Let $X$ be a smooth projective variety over $\mathbb{C}$. For an ample divisor H, we can define the slop of vector bundle with respect to $H$, then we can define stablilty of vector bundle with respect to $H$. However it might be possible that an $H$-stable vector bundle is no longer stable with respect to another ample divisor $H'$.

On the other hand the famous theory of Uhlenbeck-Yau about irreducible representation and stable bundle implies that if a vector bundle has trivial Chern classes, then its stablility does not depend on the ample divisor. I wonder is there a direct proof of this fact without using Uhlenbeck-Yau thoery?

A natural question to ask : does the statement hold in charateristic p case ( one may need some condition like algebraic closed field, the variety has $W_2$-lifting, etc.)?