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13th Jan 2016

This is the only one I have experience with. I like it just fine. Google it yourself and you'll find the full text and can skim it if you want to. The problems I've done were actually pretty interesting.

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2nd Dec 2012

Minkowski space ans special relativity are sort of the same thing; to speak of SR is to, implicitly, speak of Minkowski space. A lot of the interesting bits from the analysis of Minkowski space come naturally from just following out the logic of SR, which you can go with high school math and a decent textbook. To *really* get a sense of why Minkowski space is important (or even what it really is), you need general relativity, which is much more complicated. That requires differential geometry, which requires a bunch of other math (some analysis, linear algebra, etc.). Still, though, you're best bet is an intro GR text book, such as Schutz, which does most of the math of general relativity, albeit on a superficial level, and absolutely everything nontrivially interesting in SR.

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14th Jan 2018

Continuum mechanics is useful for both GR and engineering. If you've come across the stress tensor, which is represented as a symmetric 3x3 matrix, this matrix is augmented to a 4x4 symmetric matrix by adding in the (mass + energy) density in the corner, and the momentum density = flow of (mass + energy) on the edges. The stress 3x3 part is the flow of momentum. GR equates this 4x4 object with a function of something called the curvature of spacetime. I think the first ~eight chapters of Shutz (PDF) are a beautiful introduction.

[Edit] Pure geometry shows that this function of the curvature is a symmetric tensor field (a matrix at each point) that satisfies a divergence-free type condition. When interpreted in terms of the stress energy tensor, the symmetry gives the well known: i) symmetry of the stress tensor, ii) equality of the momentum density and rate of flow of mass through surfaces at a point. The divergence-free condition gives the well known: i) local conservation of (mass+energy), ii) local conservation of momentum.

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30th Oct 2016

>This is perfect! Thank you so much. I've also encountered the term "ringdown phase" so you instantly nailed my follow-up question :)

I'm glad I could help. :)

>Do you know where I could find more details on the actual mathematical equations that govern the gravitational waves? Specifically, I'm trying to figure out how exactly that GR predicts gravitational waves. I can't find any good info anywhere, other than the simple "GR predicts that gravity propagates at *c*" but certainly there has to be more to it.

The mathematics is actually quite tricky. Really understanding it requires an understanding of general relativity which requires an understanding of differential geometry.

If you're interested in pursuing this, I'd recommend taking a look at A first course in general relativity by Schutz or Spacetime and geometry by Carroll. But I warn you these texts are not for the faint of heart.

> How did GR models predict these chirps?

This is actually a bit easier to see. We have a family of approximation techniques for calculating gravitational waves. One such technique is the post-Newtonian expansion. The algebra is *horrendous* but doesn't require any differential geometry.

Sadly, I don't know of any discussions for non-experts. But I can point you to introductions used by scientists.

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28th Oct 2012

Hi, grad student studying General Relativity here. I honestly don't know anyone who uses Penrose's methods for tensor algebra. It may be great, once you learn it, but no one seems to bother. Instead I'd point you to The_MPC's response. Another approach is to look at some introductory GR textbook, since these always introduce tensors, tensor notation and tensor algebra as if you're never seen them before (which most students haven't). You can look at Schutz's excellent book, Hartle's book which has some very approachable exercises, or Carroll's now standard graduate text. Find them at your university library!

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