Question on General Relativity

In summary, the conversation discusses the Newtonian limit of linearized gravity in chapter 4.4a of General Relativity by Wald. It explains that in weak gravity, the linear approximation of GR is valid and there is a global inertial coordinate system where the energy-momentum tensor can be approximated as T_{ab} \approx \rho t_a t_b. The speaker then questions how this relates to the velocity of the observer and the coordinate system, and it is clarified that the components of the velocity vector are given by v^{\mu} = \frac{dx^{\mu}}{d\tau} \approx (1,0,0,0), which is the non-relativistic limit.
  • #1
eoghan
210
7
Hi!
I'm reading General Relativity by Wald. In chpater 4.4a about Newtonian limit of linearized gravity, it says:
"When gravity is weak, the linear approximation to GR should be valid. The assumptions about the sources (relative motion << c and material stresses << mass-energy density) then can be formulated more precisely as follows: there exists a global inertial coordinate system of [itex]\eta_{ab}[/itex] such that:
[tex]
T_{ab} \approx \rho t_a t_b
[/tex]
where [itex]t_a=(\frac{\partial}{\partial x^0})_a[/itex] is the "time direction" of this coordinate system."

I've always thought that
[tex]
T_{ab} \approx \rho v_a v_b
[/tex]
where v is the velocity of the observer (or in other words, the relative velocity between the source and the observer). So, how can I say that
[tex]
v_a=(\frac{\partial}{\partial x^0})_a
[/tex]
?
 
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  • #2
That means that the components [itex]v^{\mu}[/itex] of the velocity vector are given by

[tex]
v^{\mu} = \frac{dx^{\mu}}{d\tau} \approx (1,0,0,0)
[/tex]

This is the same as saying

[tex]
\frac{dx^0}{d\tau} > > \frac{dx^i}{d\tau}
[/tex]

which is the non-relativistic limit.
 
  • #3
Thank you!
 

FAQ: Question on General Relativity

What is General Relativity?

General Relativity is a theory of gravity proposed by Albert Einstein in 1915. It describes gravity as the curvature of space and time caused by the presence of massive objects.

How does General Relativity differ from Newton's theory of gravity?

Newton's theory of gravity describes gravity as a force between two objects, while General Relativity explains it as a result of the curvature of space and time.

What is the significance of General Relativity?

General Relativity has been confirmed by numerous experiments and observations, and it is considered one of the most successful theories in physics. It has also led to important discoveries, such as the prediction of black holes.

Can you explain the concept of spacetime in General Relativity?

In General Relativity, spacetime is a four-dimensional mathematical framework that combines three-dimensional space and one-dimensional time. It is used to describe the curvature of space and time caused by massive objects.

How has General Relativity been tested and verified?

General Relativity has been tested and verified through various experiments, such as the bending of light by massive objects, the precession of Mercury's orbit, and the observation of gravitational waves. It has also been confirmed by numerous astronomical observations and measurements.

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