# Is there a limit to how much spacetime can be curved?

My question is about the fact that general relativity predicts bending of space and time. However, I have not seen anything regarding the limits to how much space or time can be bent. So my question is that is there anything (like a hypothetical short ranged repulsive force) that actually puts some limit or is any 'warping' possible.

• How would you quantify the "amount" of warping? The magnitude of the Ricci scalar at a point seems like a natural candidate. Jan 7 at 9:12
• @NiharKarve Ricci scalar is not the right indicator because it can be zero even when the curvature tensor diverges. Jan 7 at 10:38
• @AndrewSteane you're right. I was just trying to think of a way in which OP's idea of magnitude of curvature could be converted to GR terms. Of course you'll actually need to analyse all the scalars that can be formed from the Riemann curvature tensor to see whether there's a honest spacetime singularity Jan 7 at 10:50
• We can probably use the principal invariants of the curvature tensor, such as the Kretschmann scalar. Jan 13 at 2:12

The short answer is no. The components of the Riemann tensor, which is an object measuring the curvature of the manifold at a point, can take any real number value. In classical GR, there's nothing which bounds these numbers, but when they diverge to infinity at a point it indicates a problem with our classical description (see discussions of singularities in GR for more details about this).

• I don't think the components are in any sense physically meaningful. Seems to me that unless the Riemann tensor is identically 0 you can make any one component arbitrarily large by applying diffeomorphisms of spacetime. Jan 8 at 9:42
• Yes exactly we can make any component arbitaryily large so no limit Jan 8 at 11:24

The only thing I would consider to be a "limit" to spacetime curving in general relativity is a gravitational singularity:

A gravitational singularity, spacetime singularity or simply singularity is a location in spacetime where the mass and gravitational field of a celestial body is predicted to become infinite by general relativity in a way that does not depend on the coordinate system.

Gravitational Singularity - Wikipedia

The most common singularities are in black holes where the density and thus the "warping" of spacetime is considered to be infinite. However, this singularity cannot be described by general relativity - a theory of quantum gravity would be needed.

This answer does not make any statement on how much curvature can be described by general relativity; I am probably missing something here (I also only have a basic non-mathematical understanding of GR). I hope someone else can go into more detail.