Where can I find examples for solving equations of motion in Relativity?

  • Thread starter Thread starter jixe
  • Start date Start date
  • Tags Tags
    Relativity
jixe
Messages
4
Reaction score
0
Hi,

I am a new GR student and struggling a bit, to be honest. Usually in this situation I saturate myself with working through examples and eventually the penny drops, but I have not been able to find a text or any lecture notes etc. that provides examples of things like solving geodesic equations of motion given a metric ( they don't all seem responsive to the Lagrangian approach) or rewriting metrics or equations of motion in a different coordinate system etc.etc.
Can anyone help by suggesting a text?

Thanks
 
Physics news on Phys.org
Thanks robphy. I'll have a look at those.
 
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...
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(...
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...

Similar threads

Replies
2
Views
2K
Replies
57
Views
3K
Replies
7
Views
3K
Replies
12
Views
2K
Replies
11
Views
2K
Replies
38
Views
4K
Back
Top