Space curvature Definition and 23 Threads

As discussed in this thread, for a symmetric spacetime (i.e. with a KVF) there are conserved quantities as constants of motion. For instance in Schwarzschild spacetime there is a timelike KVF, hence for example the contraction of a geodesic tangent vector (4-velocity) and the timelike KVF...

Pseudo-Riemannian manifolds (such as spacetime) are locally Minkowskian and this is very important for relativity since even in a highly curved spacetime, one could locally approximate the spacetime into a flat minkowski one. However, this would be an approximation. Perhaps this is a naive...

Disclaimer - I am not an expert by any means so this might be as much about confirming my understanding as an inquiry from the general public... as such, it might be fairly conversational as I attempt to clearly communicate my thoughts and understanding. Please excuse this. If gravity is the...

When people try to explain how gravity works, the following example is constantly used . However, I don’t understand how this explains HOW gravity works. By using this example, gravity itself is used as a bias to explain how gravity works. How can explain gravity by saying “things fall along...

Hi everyone. I'd like to verify my thoughts about travellig through space using a space curvature. Imagine you have a spaceship and you want to travel some distance. Your ship launches an object into space that has huge mass and density. It curves space. Now, you enter the curved space and...

Excuse me for bad wording in the title, but there is only so much you can do with the character limit. So, has there ever been a proposal for a mechanism through which negative energy density could be created? Or the only possibility considered so far was that it would have been created in the...

So I'm an Software Engineer, not a physicist, nor a mathematician. So I like to work in the qualitative, not the quantitative. Today I hit on a problem. I've been trying to remove the concept of "down" or "inward" from my thinking of gravity and GR. When people show the concept of space/time...

I'm a complete rookie in this field so please correct me where I go wrong, I just really want a better understanding of this subject. So as far as I am aware, mass causes the space surrounding it to curve or bend. What I want to know is how much does it bend the space? is the bending of space...

I have some questions about the curvature of space (NB not of spacetime) near a planet like Earth. Unambiguously defining space curvature requires choice of a coordinate system, so I choose the Swarzschild system. Here are my questions: Would constant-time hypersurfaces under the Swarzschild...

I want to program space curvature vizualizaion. I want to have an observer as a player that moves in 3d curved space and surrounding objects that will show curvature by distortion when player passes near them. I am concerned about some points: 1. What curvature to choose in order to experience...

Dear PF Forum, I just want to ask a simple question. Even if we are at rest (ignoring that the Earth rotates, evolves around the sun, orbitting SMBH and Milky way orbitting what? Virgo Supercluster? And Virgo Supercluster to what?), A. So even if we are at "rest" (blue line), are we always...

Gravity causes spacetime to warp. Relative speed also causes an apparent warp from the point of view of the stationary observer. But warp due to relative speed will cause rods to contract, rods will effectively measure shorter for the stationary observer. Accordingly we should also infer that...

Currently reading Peter Coles, Cosmology a very short introduction. There is a bit I don't understand. In a section discussing Friedmann Models, and how going on the cosmological principle density of the universe is the same in every place, and therefore space must be warped in the same way at...

When does the arc of the space curvature is large and when is it small?

Now, I know that tittle is messy, so I'm going to explain it as clearly I can. One of the proofs to the fact that time is relative is, as I've heard. Putting one clock on the ground, and another a few feets above it. When these clocks measure time, the one above the ground will do it faster...

Hello there. I'm new to the forums obviously. And I'm also quite new to physics. I've read many existing answers about how this works but I can't really understand how it would logically work out. From what I've understood. Gravity is not a force. Objects move in a straight line unaltered by...

Can we say that each subatomic particle affects space time such that collectively as big as a planet it explains why there is gravity? Thank you very much.

Hi, i read a few books (pop ones) and one thing that left me thoroughly confused was the relation between graviton and space curvature, is there any relation between the two... if we find a graviton then does it mean that space is not curved? regards Monty

Yes, general relativity is out of my depths for now. Now I've often seen drawings of a gravitational source represented by a dimple ( downward ) on a surface. Yet GR never speaks of a fifth dimension. Nor have I ever seen a dimple upwards that I would suppose would represent repulsive gravity...

I will be writing my final exam tomorrow evening, and I am currently terribly stuck on the following practice problems. I have posted my thoughts below each problem. They look tricky to me. It would be very nice if someone could help me out and I will remain eternally grateful for your help...

hi how is space curvature around a mass. i mean what's its direction in real 3D space? [ i know it is simillar to a rubber sheet with a ball on it, but it is 2 dimentional. i want its real demonstration. just like real world.]

Is it true that space can be curved around and loop itself to a point in the past? If this is true, then time travel to the future and the past should be theoreticly posible. I'm trying to further uderstand relativity, this is why I ask. If we could travel to the past, maybe we can really see...

ok, i know that this has in someway been answered before, and i am new here, i also am by far not a geometry major, but that is why i am asking here, because you peopl eknow this stuff. so here is the question the standard definition of parallel lines are two lines on the same plane that are...