All Questions
122
questions
1
vote
0
answers
39
views
How does the light from distant stars change for an observer at the center of the collapsing or falling sphere?
At the center of a spherically symmetric thin solid static shell lies a point observer. For this observer, distant stars appear violet shifted slightly more $\frac{{G \cdot M}}{{{c^2} \cdot r}}$ ($\...
- 201
2
votes
0
answers
69
views
Compute the difference between the Christoffel symbols compatible with two different metric tensors
Imagine I have two metric tensors $g_{\alpha\beta}$ and $\hat{g}_{\alpha\beta}$ on the same manifold M and two metric-compatible, torsion free Christoffel symbols $\Gamma^{\mu}_{\alpha\beta}$
$$\Gamma^...
- 4,827
1
vote
1
answer
68
views
How does the metric transition from a falling dust-like sphere to the Schwarzschild metric?
Outside a static spherically symmetric body in vacuum lies the Schwarzschild metric. However, when observing a falling sphere from a point near the sphere, it no longer appears spherical. Its opposite ...
- 201
0
votes
0
answers
20
views
What modifications/corrections are made by $f(R)$ gravity model on Morris-Thorne wormhole metric?
What modifications/corrections are made by the $f(R)$ gravity model on the Morris-Thorne wormhole metric? Specifically, how does the physics associated with the metric change in $f(R)$ gravity compare ...
4
votes
1
answer
113
views
What is the gravitational field of an accelerated particle?
Could we simply change coordinates of the Schwarzschild metric in order to obtain the metric of a moving massive particle? Which would those coordinates be? Rindler coordinates? Maybe there is a ...
- 391
2
votes
2
answers
94
views
Why is the density in GR equal to $\rho_0\dfrac{dx^0}{ds}\sqrt{-g}$?
In general relativity, the continuity equation says
$$
\partial_{\mu}\left(\rho_0c\dfrac{dx^{\mu}}{ds}\sqrt{-g}\right) = 0
$$
with $\rho_0$ being the proper density, as seen by an observer who is at ...
- 391
2
votes
2
answers
2k
views
What kind of coordinate change is needed to make gravity disappear?
I understand that the Christoffel symbols associated with the metric will vanish locally once you perform the appropiate change of coordinates. These new coordinates correspond to an observer in free-...
- 391
1
vote
0
answers
97
views
Writing a gravity equation
I need a maple cod to variation this action with respect to tensor metric $g_{\mu\nu}$.
This called the Einstein equation. To obtain the Einstein equation, we vary the action with respect to the ...
1
vote
1
answer
151
views
Star Radius in the Oppenheimer-Snyder metric using ADM formalism
I'm working with gravitational collapse models, in particular with the Oppenheimer-Snyder model.
Short list of the assumptions for those unfamiliar with the model, you have a spherical symmetric ...
- 1,611
0
votes
0
answers
40
views
Does a tangential vector experience length contraction when moved in radial direction through Schwarzschild metric?
Let's have a look at the Schwarzschild solution. Let's consider only the spatial part since my question is only regarding length contraction.
There is the coefficient of the radial component, it's $\...
- 93
4
votes
1
answer
334
views
How to determine whether a metric meets the Kerr-Schild form?
A Kerr-Schild metric can be expressed as $$g_{\mu\nu}=\eta_{\mu\nu}+\phi k_\mu k_\nu,$$ where
$\eta_{\mu\nu}$ is Minkowski metric, $\phi$ is a scalar function and $k_\mu$ is a (co)vector field which ...
- 113
2
votes
1
answer
143
views
Question on Tolman-Oppenheimer-Volkoff (TOV) equation for time-dependent spacetimes [closed]
Is there a way to conceive a TOV equation, and therefore the stability analysis for a metric like:
$$ ds^2 = -dt^2 + a^2(t,r)\big(dr^2 + r^2d\Omega ^2\big)~?\tag{1}$$
- 3,085
1
vote
1
answer
123
views
How is this approximation of gravity involving Rindler coordinates valid?
I have seen that it is possible to approximate the metric in the presence of a gravitational field by the Rindler metric:
Does a uniform gravitational field exist? Is there any acceleration in a ...
- 8,640
2
votes
1
answer
69
views
Question on the spacetime outside Earth
The general metric for a slowly rotating body is $[1]$:
$$ds^{2} = -B(r)dt^{2}+A(r)dr^{2}+r^{2}[d\theta^{2}+sin^{2}\theta(d\phi-\Omega(r,\theta)dt)^{2}]\tag{1}$$
My question is:
Considering $\Omega = \...
- 3,085
0
votes
1
answer
132
views
Junction Conditions: In what cases is matching the extrinsic curvature at a boundary tantamount to matching metric derivatives at the boundary?
My understanding of the Israel junction conditions are as they are laid out in Poisson's "A Relativist's Toolkit", namely that if one wishes to join 2 different spacetimes across some ...
- 19