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# Questions tagged [curvature]

Use this for questions pertaining to curvature of manifolds. Does not need to be specific to general relativity, but also for curvature of e.g. a [tag:calabi-yau] manifold.

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### How to interprete this singularity?

I am calculating the Kretschmann scalar for the Schwartzchild metric. This is the graphic I get: Where $R$ is the radial coordinate and $x=\cos(\theta)$. So, there is the singularity at $R=0$ as it ...
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### Determining geometry/topology from a Line Element

Is it possible given a line element, to determine its geometry? For example whether the line element $ds^2$ of a 2D surface corresponds to $\mathbb{R}^2$ or $S^2$ geometry?
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### Part of a bigger question about spacetime geometry

This is a two-part question. First: I'm imagining that a laser with infinite coherence length is used to shine light toward a black hole from far away. A mirror is placed a few Schwarzchild radii ...
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### Curvature and Symmetries of spacetime

Is there any relation between symmetries of spacetime and the curvature invariants? For example is spherical symmetric spacetimes, necessarily have positive curvature? Could we define any spherical ...
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### How can the Milne model of the Universe have curvature? [duplicate]

The title says it all. The Milne model of the universe is a model where the universe is empty, there is no matter at all, yet the spatial curvature is different from 0. I'd expect that a spacetime ...
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### maximally symmetric spacetime

An empty spacetime has zero or constant Ricci Scalar (depending on the cosmological constant). Is there a theorem which guarantees that such a spacetime should be Minkowski or dS/AdS? In other words, ...
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### Spacetime curvature is relative?

I have the following conceptual doubt. These are my assumptions: 1) The geometry of spacetime is the same for all observers, regardless their motion 2) All motion is relative (both uniform and not ...
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### Euclidean view in curved manifold

Let's suppose I am an ant who lives in a 2D curved space. Locally the world seems 2d-euclidean to me, but it is not if I consider a large portion of space. Now let's consider a human being who lives ...
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### Pseudo-Riemannian 2D manifold (visualize time curvature)

My goal is to visualize somehow the curvature of time, as opposed to the curvature of space. I know that we generally talk about spacetime curvature altogether; however, the fact that spacetime has ...
201 views

### Why does nobody ever consider the possibility that the universe is not smooth?

Disclaimer: I'm not an astronomer, physicist, mathematician, etc. so this is a question from a complete newbie. One of the greatest mysteries of our age is "where is the dark matter?" The universe ...
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### Weak Solutions to the Einstein Equation across a Junction

Consider the principle part, i.e., the part which contains the highest derivatives of the metric (which is the $2^{nd}$ derivative) is \mathcal{P}\{R_{ab}\}=\frac{1}{2}g^{cd}\left(\partial_{a}\...
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### Does cosmological expansion change the gravitational field around a massive body?

Do expanding universe affect the curvature of spacetime? If so, does Einstein's field equation account for the change in curvature (gravitational field) around massive object in the expanding universe?...
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### Intrinsic curvature calculation

Gauss theorem egregium says that it is possible for the inhabitants of a 2d surface to calculate the surface curvature without knowing that it is embedded in a 3d euclidean space, simply calculating ...
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### Curved space relative motion

Suppose I live in a 2d curved space. I can describe intrinsically the motion of a particle which moves in my 2d manifold using time "t" as a parameter. Now suppose there is a second observer (let's ...
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### Spacetime curvature replaces acceleration?

In my understanding, not only mass but any kind of energy/ force bends spacetime. So is it correct to say that every object in the world moves along geodesic? If the object is submit to a force, it ...
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### Relative kinematics curved space

I know that in a general curved manifold it is possible to describe parametric curves. Then, the length of the curve will be a indipendent from the coordinate system used --> the metric tensor ...
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### Angular velocity in curved space (2d manifold)

In 3d Euclidean geometry, the velocity of any point of a rigid body is given by the cross product between its angular velocity and the position vector which links the instantaneous rotation center to ...
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### Why spacetime fabric don't tears due to mass of heavy black hole?

In GR, All objects create curvatures in the space-time fabric. Why space-time fabric doesn't tear due to the mass of a heavy black hole? What is it made of?