Jaime Rudas's latest activity

This can't be right. By that logic, you can't embed a 2-sphere in Euclidean 3-space since it has positive scalar curvature and every...

Regarding this, I have the following question: Is it possible to embed a flat (Euclidean) two-dimensional surface in a curved...

No, that's not correct. Knowing the spacetime curvature does not tell you the deformation, because spacetime curvature only tells you...

If the paper were oriented radially, then yes, you would be able to draw a triangle on it whose angles would not add up to 180 degrees...

It depends on how the paper is oriented and what its state of motion is. But for a piece of paper of ordinary size and a black hole of...

That's correct. Note, though, that when you have a star in the center instead of a black hole, the spacetime geometry inside the star is...

From this, I understand that for a sphere of area ##A## around a very massive and dense star, its radius ##R## will be greater than...

That's not what I said. What I said is that, if you're observing from a distance objects that are at rest fairly close to a black hole's...

On the other hand, the margin of error in calculating the age of the universe is on the order of hundreds of millions of years, so what...

I consider the radius of the observable universe to be, by definition, the greatest distance that anything could reach during the age of...

I think you underestimate the enormous retrospective adaptability that these "theories" have always demonstrated.

There is a theorem, i think Hilbert, that says that a constant negative curvature surface cannot be embedded isometrically in three...

See this answer: https://physics.stackexchange.com/a/43061

The Gaussian curvature ##K## of the hyperboloid ##x^2+y^2-z^2=1## is ##\frac {-1}{(1+2z^2)^2}##. Thus, when ##z=0##, the curvature...

The German Wikipedia says: Which, translated, would be: I understood that the hyperboloid didn't have constant Gaussian curvature. Am...