# General relativity: is curvature of spacetime really required or just a convenient representation?

I'm not really far into the general theory of relativity but already have an important question: are there formulations that can do without spacetime curvature and describe the general theory of relativity/all associated gravitational effects in global cartesian coordinates? Idea: Einstein chose spacetime curvature so that one had not to build gravitational effects into the rest of physics equations like Maxwell's equations. I assume that spacetime curvature provides a convenient way to apply physics laws not related to gravity unmodified locally because at small distances we may use special relativity as an approximation.

Please correct me everywhere I am wrong.

• @Sofia: Embedding curved spaces in flat space doesn't get rid of the fact that they are curved (a sphere is still curved after embedding it in $\mathbb{R}^3$). And I say that "we" don't want to get rid of the curvature because geometric theories like gauge theories and GR perfectly show how "forces" arise from an action principle - which is aesthetically satisfying and amenable to quantization. I see no advantage in trying to get away from geometric theories, since they are a success story (e.g., I think of gauge theories here, and how they solved the confusion that was the particle zoo). – ACuriousMind Jan 14 '15 at 17:32