I am wondering if gravity gets or would get stronger with ultra-compression (relativistic level) of matter? This may sound stupid but this is how my thought process went.
Let us assume we have an object at position $x$ and now let us assume we want to pin-point the exact position of the object therefore we start compressing the object to get exact position therefore our $\Delta x$ will get closer and closer to $x$ however if you think about it in quantum sense you will discover that the Heisenberg uncertainty will start to act, so we can say the $\Delta \vec p$ will increase in other words the velocity will increase because of the inequality:
$$\Delta x \Delta \vec p \geq \frac{\hbar}{2}$$
Now since using the Special relativity transformations we can say as a velocity of an object is increased the mass must also increase by:
$$m' = \frac{m} {\sqrt{1 - \frac{v^2}{c^2}}}$$
I can therefore say since the mass increase while compressing due to the uncertainty in momentum.
As a result of this we can say that the overall-mass will increase $m'$ due to compression and now if we were to substitute these into the Newtonian Gravity equations we will get more gravitational force than expected after compression:
$$F' = \frac{Gm'}{r^2} $$
Which is definitely bigger than if the object was not compressed, to express this we can mathematically make this into a inequality:
$$\frac{Gm'}{r^2} > \frac{Gm}{r^2}$$
As a result I could back-up my theory, but using this can we say that the gravity near neutron-stars or black-holes is slightly stronger than expected by the gravitational equation. Is there any proof of this happening or if not what is wrong with my ideology and could someone correct it for me?