General relativity | Ricci tensor | Ricci scalar | Stress energy momentum tensor | Einstein tensor

#ricciscalar #riccicurvaturetensor #stressenergymomentumtensor #generalrelativity
About This Video
This video explains the components of Einstein's field equations. Ricci scalar, Ricci curvature tensor, and stress energy-momentum tensor have been explained in detail. For those who are dealing with the General Theory of Relativity, understanding each and every component of Einstein's Field Equations plays a crucial role.
I have explained in the simplest possible manner the three components of EFE:
00:00 - 02:08 - Introduction & a note of thanks
02:09 - 07:50 - A quick recap (From the previous video)
07:51 - 09:32 - Components of Einstein's field equations
09:33 - 11:22 - Summarizing
11:23 - 19:06 - Alternative way of writing the equation
19:07 - 34:10 - Stress energy momentum tensor, curvature & matter
34:11 - 34:42 - Take a break
34:43 - 36:38 - Ricci curvature tensor
36:39 - 43:19 - Change of volume under linear transformation
43:20 - 50:16 - What is volume form / element ?
50:17 - 53:32 - Geodesics along the sphere
53:33 - 56:01 - Ricci scalar
56:02 - 58:21 - Geodesic deviations
58:22 - 1:00:37 - Summary
(a) The Ricci curvature tensor shows the volume change along the geodesic.
(b)The Ricci scalar denotes the amount of deviation of a ball from a Euclidean space to a non-Euclidean space
(c) The stress energy-momentum tensor deals with the entire matter movement part in spacetime.
Well, apart from this there are a lot of intricacies which I have covered in this video, like reducing the 16 components of the metric tensor to 10 components, understanding what is µ and ν.
I have also given a few examples of linear transformation and volume change under linear transformation. I have given a couple of examples on volume change under linear transformation and what is volume element or volume form. Lastly, all these merge to the final understanding of EFE and the three components that I mentioned earlier.
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[@Tom-sp3gy]

What clarity of content ! Thankyou sir so much for your fantastic lecture ... please upload more such excellent advanced level material ... your voice and illustrations makes it so easy to not just keep attention but also gain a deep technical appreciation of an otherwise very difficult subject

[@physicsforstudents]

Thank you very much. I am feeling very happy that you liked it. Yes, definitely I would try to make videos where the difficult concepts are laid our clearly. The basic objective of this channel is to clear out difficult concepts so that people can understand.

[@physicsforstudents]

Visit my website to know more; www.physicsforstudents.com You can submit your articles, scientific writings here. Free! We will peer review and publish.

[@goddessservant6669]

Thank you sir ! Excellent clear exposition ! Much appreciation and respect from the USA

[@physicsforstudents]

Thank you very much. Please subscribe to this channel. Also , recently I have posted a new video on E=mc2, the historical roots. Kindly look into it.

[@goddessservant6669]

@@physicsforstudents I subscribed about two seconds after I saw this video sir. 😁 I will seek out your other videos. Thank you !

[@physicsforstudents]

@@goddessservant6669 That is wonderful....

[@physicsforstudents]

Visit my website to know more; www.physicsforstudents.com You can submit your articles, scientific writings here. Free! We will peer review and publish.

[@pradiptadebnath7846]

Excellent video. A complete guide to understand General relativity.

[@souravdey1227]

Finally my life's dream comes true. I have been trying to understand these for so so long. Sir, can you please do two separate series, one purely tensor calculus and another one on introductory string theory?

[@physicsforstudents]

I am thankful that you have found the video useful and that it has helped you to achieve your dreams. First, go through this video also kzbin.info/www/bejne/jpmah3t5j89ghZI It is much more detailed. Second, for Tensor calculus, please watch this video kzbin.info/www/bejne/i6i0dmyDbZaIabc For string theory, 😊😊😊😊 I need to think. Thank you for your encouraging comments.

[@souravdey1227]

@@physicsforstudents Thank you so much for the guidance Sir. I will surely do it as advised.

[@frankdimeglio8216]

