All Questions
Tagged with gravity general-relativity
2,007
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Equation of motion for gravity in scalar-tensor theory
I'm trying to derive equation of motion in Higgs scalar-tensor theory with the Lagrangian given by
$$\mathcal{L}=[\frac{1}{16\pi}\alpha \phi^{\dagger}\phi R+ \frac{1}{2}\phi^{\dagger}_{;\mu}\phi^{;\mu}...
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2
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1
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How to relate a gravitational plane wave to the GW from a binary system?
I have two different forms of gravitational waves that I am trying to reconcile.
A monochromatic GW with angular frequency $\Omega$ propagating in the $\textbf{n}$-direction can be expressed as
$$ ...
- 1,751
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1
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Time dilation and angular velocity
Is angular velocity (the horizontal rotation of a massive disc falling through the air) sensitive to time dilation or invariant to it? Will its angular velocity (speed of rotation) increase, decrease ...
- 95
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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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Question regarding the backreaction of a scalar field in curved spacetime
Lets assume that I start with the following action:
$$
{\mathcal L}_1 = \frac{1}{2} \sqrt{-g} \left( \partial_\mu \phi \partial^\mu \phi - m^2 \phi \right)
$$
where $g_{\mu \nu}$ is a FRW metric and $\...
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References on Newton-Cartan Gravity
I'm interested in learning a bit about Newton-Cartan gravity, and I would like some references on the topic. I am already familiar with differential geometry and general relativity, so those could be ...
-1
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Apparent paradox in general relativity wrt relative gravity, spacetime curvature and time dilation [closed]
Imagine Alice is near a massive black hole and Bob is on the Earth.
Obviously their gravitational fields are different for each other. In other words, their spacetime is flat for themselves but curved ...
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Gravitational Time Dilation: How to find the time difference between orbits at different radii? [closed]
I want to calculate the difference in time measured by a clock at on earths surface (r=6000km), and a geostationary satellite (r=26000km). My approach is as follows:
For simplicity, we consider curves ...
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4
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2
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628
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GR contribution to time dilation when both clocks are falling freely
When reading simplified explanations of time dilation experienced by satellites, such as those used for the GPS and other satellite navigation systems, the time dilation is often presented as having ...
2
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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 $\Gamma^{\mu}_{\alpha\beta}$
$$\Gamma^...
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How does the metric transition from a falling dust-like sphere to the Schwarzschild metric?
Outside a static spherically symmetric body in vacuum lies the Schwarzschild metric. However, when observing a falling sphere from a point near the sphere, it no longer appears spherical. Its opposite ...
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2
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Is the tidal force the only real force-like quality of gravity?
The force we feel when standing on the Earth is electromagnetic in nature. We are accelerated upwards without a coordinate acceleration following due to the curvature of spacetime (that would be the ...
- 450
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When we are on the ground do we still accelerate with 9.8 m/s²? [duplicate]
Do we accelerate with 9.8 m/s² when we are on the ground , if so why we do not fall inside the eart . How is the net force is zero , how many real forces acts on the body ?
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The Lebesgue covering dimension of the Cosmic String interval topology
Take the spacetime $(M,g)$ that satisfies Einstein's Field Equations exactly where $g$ is locally:
$$g= - c^2 dt^2 + d \rho^2 + (\kappa^2 \rho^2 - a^2) d \phi^2 - 2 ac d\phi dt + dz^2 \ $$
in the ...
- 1,268
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Shape of rotating celestial body in general relativity
It is know from hydrostatic equilibrium and Newton mechanic that rotating celestial bodies have a shape of oblate spheroids and this is confirmed by observations of Sun, Earth, etc. But I wonder what ...
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