Relativity 109d: Gravitational Waves - Transverse-Traceless Gauge (Plus and Cross Polarizations)

Some helpful PDFs on the Lorenz Gauge:

Other Sources on Gravitational Waves:

0:00 Polarization
1:58 Intro to Transverse Traceless Gauge
3:13 Review of Plane Waves
7:44 The components of the wave amplitude
9:38 The Transverse-Traceless Gauge
13:18 h-bar equals h
14:31 Determining components of Wave Amplitude
17:12 + and x polarizations
18:07 Summary

[StefSubZero]

Very good video, the first time i studied this part I felt like i did not understand very well some parts but this cleared up my thoughts. Cheers!

[sonarbangla]

In other words gravitational wave spacing is CONSTANT and non diminating, like all other waves, so they pervade the whole of space up to infinity, without weakening. Very well explained, thank you.

[jeancorriveau]

I've been scratching my head to understand while reading other sources with little success. This video makes me grasp the context. As for the GR equations, maybe eigenchris provides other videos.

[imaginingPhysics]

In what sense do gravitational waves carry energy? I have understood that "gravitational energy" is not a well defined thing in GR. The energy momentum tensor does not take it into account for example. And by a coordinate transformation one can shift into a frame where there is no "gravity", hence no gravitational energy.

Yet it has some kind of energy, since a black hole binary "loses energy" in gravitational waves which causes them to collide.
So, what energy do g-waves carry?

[ChronusZed]

Am I correct in understanding the geometric idea behind the TT gauge (compared to a generic Lorenz gauge) is that we're essentially forcing (1) translations along U should generate geodesics, and (2) the metric volume should match the Minkowski-Euclidean volume to first order?

[keshavshrestha]

Great video, After 19:29, How we can be sure that two independent components are non zero components of polarisation tensor? Is it not necessary to check whether two independent components are zero or non zero?

[cirno]

I'm confused about 9:43, shouldn't that expression mean that the ROWS of the amplitude matrix should be orthogonal to the wave covector components?

[utof]

One day i will get to this... still didnt get tensors tho :D

[longsarith]

Excuse me, Sir! I don't follow at point 14:31. Why taking trace on amplitude (A) gives us zero?

[mongooseman]

9:00 : "since gravitational waves are waves in the metric, and the metric is symmetric (...)" hahaha

[Schraiber]

Great video as always! I guess a couple things aren't obvious to me:

1) How do we know the transverse-traceless gauge is a Lorenz gauge? I suppose one can just crank through some calculus and algebra from the definitions and it works?

2) In practice, we choose a coordinate system to measure gravitational waves experimentally (like at LIGO). Is the choice we make a Lorenz gauge?

[darshkhandelwal]

Why do we need the orthogonality condition? Can't the angle of the velocity of the observer and the gravitational waves be different than this condition? Pls help

[vinnyhorapeti]

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