Shape of spacetime

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hello,

quick question, If i am interested in the shape of space time, am i interested in the curvature tensor, or the metric?

Thanks
 

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bcrowell
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quick question, If i am interested in the shape of space time, am i interested in the curvature tensor, or the metric?
The curvature tensor is more relevant. E.g., you can have a metric that looks very complicated, but is actually a flat-space metric expressed in funky coordinates. In this situation, the curvature tensor would vanish, and knowing that would be more informative than just staring at the metric.
 

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