​@@souravdey1227 THE ULTIMATE AND CLEAR MATHEMATICAL PROOF OF THE FACT THAT E=MC2 IS F=MA: Ultimately and truly, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. SO, time DILATION ULTIMATELY proves ON BALANCE that E=mc2 IS F=ma; AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. Great !!! "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. E=MC2 IS F=MA. Consider the man who IS standing on what is the EARTH/ground. Touch AND feeling BLEND, as ELECTROMAGNETISM/energy is gravity; as E=mc2 IS F=ma. GREAT !!! E=mc2 IS F=ma. The linked AND BALANCED opposite of what is THE SUN is A POINT in the night sky. The stars AND PLANETS are POINTS in the night sky. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), AS the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT; AS ELECTROMAGNETISM/ENERGY IS GRAVITY; AS E=mc2 IS F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. Therefore, the linked AND BALANCED opposite of what is THE EARTH is ALSO A POINT in the night sky. Great. Gravity IS ELECTROMAGNETISM/energy. ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 IS F=ma. Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED opposites, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Accordingly, the Earth AND the Sun are linked AND BALANCED opposites; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy, AS E=mc2 IS F=ma. The stars AND PLANETS are POINTS in the night sky. It ALL CLEARLY makes perfect sense. Great !!!!!! Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. E=MC2 IS F=MA. The EARTH and the SUN thus constitute and comprise what are the MIDDLE AND THE FULL DISTANCE in/of SPACE (IN BALANCE) in full and BALANCED compliance and conformity with the CLEAR and universal fact that E=mc2 IS F=ma, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Great !!!! It ALL CLEARLY does make perfect sense. (The stars AND PLANETS are POINTS in the night sky.) INDEED, BALANCE and completeness go hand in hand. Now, very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. Great. NOW, OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. Notice the black space of THE EYE. The stars AND PLANETS are POINTS in the night sky. THE DOME of a person's EYE is ALSO VISIBLE. Now, carefully consider what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. Great. E=mc2 IS F=ma. It is CLEAR. THE EARTH is ALSO BLUE (AS WATER). GREAT. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience, as E=mc2 IS F=ma; as ELECTROMAGNETISM/energy is gravity. Gravity IS ELECTROMAGNETISM/energy. It ALL CLEARLY makes perfect sense. Inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/as) GRAVITATIONAL force/energy, as this unifies AND balances gravity AND ELECTROMAGNETISM/energy; as this balances gravity AND inertia. (This clearly explains BOTH F=ma AND E=mc2, AS ELECTROMAGNETISM/ENERGY IS GRAVITY !!!) ACCORDINGLY, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. SO, the BALANCE of being AND EXPERIENCE is essential; AS E=mc2 IS F=ma. Our EXPERIENCE is NECESSARILY that of what is the FULL DISTANCE in/of SPACE, AS we are BALANCED between what are THE SUN AND c (A POINT); AS E=mc2 IS F=ma. The stars AND PLANETS are POINTS in the night sky. SO, a given PLANET (INCLUDING WHAT IS THE EARTH) sweeps out equal areas in equal times; AND this is THEN consistent WITH/as F=ma, E=mc2, AND what is perpetual motion; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. E=mc2 IS F=ma. BALANCE and completeness go hand in hand. It ALL CLEARLY does make perfect sense. THINK about what is QUANTUM GRAVITY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Indeed, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Therefore, the rotation of WHAT IS THE MOON matches it's revolution !!! Objects fall at the SAME RATE (neglecting air resistance, of course), AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. Gravitational force/ENERGY is proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Stellar clustering ALSO proves ON BALANCE that ELECTROMAGNETISM/energy is gravity, AS E=mc2 IS F=ma. Magnificent !!! E=mc2 IS F=ma. Is a two dimensional surface or SPACE visible or invisible ? The answer is that it is BOTH. So, the electron AND photon are structureless. A PLANET (INCLUDING WHAT IS THE EARTH) is a balanced MIDDLE DISTANCE form in relation to E=mc2 AS F=ma. A PLANET (INCLUDING WHAT IS THE EARTH) is a balanced MIDDLE DISTANCE form in relation to the Sun AND c (A POINT). The stars AND PLANETS are POINTS in the night sky. E=MC2 IS F=MA. ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. Gravity AND ELECTROMAGNETISM/energy are linked AND BALANCED opposites, AS E=mc2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. BALANCE AND completeness go hand in hand. Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. E=MC2 IS F=MA. It ALL CLEARLY makes perfect sense. The BALANCE of being AND EXPERIENCE is essential. The INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. INSTANTANEITY is thus FUNDAMENTAL to what is the FULL and proper UNDERSTANDING of physics/physical experience. (THOUGHTS ARE INVISIBLE.) It is a very great truth that THE SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. MOREOVER, the ability of THOUGHT to DESCRIBE OR RECONFIGURE sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience. Beautiful. It ALL CLEARLY makes perfect sense. E=mc2 IS F=ma. By Frank Martin DiMeglio

[@randymartin5500]

Fantastic thank you!

[@CallOFDutyMVP666]

Truly excellent resource. One of a kind !!!

[@physicsforstudents]

Thank you very much. You can also watch my other videos.

[@RahulSharmaSingularity]

Absolutely Amazing and Lucid ! Already a big fan and follower !

[@physicsforstudents]

Thank you.

[@peterdore229]

Excellent lecture and the right level of treatment of all the parts of the topic. Thank you.

[@physicsforstudents]

Thank you very much. Keep an eye for more videos on this subject. However, you can also look into my website: www.physicsforstudents.com

[@ahmadsandhu6143]

Such a clear exolanation of a graleat idea The way you explain is amazing

[@physicsforstudents]

Thank you very much for your comments. Keep watching.

