What is curved spacetime: Definition and 3 Discussions

Curved space often refers to a spatial geometry which is not "flat", where a flat space has zero curvature, as described by Euclidean geometry. Curved spaces can generally be described by Riemannian geometry though some simple cases can be described in other ways. Curved spaces play an essential role in general relativity, where gravity is often visualized as curved space. The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation for the description of the expansion of space and shape of the universe.

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  1. Vanadium 50

    I Black Holes in Curved Spacetime

    We've been talking in another thread about supermassive black holes. That has me thinking about really, really big BH's - so large that the spacetime curvature and evolution of the universe matters. Let's start by defining the density of a black hole as its mass divided by the volume enclosed...
  2. cianfa72

    I About global inertial frame in GR - revisited

    Hi, reading this old thread I'd like a clarification about the following: Fermi Normal hypersurface at an event on a comoving FLRW worldline is defined by the collection of spacetime orthogonal geodesics. Such geodesics should be spacelike since they are orthogonal to the timelike comoving...
  3. H

    I Curved spacetime and measurement direction

    To be specific, let's say that two photons in EPR entangled state were sent to Alice and Bob separated by billions of light years. We know that if they measure their photon polarizations in the same direction, they certainly get the same result. My question is, what is the same direction in...
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