Questions tagged [linearized-theory]

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How is the gravitoelectromagnetism approximation of GR valid if it seems to yield unstable solutions?

In the gravitoelectromagnetism approximation of GR, we have equations analogous to Maxwell's equations with some sign changes. As pointed out in another post of mine, this leads to unstable run-away ...
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Is it OK to do this manipulation at the partition function level? (auxiliary fields in quadratic gravity)

Background I am working with the following action in the Euclidean signature ($C^2$ is the Weyl quadratic term): S_B = -\frac{1}{2\kappa^2}\int d^4x\sqrt{g}\left(2\Lambda_C+\zeta R-\...
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What are the differential equations that model a self-propagating gravitational wave in space-time?

Light is a self-propagating wave, but it's very complicated. Imagine, if you will, a wave in space-time that by assumption was self-propagating like light, except that it was a gravitational wave. ...
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1 vote
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Linearization of 1D maps about a fixed unstable point [closed]

Recently, I was going through the paper Controlling Chemical Chaos in a three variable autocatalator system, by Peng et al. Here are the references Although I have been introduced to 1D maps and the ...
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Raising/lowering indices in linearized GR

In linearized general relativity, we have the unperturbed metric and the perturbed metric. In all textbook treatments, they say that they are going to raise and lower indices with the unperturbed ...
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1 vote
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How to measure quantity difference between a nonlinear system of equations and its linearization?

I faced such a problem. I have a nonlinear system for control synthesis and I should compare not only my controllers but also a linear version of my system to describe the legitimacy of this ...
80 views

Can we use flat space coordinates in linearized gravity?

I am studying the production of gravitational waves in linearized general relativity. While it is not mentioned anywhere, I am convinced, that the coordinates used in the derivations I have seen, are ...
70 views

Software for calculating perturbation effects in general relativity

I need to evaluate the Einstein tensor/ Ricci tensor and others in a perturbed metric. Suppose my metric is $g_{ab} =\eta_{ab} +h_{ab}$, where $\eta$ is the Minkowski metric, and $h$ is a small ...
118 views

Why can one neglect terms quadratic in derivatives of $h_{\mu\nu}$ in linearised gravity?

In the linear approximation, terms quadratic in the Christoffel symbols are all neglected in the Riemann Tensor. However, these are not quadratic in the $h_{\mu\nu}$ but quadratic in the derivatives ...
• 31
1 vote
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Geometrical linearization in continuum mechanics

In continuum mechanics, we often make use of "physical and geometrical linearization", e. g. during derivation the Navier-Cauchy equations (c. f. https://en.wikipedia.org/wiki/...
96 views

1st order approximation to energy-momentum tensor of gravitational field

I was studying linearized gravity and this approximation was given without any derivation. It might be clear for others but I'm quite new on GR and I'm not sure how to get this first order ...
• 3,256
1 vote
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How to find the inverse metric in this case? [duplicate]

Caroll, while proving the Newtonian limit takes $$g_{ab} = \eta_{ab} + h_{ab}$$ He then just writes down the inverse metric to 1st order as $$g^{ab} = \eta^{ab} - h^{ab}$$ I don't see how this ...
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Linearized gravity: Derivatives of the metric perturbation

In linearized gravity, the metric is given by the Minkowski metric and a small perturbation, $$g^{\mu\nu} = \eta^{\mu\nu}+h^{\mu\nu},\quad |h^{\mu\nu}|\ll 1.$$ Plugging ...
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Weak-field Einstein's equation approximation

For Einstein's equation $$G_{\mu \nu} + \Lambda g_{\mu \nu} = \frac{8 \pi G}{c^4} T_{\mu \nu}$$ with $G_{\mu \nu} = R_{\mu \nu} - \frac{1}{2} R \, g_{\mu \nu}$ where $R_{\mu \nu}$ is the Ricci ...
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1 vote
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Physical interpretation of the nil ADM mass of gravitational waves

The ADM mass is defined for any asymptotic flat spacetime. Using cartesian coordinates: \tag{1} E_{\text{ADM}} = -\: \frac{1}{16 \pi G} \, \lim_{r \, \rightarrow \, \infty}\oint_{\...
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1 vote
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How does one add matter coupling terms to the linearized Lagrangian for General Relativity?

In Spacetime and Geometry, Dr. Carroll provides a Lagrangian for Einstein's equations in vacuum assuming that the metric can be written in the form $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}$. The ...
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Linearity of electromagnetism and gravity

If we have a very strong electromagnetic field, it stops being linear, Maxwell's equations stop working ($10^6$ Tesla or $10^9$ Newton/Coulomb); Why can't we say the same thing for gravity? Since the ...
3k views

How do photons affect each other gravitationally?

Photons are energy. According to general relativity they should bend space. Assuming two photons pass one another in a large void of empty space how would they gravitationaly affect each other ...
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First order expansion of Euler-Lagrange equations

I know that in field theory Euler Lagrange equations are $p_i-d_\mu p^\mu_i=0$. (Classical notations, $p_i=\frac{\partial L}{\partial y^i}, p_i^\mu=\frac{\partial L}{\partial y^i_\mu}$). Being a ...
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I'm familiar with the Lagrangian for linearized gravity about a flat background, $$\mathcal{L} = \frac{1}{2}[(\partial_\mu h^{\mu\nu} \partial_\nu h - \partial_\mu h^{\rho \sigma} \partial_\rho h^\... 0 votes 1 answer 52 views Linearised Gravity and Motion of Particles in Background Metric Let's say we have two point particles as our matter source. Suppose we want to solve Einstein Equation Perturbatively and obtain the gravitational wave at the linear order. Let us expand around ... • 536 4 votes 1 answer 188 views Is there a Lorentz invariant approximation to General Relativity? Since General Relativity is the most accurate description of gravity is there any possible way to derive a Lorentz invariant theory from:$$R_{\mu\nu}-\frac{1}{2} g_{\mu\nu}R+\Lambda g_{\mu\nu}=kT_{\...
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I am trying to compute Linearzed Einstein Field equation in general background. I mean $g_{\mu\nu} = \bar{g}_{\mu\nu} + h_{\mu\nu}$ and compute R, $R_{\mu\nu}$ and so on. I realized the ...