A straight line is a Euclidean concept, It can only be defined in a Euclidean space, an affine space with Euclidean metric. In a more general geometry, the concept of geodesic replaces that of a "straight line".
https://en.wikipedia.org/wiki/Geodesic
A geodesic can be viewed as a curve in the space where an observer traveling along this curve at at constant speed will feel no acceleration forces. On the earth for a example they are the "great circles."