Understanding Tensors for General Relativity: A Comprehensive Guide

BiGyElLoWhAt
Gold Member
Messages
1,637
Reaction score
138
Hi all, I'm fairly new to GR, and I'm also somewhat new to tensors as well. I'm looking for some detailed explanation of a tensor, as I want to begin studying GR mathematically. I watched a video that was posted on PF not too long ago that was pretty good. I'm having trouble remembering who it was, but basically it took a cube and assigned 3-space vectors to each side, and each side was represented by a vector. I can see that as an explanation, but that doesn't let me start doing math with tensors. A link that starts with something like vector calculus and goes through tensor manipulation (algebra/calculus) (I'm assuming it's different than matrix algebra/calculus) would be ideal. Explanations are great as well. If a book is HIGHLY recommended I will go buy it, but I prefer to not work through books, it's hard to keep motivation for self study with a book for some reason.

I would say I have a reasonable conceptual understanding of tensors, but am looking into reworking through specific solutions of GR. In order to do so, I need a better understanding of tensors.

Any suggestions?
BYH
 
Physics news on Phys.org
You might give this a try: http://preposterousuniverse.com/grnotes/grtinypdf.pdf
 
Last edited by a moderator:
Hello guy with the scary picture! I highly recommend https://www.amazon.com/dp/0957389442/?tag=pfamazon01-20 . It starts with a basic review of the math you need and gently leads you through everything! It helped me a lot before I tried more academic books.
 
Last edited by a moderator:

Thread 'I don't see how a black hole's event horizon can be crossed'

OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
View full post »

Thread 'Synchronizing clocks in an inertial frame if light is anisotropic'

ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
View full post »

Thread 'Is the variation of the metric ##\delta g_{\mu\nu}## a tensor?'

From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
View full post »

Similar threads

I How do Tensors "work" in relation to linear algebraic objects?
Replies
7
Views
264
I How to calculate basis vectors from metric tensor (as a matrix)?
Replies
6
Views
400
A Principal Invariants of the Weyl Tensor
Replies
6
Views
2K
I Purpose of Tensors, Indices in Tensor Calculus Explained
Replies
10
Views
3K
A GW Binary Merger: Riemann Tensor in Source & TT-Gauge
Replies
4
Views
2K
A Coupling torsion to electromagnetism and torsion tensor decomposition
Replies
5
Views
1K
B Why do people care about vacuum solutions in GR?
Replies
9
Views
1K
A Weyl tensor and coordinate acceleration
Replies
12
Views
2K
I GR: Practical Problem Sets w/ Solutions
Replies
2
Views
2K
I How do non-diagonal indices of a metric allow for local flatness?
Replies
22
Views
406

Hot Threads

Recent Insights

Back
Top