Understanding Tensors for General Relativity: A Comprehensive Guide

Click For Summary
Understanding tensors is crucial for studying General Relativity (GR) mathematically, especially for those new to the topic. A visual explanation involving a cube and vectors on its sides can aid conceptual understanding, but practical tensor manipulation requires more structured resources. Recommendations include a specific online guide and a highly regarded book that reviews necessary mathematics before delving into tensors. These resources are designed to facilitate self-study and maintain motivation. A solid grasp of tensors is essential for tackling specific solutions in GR.
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:
Last edited by a moderator:

Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
View full post »

Similar threads

Undergrad How do Tensors "work" in relation to linear algebraic objects?
  • · Replies 7 ·
Replies
7
Views
753
Undergrad How to calculate basis vectors from metric tensor (as a matrix)?
  • · Replies 6 ·
Replies
6
Views
833
Graduate Principal Invariants of the Weyl Tensor
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Purpose of Tensors, Indices in Tensor Calculus Explained
  • · Replies 10 ·
Replies
10
Views
3K
Graduate GW Binary Merger: Riemann Tensor in Source & TT-Gauge
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Coupling torsion to electromagnetism and torsion tensor decomposition
  • · Replies 5 ·
Replies
5
Views
1K
High School Why do people care about vacuum solutions in GR?
  • · Replies 9 ·
Replies
9
Views
1K
Graduate Weyl tensor and coordinate acceleration
  • · Replies 12 ·
Replies
12
Views
2K
Undergrad GR: Practical Problem Sets w/ Solutions
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How do non-diagonal indices of a metric allow for local flatness?
  • · Replies 22 ·
Replies
22
Views
885