Shape of Spacetime: Curvature Tensor or Metric?

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SUMMARY

The discussion centers on the relationship between the curvature tensor and the metric in understanding the shape of spacetime. It is established that the curvature tensor is more relevant for this purpose, as it provides critical information about the geometric properties of spacetime. A complex metric may disguise a flat-space scenario, where the curvature tensor would be zero, highlighting the importance of analyzing the curvature tensor over the metric alone.

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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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jfy4 said:
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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