Definition of Spatial Velocity in GR Homework

  • Thread starter Thread starter Reedeegi
  • Start date Start date
  • Tags Tags
    Velocity
Reedeegi
Messages
97
Reaction score
0
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]
 
Physics news on Phys.org
Check out this post. They must be talking about the 3-vector I call \vec v. (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.
 
Last edited:

Thread 'Describing the Big Bang'

I started reading a National Geographic article related to the Big Bang. It starts these statements: Gazing up at the stars at night, it’s easy to imagine that space goes on forever. But cosmologists know that the universe actually has limits. First, their best models indicate that space and time had a beginning, a subatomic point called a singularity. This point of intense heat and density rapidly ballooned outward. My first reaction was that this is a layman's approximation to...
View full post »
Thread 'Dirac's integral for the energy-momentum of the gravitational field'

Thread 'Dirac's integral for the energy-momentum of the gravitational field'

See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2) over the 4D "hypercylinder" defined by ##T_1 \le x^0 \le T_2## and ##\mathbf{|x|} \le R##, where ##R## is sufficiently large to include all the matter-energy fields in the system. Then \begin{align} 0 &= \int_V \left[ ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g}\, \right]_{,\nu} d^4 x = \int_{\partial V} ({t_\mu}^\nu + T_\mu^\nu)\sqrt{-g} \, dS_\nu \nonumber\\ &= \left(...
View full post »

Thread 'A sufficient condition for integrability of equation ##\nabla g=0##'

In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
View full post »

Similar threads

A Relativistic Relative Velocity Comp.: Bini, D. et al. (1995)
Replies
9
Views
2K
A Looking for linear frame dragging formula
Replies
3
Views
198
I Only Minkowski or Galilei from Commutative Velocity Composition
Replies
1
Views
2K
A Flow as a fluid-orthogonal foliation
Replies
11
Views
2K
A Relativistic Hydrodynamics Eqn for Perfect Fluid: Insight Needed
Replies
10
Views
2K
I Four-Velocity: Geometric Definition
Replies
17
Views
2K
I Why Must Pure Force Depend on 4-Velocity?
Replies
47
Views
5K
I I want a good reference to a discussion of the meaning of "the speed of light is constant"
2
Replies
60
Views
4K
I Einstein Definition of Simultaneity for Langevin Observers
Replies
12
Views
2K
I What is the velocity of the photon through the fourth dimension x4?
Replies
14
Views
3K

Hot Threads

Recent Insights

Back
Top