Questions tagged [linearized-theory]

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73 questions
38 views

Linearizing the Lugiato-Lefever Partial Differential Equation

Problem Statement: Given the Lugiato-Lefever equation, linearize the equation and determine the dynamics near a stationary solution by looking for a stationary solution with a small perturbation. ...
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General Relativity Lorentz-like equation

In the literature, it says that, in the weak-field, $$g_{µν} = η_{µν} +h_{µν},$$ slow-motion limit, the Geodesic equation reduces to the Lorentz-like equation. Can anyone explain this?
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Perturbed Ricci tensor due to metric perturbation i.e. $R^{(2)}_{\mu\nu}[h]$ in Linearized theory of Einstein field equation

This is an equation (7.153) from Chapter-7 of Sean Carroll's An introduction to General Relativity: Spacetime and Geometry book. I think all of you who studied GR and went thorugh Carroll's book have ...
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Reference on quantization of linearized gravity

I often see claims saying that quantization of linearized gravity can be done. Is there some standard references for it? such as original papers/ review papers / textbooks etc.
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Perturbation to the flat space metric

from the geodesic equation for non-relativistic case where $$v_i\ll c$$ $$\frac{dx^i}{dt}\ll1,{\rm for }\ c =1$$ $$\frac{dx^i}{d\tau}\ll\frac{dt}{d\tau}$$using this the geodesic equation for proper ...
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How to get space component of weak field (linearized) metric?

For Minkowski space with a weak gravitational field the metric takes the form $$ds^2 = (1+2\phi)dt^2 -(1-2\phi)(dx^2+dy^2+dz^2),$$ where $\phi$ is the Newtonian gravitational potential. You can get ...
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Is Stokes equation a reduction of Navier-Stokes equations?

The following Stokes problem: $$\begin{cases}-\nu\Delta u+\nabla p=f&,\textrm{in }\Omega\\ \nabla\cdot u=0&, \textrm{in } \Omega\end{cases}$$ is a reduction of the Navier--Stokes equations? ...
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Trace-reversed EFE and linearized gravity

I have a question about the linearized Einstein Field Equations, and in particular about the Newtonian limit. It goes as follows. If one uses the trace-reversed form of the EFE for the 00-component ...
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How to use Ashtekar's variables in classical gravitational physics?

I have often heard of Ashtekar's variables in General Relativity, because of the naturalness with which they would allow a canonical formulation of gravity, useful for a hypothetical quantum gravity ...
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Understanding Boyle's Law and Charles's Law

Boyle's Law is defined as follows: $PV=k$ This implies that $P_{1}V_{1}=P_{2}V_{2}$ is true while temperature and mass of confined gas is constant. This would mean that $P_{2}=P_{1}V_{1}/V_{2}$ ...
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This question is in reference to Exercise 30.4.2 in Thomas Moore's A General Relativity Workbook, which asks you to show that a gauge transformation of the trace-reversed metric perturbation $H_{\mu\... 0answers 68 views A question about the metric in linearised gravity In linearised gravity the usual approach is to perturb the metric around some fixed background (often taken to be Minkowksi). My question is, does one literally perturb the metric tensor itself, i.e.$...
Some applications of fluid dynamics consider the linearised Navier-stokes equation where the advection term $(\vec{u}\cdot\vec{\nabla})\vec{u}$ is dropped. I am trying to build a convincing argument ...