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i am new at relativity, it said mass can curve spacetime, does this mean spacetime will curve to a new 5th dimension (1-3 for space dimension, 4 for time dimension)?
No, it doesn't mean that.i am new at relativity, it said mass can curve spacetime, does this mean spacetime will curve to a new 5th dimension (1-3 for space dimension, 4 for time dimension)?
Bit of a contrived example, but consider the surface of a hemisphere. Project this surface vertically onto its equatorial plane. Inherit the distance metric from the original hemisphere to judge "straight lines" in the resulting space. It now has intrinsic but not extrinsic curvature.I suppose it might have intrinsic curvature but not extrinsic
Or the other way around, I guess. Embed the manifold in a higher dimensional manifold whose metric is contrived to match that of the embedded manifold where appropriate.Bit of a contrived example, but consider the surface of a hemisphere. Project this surface vertically onto its equatorial plane. Inherit the distance metric from the original hemisphere to judge "straight lines" in the resulting space. It now has intrinsic but not extrinsic curvature.