3
votes
4answers
151 views

What does it mean by complex frequencies? (Quasinormal Modes)

Something I've taken for granted and not yet thought about physically, is how the frequency of quasinormal modes related to a black hole are $\textit{complex}$. I know that it's something to do with ...
3
votes
1answer
128 views

Metric Perturbations in General Relativity and quasi-normal modes?

I am familiar with the tools that appear in (linear) perturbation theory for general relativity, that is namely that one writes: $$g_{\mu \nu} = g^{(0)}_{\mu \nu} + \epsilon g^{(1)}_{\mu \nu} + ...
1
vote
1answer
276 views

Riemann curvature tensor in first order perturbation theory as a Lie derivative of Riemann curvature tensor in zero order

I am having a difficulty solving my homework so I was hoping I could get some help, so here it is. It is about gravitational waves and first order gravitational perturbation theory, I have to prove ...
1
vote
0answers
71 views

What if UV behaviour of gravity was perturbative?

I understand that the UV behaviour of gravity ought to be dominated by black hole production and that graviton-graviton scattering ought to blow up above the Planck scale. Suppose, however, that ...
7
votes
3answers
283 views

Do gravitational waves cause time dilatation?

The effect of gravitational waves in transverse traceless gauge on matter is represented by the expansion and contraction of a ring of test particles in the direction of polarization of the wave. ...
2
votes
0answers
92 views

General formula to compute the redshift (first order perturbations)

Consider an expanding universe with the following metric in conformal time/co-moving coordinates: ...
3
votes
1answer
157 views

Interpreting perturbation theory in general relativity

In quantum mechanics we start with a Hamiltonian $H_0$ for which we know the exact eigenstates and energy eigenvalues. We perturb it by a known term $H$, and then attempt to compute (approximately) ...
0
votes
2answers
180 views

How explain this perturbing equation about the 43 arcseconds?

The planetary orbits have been studied as ellipses but the solar system is in motion in relation to the distant stars. Their path is along the tip of an helix and the ecliptic plane is a convenient ...
1
vote
1answer
72 views

Linear Metric Perturbation and Brans-Dicke Theory

Recently, I have been researching about modified gravity theories and one of the theories has been the theory of the graviton. If one starts with the metric tensor $g_{\mu\nu}$ and then performs the ...
4
votes
1answer
120 views

Are third derivatives of metric perturbations zero?

I'm working on a problem related to fluid perturbations of stars. I'm following this paper. They start with the Einstein equation: $$G_{\alpha \beta} = 8 \pi G T_{\alpha \beta}$$ and then perturb the ...
0
votes
1answer
70 views

Why must the gravitational wave components be much less than unity?

We start with the metric tensor \begin{equation} g_{\mu\nu}(x) = \eta_{\mu\nu} + h_{\mu\nu}(x) \end{equation} in the linearised theory, or \begin{equation} g_{\mu\nu}(x) = \bar{g}_{\mu\nu}(x) + ...
1
vote
2answers
142 views

Most suitable metric for the Solar system?

If I wanted to solve the Einstein equations for the solar system, which choice of $g_{\mu\nu}$ and $T_{\mu\nu}$ is more suitable? I thought about using a Schwarzschild metric near each planet, but ...
3
votes
1answer
185 views

Where does this equation for a perturbed metric come from?

I'm reading an article which includes the following equation involving a perturbed metric: $$G_{AB} = \eta_{AB} + \overset{1}{\gamma}_{AB} + 2\overset{1}{\chi}_{(A,B)}\tag{4.1}$$ I don't understand ...
6
votes
2answers
413 views

Linearizing Gravity to ${\cal O}(h^3)$

I've seen the action of linearized gravity in many places. We basically have $${\cal L} ~\sim~ \frac{1}{G_N}\left( - \frac{1}{2}h^{\alpha\beta} \Box h_{\alpha\beta} + \frac{1}{4} h \Box h + {\cal ...
6
votes
2answers
532 views

Does perturbation theory break down for quantum gravity?

Perturbation theory presumes we have a valid family of models over some continuous (infinitely differentiable, in fact) range for some parameters, i.e. coupling constants. We have some special values ...
4
votes
3answers
474 views

References for ADM formalism and cosmological perturbation theory [closed]

What would you consider the best online resources for learning the 3+1 ADM formalism and gauge invariant perturbation theory in cosmology? (Assuming intermediate level GR and QFT familiarity)