Energy momentum tensor - 1

This video looks at the idea of an energy-momentum tensor and how it describes the distribution of matter and energy in space-time. It achieves this by deriving the tensor for a swarm of non-interacting particles on some Lorentzian manifold.

[@premkhurana3691]

One of most finest channel for general relativity and tensor calculus

[@TensorCalculusRobertDavie]

Thank you for that! Glad you find it useful.

[@reimannx33]

Well done. You cut through much of unnecessary verbiage and associated notational complications. You presented the concepts and mathematical representation with great precision and clarity. Thanks!

[@TensorCalculusRobertDavie]

Hello Ron and thank you for your comment. Glad you liked the video.

[@SavedServant]

I haven't finished my engineering degree yet, and I can still go through and understand/learn this. Incredibly well done. I don't feel like I should be able to grasp these concepts unrelated to my field, but it's making sense. Thanks!

[@TensorCalculusRobertDavie]

Hello Taylor and thank you very much for your comment. I am glad to hear that you have found it accessible as that is the goal of this channel. Thanks again.

[@albarylaibida1214]

Awesome! Keep going with this wonderful work.

[@TensorCalculusRobertDavie]

Hello Albary and thank you for your comment.

[@lionelronaldo1574]

Great video waiting for the second one

[@TensorCalculusRobertDavie]

Thank you!

[@marioraianeto3775]

Professor Robert: Firstly, greetings from Brazil! Your lectures are quite nice. I would like to sugest one particular topic on energy momentum tensor: Energy Conditions. I would like to see explicit calculations and examples (with a discussion on observers and measure), just like you have been doing in your video lectures. Thanks, and stay safe. Mário Raia Neto.

[@TensorCalculusRobertDavie]

Hello Mario and thank you for comment and greetings to you from Australia. I will cover energy conditions at some stage in the future. Also, I think you mean professor in the sense of teacher as is the case in Italian? Stay safe!

[@marioraianeto3775]

​ Cool, I will wait the videos then. And, yes, you're correct. The term "professor" could be interpreted here the same as "teacher" (because I don't know if you're a professor, in the sense of university teaching). But here in Brazil we do not have this difference.

[@sanidhyasinha5735]

Thank you very much. nice explanation.

[@TensorCalculusRobertDavie]

You're welcome.

[@vicentematricardi3596]

Hi Roberto, I'm glad to see you around here again, how are things in your country? I hope you are not neglected, trust is the worst enemy, thanks for uploading a video class again, Greetings !!!!

[@TensorCalculusRobertDavie]

Hello Vicente and greetings from Australia. Australia is close to eradicating the virus while our neighbour, New Zealand, has just succeeded in doing so. Glad to hear from you again? Hope all is well in Spain? Stay safe!

[@vicentematricardi3596]

@@TensorCalculusRobertDavie Hello Robert, I live in Argentina, my parents are both Italian, I was lucky to know Italy a few years ago, in short, the world is small with this marvel of the internet, my passion is electronics but it is more than clear that these topics that you shows are exciting, they are the creation itself, again a big greeting and a Virtual Embrace, do not neglect, no one can be sure in this crazy world, !!!!!

[@Cosmalano]

Brilliant video, thanks for including the constants. Made it very transparent. And thanks for the citations, Wald and MTW are the most trustworthy resources on GR in my opinion. A bit off topic but I have a question for you: MTW discusses a geometrical interpretation of the Einstein tensor in chapter 15 and says it is the “moment of rotation”. I feel I’m so close to grasping what this means, but it’s just not clicking. Any chance you’ll do a video discussing how to interpret this tensor in the near future? The internet is entirely devoid of a lucid explanation on the topic, I’ve checked all over.

[@TensorCalculusRobertDavie]

Thank you Seth. My apologies I haven't made a video on the Covid situation in the US but I think there are other issues that have overtaken the virus. I agree with you on Wald and MTW. Give me some time and I will look into your question, but it might take a while? Sorry!

[@Cosmalano]

Tensor Calculus - Robert Davie that’s absolutely alright, no worries. Right now yes, we are seeing a boiling over of other issues that have been a long time coming and needed to be addressed desperately, so the virus has been mostly ignored the past few weeks. I’m worried because I think the infection rate is increasing again as of the reopening of some states, and I’m worried those in power will try to blame the protesters for this increase. No worries again about taking a while, I believe the intuition im looking for is mostly about the second Bianchi identity, which Cartan illustrated as a manifestation of “the boundary of a boundary is zero”. I’m comfortable with this, but what that boundary is, not the boundary of the boundary but the boundary itself, the moment of rotation trivector associated with a volume element, I am not comfortable with; I dont have an intuition. I get it for the 3 dimensional case where the boundary is a collection of squares and around the whole cube the rotation is zero, but in the 4 dimensional case where the boundary is a collection of cubes, I don’t understand why each individual cube doesnt have a rotation of zero. Nor do I get what a “moment of rotation” is.

[@kaluzaklein5246]

thanks

[@TensorCalculusRobertDavie]

Glad you found it useful.

[@user-tf2lg8yp6j]

Why does this video has over ten ad?

[@TensorCalculusRobertDavie]

I had no idea there were so many? Sorry about that.

[@yveslesage1812]

A

[@longsarith8106]

in the rest frame , why Energy density equal to density of particles time speed of light square only? in the rest frame particles also moving through the stationary box too. why we don't time Gama? because in rest frame mass of particles is relativistic mass , because all particles is moves.

[@TensorCalculusRobertDavie]

In the rest frame the particles are not moving with respect to that frame.

[@allenho2778]

I always know Minkowski metric as (1 -1 -1 -1) rather than (-1 1 1 1).

[@TensorCalculusRobertDavie]

Hello Allen. You are free to choose either metric signature but for this channel I prefer (- + + +). Each has its own advantage such as taking the magnitude of the velocity vector which gives you g_abV^aV_b = -c^2 for the signature this channel uses but +c^ for the other signature. It really is a matter of choice and does not depend upon the choice of coordinates. www.wikiwand.com/en/Sign_convention#/Metric_signature www.wikiwand.com/en/Spacetime#/Spacetime_in_special_relativity

[@RK-jy6es]

Excellent presentation but too many advertisement...

[@TensorCalculusRobertDavie]

Thank you for that and I will have a look at the advertisement situation.

[@yveslesage1812]

A