This question of mine actually started shaping in my head first while I was looking for the most fundamental answer for speed of light's value and its property of being the limit. I have convinced myself that it's due to the structure of spacetime, or in other words, because that the spacetime interval is expressed as $ds^2=dx^2+dy^2+dz^2-c^2dt^2$ which is not euclidean (for the limit property part) and has the value $9\times10^{10}$ in front of the $dt^2$ term (for the value part). So from this conclusion, and by knowing the fact that the coefficients of those coordinate terms can change with a "curvature" in spacetime, I wonder if the speed of light can have some other value in different curved regions in spacetime. I don't mean it as differing between different observers in that same curved region but as differing between different observers in different regions with different curvatures.

This question of mine started shaping in my head first while I was looking for the most fundamental answer for the speed of light's value and its property of being the limit. 

I have convinced myself that it's due to the structure of spacetime, or in other words because the spacetime interval is expressed as $ds^2=dx^2+dy^2+dz^2-c^2dt^2$ which is not Euclidean (for the limit property part) and has the value $9\times10^{10}$ in front of the $dt^2$ term (for the value part). 

So from this conclusion, and by knowing the fact that the coefficients of those coordinate terms can change with a "curvature" in spacetime, I wonder if the speed of light can have some other value in different curved regions in spacetime. 

I don't mean it as differing between different observers in that same curved region but as differing between different observers in different regions with different curvatures.