All Questions
Tagged with terminology general-relativity
86
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GR and Riemann Surfaces -- does the complex plane have anything to do with it?
I have only the vaguest understanding of Riemann Surfaces -- my sense is that Einstein used them in General Relativity because of their shape.
But Riemann Surfaces I think are not just deformations of ...
- 2,238
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66
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Name of metric used by Friedmann
In his original paper, Friedmann used the following dynamic and symmetrical metric:
$$\mathrm{d}s^2=a(t)^2\left(\mathrm{d}\chi^2+\sin (\chi)^2\left(\mathrm{d}\theta^2+\sin (\theta)^2 \mathrm{d}\phi^2\...
- 181
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2
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Equations of motion in general relativity: Einstein field equations vs geodesic equation
It is said that the equations of motion of a theory are those whose solutions give the coordinates/trajectory of the system.
I was wondering: which is the correct equation of motion in the theory of ...
- 309
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826
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Why do we call the Riemann curvature tensor the curvature of spacetime rather than the curvature tensor of its tangent bundle?
I was studying the mathematical description of gauge theories (in terms of bundle, connection, curvature,...) and something bothers me in the terminology when I compare it with general relativity.
In ...
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What is a hypersurface?
What is the concept of hypersurface in general relativity? I know it could be characterized into three categories but how do we define hypersurface (in general) in physics? I didn't get what thing it ...
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Dust solutions in general relativity
What is the precise definition of a dust solution in general relativity?
If the Einstein tensor of a metric has only the first diagonal term non-zero, it that sufficient for that solution to be called ...
- 97
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1
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82
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What is a "timelike half-curve"?
I know what a timelike curve is. But what is a time-like half-curve, as in the definition of a Malament-Hogarth spacetime (below), which appears in this paper?
Definition: A spacetime $(M,g)$ is ...
- 121
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75
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Looking for the name of the spacetime interval with exponential
I have the following invariant: $$ds^2=e^{v(r,t)} c^2 dt^2 -r^2\left( d \theta^2 + sin^2(\theta) d \phi^2 \right) - e^{\lambda(r,t)}d r^2$$
for the centrally symmetric gravitational field. And I would ...
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Why do we call it "Euclidean Quantum Gravity" instead of "Riemannian Quantum Gravity"?
Euclidean quantum gravity is an approach to quantum gravity based on working with Riemannian-signature manifolds and eventually relating the results to our Lorentzian spacetime by means of analytic ...
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Conceptual relations between tick indications of a clock and corresponding tick-response indications of a receiver observing that clock
Descriptions of setups and findings involving clocks can also involve distinct observers (in the following a.k.a. receivers) which (in general) perceived, and possibly then analyze, relevant signals ...
- 4,306
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137
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Hawking & Ellis: typo on page 16?
On page 16 of The Large Scale Structure of Space-Time (1973) by Hawking and Ellis, they describe the basics of tangent spaces. This line appears near the top of the page:
Thus the tangent vectors at $...
- 824
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2
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622
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Confused on the types of solutions to Einstein field equations in General Relativity
Context
While reading about the types of solutions to The Einstein Field Equations in General Relativity, I came across the following article.
Where they explain that Karl Schwarzschild provided the ...
- 398
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"Lorentz gauge" or "Lorenz gauge"?
In electrodynamics there is a gauge condition named after Ludvig Lorenz: $$\partial^\mu A_\mu = 0.$$
In general relativity we also have a gauge condition defined as follow:
$$\partial_\mu \gamma^{\mu\...
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981
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What is the difference between the metric (tensor), $g_{\mu\nu}$, and the invariant interval, ${ds}^2$?
Here is a question from a problem sheet I found which I'm going to use to illustrate a point:
The $\color{red}{\text{metric}}$ on a unit sphere is $${ds}^2={d \theta}^2+{\sin}^2\theta\, {d\phi}^2\tag{...
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The "Proper Time Experiments" of C. O. Alley et al.: Did the airborne clocks run longer than the groundbased clocks (rather than running faster)?
Description and results of the so-called "proper time experiments" which were carried out 1975-76 based at the Patuxent Naval Air Test Center, a.k.a. "the Maryland experiment", are ...
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