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Results tagged with general-relativity
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user 124838
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.
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1
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123
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Has this metric (which seems like flat space but isn't) been studied before
I am investigating the metric
$ds^2 = -dt^2 + (1+C)dr^2 + r^2 d\theta^2 + r^2 \sin^2\theta d\phi^2, $
where $C$ is a constant. This intuitively seems like flat space but actually has a non-zero Kret …
0
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1
answer
420
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What is this spacetime metric?
Does anyone know whether this metric has been studied before or if it has a proper name?
$$ds^2 = -dt^2 + e^{2At} dx^2 + e^{2Bt} dy^2 + e^{2Ct} dz^2$$
i.e. a de Sitter metric which has a different e …
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0
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142
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What is the physical reasoning for the weak-field approximation to gravity having a curvatur...
The metric for the weak field approximation to gravity is given by
$ds^2 = -(1-\Phi(r))dt^2 + (1+\Psi(r))\left(dr^2 + r^2d\theta^2 + r^2\sin^2\theta d\phi^2\right)$
When $\Phi(r)=\Psi(r)$, e.g. when …
1
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0
answers
72
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Do negative residues in any decomposition of the graviton propagator lead to ghosts?
When looking at the linearised graviton propagator around a background, one can use several decompositions, e.g. decomposing the perturbation to the background metric $g_{\mu\nu}$ into
$h_{\mu\nu} = …
0
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1
answer
109
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Plane wave propagating in de Sitter spactime
Around a flat background, a plane wave propagating in the $z$ direction is given by
$h_{\mu\nu} = \epsilon_{\mu\nu} \cos(\omega t -kz)$.
What is the generalisation of this to a de Sitter background …
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Plane wave propagating in de Sitter spactime
To lowest order in $\Lambda$, i.e. taking the metric to be Minkowski plus a perturbation from $\Lambda$, plus a perturbation from the plane wave, the plane wave is given in the following papers
The …
2
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1
answer
98
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2nd order perturbation of a charged rotating body
What is the 2nd order perturbation to the flat Minkowski metric $\eta_{ab}$ caused by a charged, rotating body? In particular, if we take a metric $\eta_{ab} + h_{ab} $, what $h_{ab}$ satisfies the Ei …
3
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0
answers
154
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Difficult coordinate transformation
I am trying to introduce a tortoise coordinate for a modified Schwarzschild metric
$$\mathrm{d}s^2=\left(1-\frac{2M\mathop{}\!\mathrm{erf}(r)}{r}\right) \mathrm{d}t^2 + \left(1-\frac{2M\mathop{}\!\ma …
8
votes
1
answer
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Fourier transform in curved spacetimes
When in a flat spacetime, one can use the identity
$$\int^\infty_{-\infty} d^3k~ e^{i \bf{ k \cdot r}} f(k)=\int^\infty_{-\infty} dk ~ k f(k)\sin(kr) $$
Does this generalise to curved spacetimes, f …
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Tensor Index Notation Manipulation
You raise tensors using your metric tensor. For flat spacetime, this is the Minkowski metric $\eta_{\mu\nu}$. You must contract the Minkowski metric with one of the indices of your tensor in order to …
1
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1
answer
429
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Quadrupole moment of Kerr spacetime
In this paper, the Kerr black hole is described as having quadrupole moment of $q=J^2/M$ (which means $q=a^2M$ using $J=aM$) whereas in this paper it says in the abstract that the limiting case of Ker …
0
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1
answer
574
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Deriving the Schwarzschild metric in the weak-field regime
I am trying to derive the weak-field Schwarzschild metric, but starting from the same form as Schwarzschild:
$ds^2=-(1+2\Phi(r))dt^2+(1-2\Psi(r))dr^2 +r^2 d\Omega^2$
which has $R=-2\partial_r^2 \Phi …
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Deriving a Schwarzschild radius using relativistic mass
John Rennie, I think we should clarify that when you go from the second metric to the first, you first perform the transformation $dx^2+dy^2 + dz^2=dr^2 + r^2 d\theta^2+r^2\sin^2\theta d\phi^2$, which …
3
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1
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715
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Commutation relations for inverse d'Alembertian operator
Is there a commutation relation for the inverse d'Alembertian operator in general relativity? i.e. if we define $\Box = g^{\mu\nu}\nabla_\mu\nabla_\nu$ and $\Box \Box^{-1}X_{\alpha_1,\alpha_2...}=X_{\ …