All Questions
Tagged with gravity metric-tensor
138
questions
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39
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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
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69
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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 $\Gamma^{\mu}_{\alpha\beta}$
$$\Gamma^...
- 4,827
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68
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How does the metric transition from a falling dust-like sphere to the Schwarzschild metric?
Outside a static spherically symmetric body in vacuum lies the Schwarzschild metric. However, when observing a falling sphere from a point near the sphere, it no longer appears spherical. Its opposite ...
- 201
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32
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General formulea for describing the refractive index at any point within the a black hole's gravitational field approaching the event horizon?
So, say I describe a perfectly linear field expanding outward from a point (A signed distance field of a sphere, basically) (as described by sqrt(x^2 + y^2 + z^2) ...
- 111
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What modifications/corrections are made by $f(R)$ gravity model on Morris-Thorne wormhole metric?
What modifications/corrections are made by the $f(R)$ gravity model on the Morris-Thorne wormhole metric? Specifically, how does the physics associated with the metric change in $f(R)$ gravity compare ...
4
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1
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113
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What is the gravitational field of an accelerated particle?
Could we simply change coordinates of the Schwarzschild metric in order to obtain the metric of a moving massive particle? Which would those coordinates be? Rindler coordinates? Maybe there is a ...
- 391
2
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2
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94
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Why is the density in GR equal to $\rho_0\dfrac{dx^0}{ds}\sqrt{-g}$?
In general relativity, the continuity equation says
$$
\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
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80
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Heisenberg's microscope and gravity [closed]
Is the Heisenberg's microscope gedanken experiment valid when considering spacetime kinematics?
That is, if we consider a small region of space and try to measure its curvature, then we may use ...
- 735
2
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2
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2k
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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
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48
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Calculating an arbitrary metric tensor (field) in vacuum: Make use of the constant speed of light?
The metric (=field of metric tensors) is the solution of Einstein's field equations when a special distribution of matter is given. It is among the unsolved problems of physics to calculate the metric ...
- 93
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97
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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
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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
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0
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40
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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
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334
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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,$$ where
$\eta_{\mu\nu}$ is Minkowski metric, $\phi$ is a scalar function and $k_\mu$ is a (co)vector field which ...
- 113
2
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1
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143
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Question on Tolman-Oppenheimer-Volkoff (TOV) equation for time-dependent spacetimes [closed]
Is there a way to conceive a TOV equation, and therefore the stability analysis for a metric like:
$$ ds^2 = -dt^2 + a^2(t,r)\big(dr^2 + r^2d\Omega ^2\big)~?\tag{1}$$
- 3,085