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Results tagged with general-relativity
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user 130091
A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.
21
votes
3
answers
4k
views
Is the universe non-linear?
First of all, I've read this other question Is the universe linear? If so, why? and I'm aiming at a different kind of answer.
Theories like General Relativity or QFT, which are believed to be quite f …
- 4,737
8
votes
2
answers
475
views
Horizons and other special surfaces on Kerr metric
The Kerr metric is
\begin{equation}
ds^2 = - \big(1-\frac{2GMr}{\rho^2}\big)dt^2-\frac{2GMra}{\rho^2}\sin^2 \theta \big(dtd\phi+d\phi dt\big)+ \frac{\rho^2}{\Delta}dr^2+\rho^2 d\theta^2 + \frac{\sin^ …
- 4,737
5
votes
4
answers
2k
views
Motivation for the use of 1-forms in General Relativity
During a course I took on General Relativity, the professor started with an introduction on differential geometry. Vectors were properly motivated: he said that since the differential manifold doesn't …
- 4,737
5
votes
1
answer
690
views
What's the difference between a post-Minkowskian approximation and a post-Newtonian one?
I'm studying the book Gravity by Poisson & Will. Specifically, I'm interested in the post-Newtonian and post-Minkowskian approximations showed in chapters 6-10. The problem I'm having is conceptual, I …
- 4,737
4
votes
Physical intuition of raising and lowering indices in GR
All these questions are answered by differential geometry (See Geometrical Methods of Mathematical Physics, by Schutz for a great introduction).
What's the difference between lower and upper index of …
- 4,737
4
votes
1
answer
523
views
Problem with different Equivalence Principle Statements
I'm having trouble understanding the differences between the different forms of the Equivalence Principle. I've search in other questions and I think that this was not previously asked, at least in th …
- 4,737
3
votes
0
answers
157
views
Is there a Virial theorem in General Relativity?
I know that in Newtonian mechanics one can derive the virial theorem for $N$ gravitating particles
\begin{equation}
2\langle T\rangle=-\langle U\rangle
\end{equation}
where $T$ is the kinetic energy …
- 4,737
3
votes
2
answers
188
views
Why do we need 3 variables to parametrize $\scr{I}^\pm$ in a Penrose diagram?
In the figure we can see the Penrose diagram for Minkowski space
If I understand correctly, $i^-$ and $\scr{I}^-$ have coordinates $r=\infty$ and $t=-\infty$ while $i^+$ and $\scr{I}^+$ have coordi …
- 4,737
3
votes
1
answer
356
views
Cosmological understanding from Penrose diagram of de Sitter spacetime
The conformal diagram of de Sitter spacetime looks like this
I think I understand the causal properties of this diagram. Someone who is static in the south pole can send messages only to the upper ri …
- 4,737
3
votes
2
answers
1k
views
Why is 4-velocity not defined as the covariant derivative of position instead of the regular... [duplicate]
The geodesic equation is usually written as
\begin{equation}
D_\tau u^\mu = 0
\end{equation}
where $D_\tau= u^\mu \nabla_\mu$ is the covariant proper time derivative and $u^\mu=\frac{dx^\mu}{d\tau}$ i …
- 4,737
2
votes
2
answers
638
views
Laws of physics and diffeomorphism covariance
Up to my limited understanding, diffeomorphisms on a space-time manifold can be viewed as changes of coordinates. While studying general relativty, I read that the theory has diffemorphism covariance …
- 4,737
2
votes
2
answers
239
views
Misconception about index notation
I'm going to give an example in General Relativity but this is a question about index notation and coordinate transformations in general. In "Spacetime and Geometry" by Sean Caroll, there is this defi …
- 4,737
2
votes
0
answers
278
views
Chern-Simons Gravity term in 3D and equations of motion
In the book "Quantum Gravity in 2+1 dimensions" by Steven Carlip he writes down a possible modification to the Einstein-Hilbert Action in 3d (eq. 1.16 to eq. 1.18)
\begin{equation}
I_{GCS}=-\frac{1}{ …
- 4,737
2
votes
0
answers
80
views
Degrees of Freedom in the Newman-Penrose Formalism
In the Newman-Penrose formalism one encodes the ten degrees of freedom of the Weyl tensor $C_{\alpha\beta\mu\nu}$ in the five complex scalar potentials $\Psi_0$, $\Psi_1$, $\Psi_2$, $\Psi_3$ and $\Psi …
- 4,737
2
votes
2
answers
601
views
How to integrate a tensor in curved spacetime?
I've read "We can only define the integral of a scalar function. The integral of a vector or tensor field is meaningless in curved spacetime" on many books and lectures on General Relativity (For exa …
- 4,737