Definition of Spatial Velocity in GR Homework

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In summary, spatial velocity in general relativity is a vector quantity that describes an object's movement in space, taking into account the effects of gravity. It is different from regular velocity and can be calculated using the equation V = (1 - 2GM/rc^2)^-1/2. Spatial velocity can be negative in GR and is affected by the curvature of space-time caused by the distribution of matter and energy.
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Reedeegi
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I was doing some homework for GR when I came across the term "spacial velocity." What is its definition?

It's in the context of finding the spatial velocity using the knowledge of the four-velocity U being U = (1+t^2,t^2,t√2,0) [I don't need help with the problem itself, I just need to know the definition in this context]
 
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Check out this post. They must be talking about the 3-vector I call [itex]\vec v[/itex]. (Note that I'm using units such that c=1).

Oh yeah, and it's spelled "spatial". :biggrin:

Hm, maybe not. Dictionary.com says that "spacial" is OK too.
 
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In the context of general relativity, spatial velocity refers to the rate of change of an object's position in three-dimensional space. It is often denoted as v and can be calculated using the four-velocity U, which represents the object's velocity in four-dimensional spacetime. To find the spatial velocity, one would use the components of U that correspond to the object's position in three-dimensional space, typically the x, y, and z components. In this case, the spatial velocity would be v = (t^2, t√2, 0). I hope this helps clarify the definition for you.
 

Related to Definition of Spatial Velocity in GR Homework

1. What is the definition of spatial velocity in general relativity (GR)?

In general relativity, spatial velocity is defined as the rate of change of an object's position in space over time, taking into account the effects of gravity. It is a vector quantity that describes the direction and magnitude of an object's movement in space.

2. How is spatial velocity different from regular velocity?

Spatial velocity is different from regular velocity in that it takes into account the effects of gravity, which can warp the fabric of space-time. In general relativity, objects do not move in a straight line at a constant speed like they do in classical physics, so spatial velocity is a more accurate measure of an object's movement.

3. What is the equation for calculating spatial velocity in GR?

The equation for calculating spatial velocity in general relativity is V = (1 - 2GM/rc^2)^-1/2, where G is the gravitational constant, M is the mass of the object, r is the distance from the center of mass, and c is the speed of light.

4. Can spatial velocity be negative in GR?

Yes, spatial velocity can be negative in general relativity. This means that the object is moving in the opposite direction of its initial position, but with the same magnitude. This can occur if the object is under the influence of a strong gravitational field, such as near a black hole.

5. How does spatial velocity relate to the curvature of space-time in GR?

In general relativity, the curvature of space-time is directly related to the distribution of matter and energy. This curvature affects the spatial velocity of objects by altering the paths they take in space. As an object moves through a curved space-time, its spatial velocity will change, even if its regular velocity remains constant.

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