# Questions tagged [linearized-theory]

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### Can linear frame dragging cause gravitational dipole radiation?

I have just learned that linear frame dragging exists in General Relativity. I have also seen simulations where a periodically accelerated and decelerated mass causes a sort of gravitational dipole ...
1 vote
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### Does Hooke's Law apply to all springs?

I understand that Hooke's Law is $F=-kx$, and that this law only applies when a spring is not "overstreched." However, does Hooke's Law apply to all springs, or only simple harmonic ...
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### Second-order Lagrangian of Einstein-Hilbert action

I'm having trouble deriving the equation (44) of https://arxiv.org/abs/1710.08863 . The question is how to get the second-order lagrangian of the Einstein-Hilbert action, i.e. \begin{equation} \...
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### How to justify this small angle approximation $\dot{\theta}^2=0$?

Suppose the equation of motion for some oscillating system takes the following form: $$\ddot{\theta}+\dot{\theta}^2\sin\theta+k^2\theta\cos\theta=0$$ Applying small angle approximation to $\theta$ ...
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### General relativity 2 particle problem with negative mass

I am looking at a problem of 2-particle system of which one has negative mass. I have situation described on Wiki under section "Runaway motion". Prticulary, if we assume, that negative mass ...
1 vote
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In linearized gravity, where we take a general background metric $g$ with perturbation $h$, the linearized Einstein equations become $$-\square h_{\alpha\beta}+\nabla^{\delta}\nabla_{\alpha}h_{\beta\... 0 votes 0 answers 70 views ### What does it mean to linearize the trace of Gauss-Codazzi relations? What does it mean to linearize the trace of the Gauss-Codazzi relations? The equations referenced above are the following: Reference to the paper: https://arxiv.org/abs/hep-th/0511096 2 votes 1 answer 154 views ### Is a perturbation of a tensor field a tensor field? Let say I take some 2-tensor field T_{\mu\nu} on some pseudo-Riemannian manifold. Now, often, we are interested in its linearization, which means that we take a family of tensor fields T_{\mu\nu}(... 1 vote 1 answer 156 views ### Derive Linearized Einstein's equation from Lagrangian approach Given the Hilbert action:$$ S_{H}=\int \sqrt{|g|}R d^{n}x $$and the metric written in terms of Minkowski and perturbed metric:$$ g_{\mu \nu}=\eta_{\mu \nu}+h_{\mu \nu}. $$I am able to derived the ... 0 votes 1 answer 95 views ### Problem with linearization of Einstein-Hilbert action in de Sitter background For some purpose, I have to calculate the well-known linearization of the Einstein-Hilbert action in the de Sitter background. I encountered a problem: assuming the de Sitter metric, my resulting ... 0 votes 1 answer 228 views ### Einstein-Hilbert Lagrangian in linearized gravity The Einstein-Hilbert Lagrangian is:$$\mathcal{L}_{EH}=\sqrt{-g} R$$where g={\rm Det}[g_{\mu\nu}] and R is the Ricci scalar. In linearized gravity g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu} and$$\... 113 views

### Gravitoelectromagnetism: How far does the analogy go?

In weak gravitaional fields, we can write equations analogous to the Maxwell equations: Gravitoelectromagnetism. Do the gravitoelectric field and the gravitomagnetic field transform like components ...
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### Details of using flat metric to raise/lower indices in linearized GR. I'm getting first order discrepancies

This question is about the use of the unperturbed (Minkowski) metric $\eta_{\mu\nu}$ (and its inverse $\eta^{\mu\nu}$) to raise and lower indices in linearized gravity. There are already several ...
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### Projection on transverse traceless Gauge

I am reading this book about Gravitational waves. On page 10 and 11 Maggiore says that Given a plane wave solution $h_{\mu\nu}$ propagating in the direction $\hat{n}$, outside the sources, already in ... From the Linearized Einstein Field Equation, we have $\Box\bar{h}_{\mu \nu} =-16\pi GT_{\mu \nu}$. How can I obtain conservation of energy and momentum, $T_{\mu \nu},^{\nu}=0$, from the previous ...