravity so far.
Quantum gravity is still a work in progress.
Therefore, all these answers have been in terms of classical theory.
Does it mean that a star can influence another star in due course of time even if they are infinite distance apart?
Define "infinite".
Extremely distant events will hit causality limits in general relativity: they are "over the horizon of the Universe" so to speak and their influence may never be felt here due to the cosmological expansion.
1. Consider that the stars are not infinitely apart but are hugely apart. When viewed from the angle that gravity is just the curvature of space time, what kind of a curvature of space is in action when the stars are so much apart that the space between them extends to huge distances and is flat for all purposes and it takes even light gazzillions of years to travel between them? I think there would be no action between such stars even if we wait for gazillions of years to pass.
You realize that "action" is a technical term in physics right?
Basically, there is nothing in GR to suggest that the kind of absolutely flat space-time you are thinking of exists. Spacetime that we see is, overall, very flat - but not
absolutely flat. Gravity certainly acts across the entire universe that we know about.
That's roughly 46 billion ly radius (visible).
That "for all purposes" has limits to it - for all
whose purposes? - there will be some purposes where the small curvature present is not sufficiently flat. Generally it is too much work to take account of every object in the Universe when we do our calculations so we make approximations in the hope that local events have an influence that far outweighs anything "out there". This is often, but not always, OK. In cosmology, for eg. you seldom get away with it.
By the same reasoning, it seems to me that galaxies cannot influence each other significantly as to cluster together.
And yet they do - so, either the consensus of physics for the last few decades is wrong and you are the first to notice or there is something wrong with the reasoning.
2. Suppose a galaxy has gravitational influence up to say 5 light years.
That would be a pointless supposition since galaxies do have gravitational influence many more than 5ly.
Our own galaxy, by itself, is 100-120,000ly across and held together by gravity - so the influence of gravity extends some 5 orders of magnitude farther than you would have anyone suppose.
You seem to be having trouble with the sorts of distances that are on the cosmological scale.
To my mind, it cannot influence another galaxy that is say 10 light years away from it even if we consider that huge amount of time has passed. It's because the first galaxy cannot 'extend' its influence beyond 5 light years. A galaxy having 'Gravity that has no limit' would require that the galaxy has infinite mass, it seems.
The current models for gravity account for the long-range effects well enough to be useful for modelling large scale structures like galactic clusters. I'm sorry that this seems impossible "to your mind" - it happens to be true.