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Suekdccia

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- TL;DR Summary
- Approximate local flatness = Approximate local symmetries?

Pseudo-Riemannian manifolds (such as spacetime) are locally Minkowskian and this is very important for relativity since even in a highly curved spacetime, one could locally approximate the spacetime into a flat minkowski one.

However, this would be an approximation. Perhaps this is a naive question but, would this mean that the local symmetries (such as Poincaré, Lorentz...) hold also only approximately?

However, this would be an approximation. Perhaps this is a naive question but, would this mean that the local symmetries (such as Poincaré, Lorentz...) hold also only approximately?