[@TGMResearch]

The absence of music in this episode is pure genius. I had not studied the theory in this detail before and enjoyed your presentation a lot. It strikes me though that strictly it is not a 4D theory. As you showed the intrinsic curvature is determined by "only" 10 unique components which suggests that the tensor representation is idealized. A dynamical approach based on the actual physical degrees of freedom should yield the same curvature without tensors.

[@physicsforstudents]

I am glad that you liked it. I made an earlier video based on a music..... Then I found that the music is too loud..... Serious topics like this should be devoid of music.... Hence I removed it..... The next video will be on Metric tensor... I already made an introductory video on what is topology. Although my channel is relatively new and the reach is very less, yet I am finding very serious people like you who are watching my videos with great interest. I am thankful to you. Please share and like .... Thank you once again ❤️❤️ from the core of my heart.🙏🙏

[@physicsforstudents]

Visit my website to know more; www.physicsforstudents.com You can submit your articles, scientific writings here. Free! We will peer review and publish.

[@sheikhmtahiryounus3880]

No words!! Very well explained all the things. Looking forward for more videos. thanks much.

[@physicsforstudents]

Thank you very much. Surey, I will be making more videos.

[@physicsforstudents]

Visit my website to know more; www.physicsforstudents.com You can submit your articles, scientific writings here. Free! We will peer review and publish.

[@jadefreeman6952]

i never quite got this before, thank you

[@physicsforstudents]

Thank you very much for your comments. Keep an eye as I am coming up with more interesting videos on General Relativity and differential geometry.

[@JoeHynes284]

thank you so much for this sir!!!

[@physicsforstudents]

Welcome son 😃😃 Watch out the next video on metric Tensor which will clear out further concepts.

[@shishirjha7744]

Crystal clear. A clas of its own. Pl cover other areas of Physics as well.

[@physicsforstudents]

Thank you very much. Watch out my next video on Metric TENSOR.

[@cosmophilosophyandscience1674]

Thanks sir ☺️👍😀

[@physicsforstudents]

Most welcome

[@dhajendrarabha2243]

Very informative video sir....

[@physicsforstudents]

Thank you very much. Please watch my other videos also.

[@dhajendrarabha2243]

@@physicsforstudents Definitely sir.....

[@earthperson79153]

This is great. Thank you professor. Do you recommend any books along with your lectures? And what is the url for your first lecture?

[@physicsforstudents]

Thank you very much for viewing my lecture. You can visit my website:www.phyiscsforstudents.com. Here you can find more stuff. I would recommend 'Gravity' by James Hartle or other books by Steven Weinberg. I am coming up with a new video on Metric tensor and I will cover up all the essential components of Einstein's field equations.

[@earthperson79153]

@@physicsforstudents many many thanks. Will do so.

[@earthperson79153]

@@physicsforstudents hi Professor, many thanks. Is there a way to let one know when your courses are posted?

[@physicsforstudents]

@@earthperson79153 Subscribe to this channel and click on the bell icon to receive all the notifications. You can email me for correspondences at: [e-mail] I will reply.

[@ggkt8546]

very​ nice

[@physicsforstudents]

Thank you very much 💗💗

[@xavidoor]

You indicate that GR field equations are differential equations in partial derivatives. However in the expression of the equations we don't see the derivatives anywhere. Are the partial derivatives embeded in the components of the Ricci tensor? What are we trying to find as solutions of the equations: is it the components of the Ricci tensor or the components of the metric tensor? Thanks for the video!

[@physicsforstudents]

A very good question. The partial differential equations are spread out everywhere. It would be too detailed and too lengthy process to show them and prove them. Internally, they are there. For example, the metric Tensor (which is the subject of my next contains partial differential equations, which, this time, I would show in thr video.) I would really appreciate the question that you have aksed. If you look into the derivation part of Ricci Tensor, there are these equations. For making the video short (although it has gone more than an hour) I slipped. Thank you, once again. Please do subscribe ❤️❤️

[@thevegg3275]

Ok, first, thank you for what you do. I really appreciate you are method of teaching complex topics of the six to students. That being said, I’ve been trying to get an answer to a question for years and no one will, or can’t answer my question. I wonder if it’s because I am not asking that a correct way. So let me try to make it as clear as I can, and I would appreciate it if you were tried to give me an answer. Using graphs one can show parallel and perpendicular projections of a vector. These projections obviously have numerical values. Values of parallel projections are called contravariant components and projections are perpendicular type are called covariant components. I believe they covaried because of the inverse nature of the basis vectors. My question is how do these four numbers get implemented into a tensor? To contravariant numbers and to covariance numbers. I realize that sometimes you only have contravariant and sometimes only covariant and sometimes you have a mixture of both, so I just don’t get where these numbers come from with respect to thinking about the graphs that I mentioned above

[@thevegg3275]

I am not sure if I phone call would be possible but I’m sure we can clear it up in five minutes with a call

[@physicsforstudents]

Well these are called indices. The four numbers , for a tensor are the number of dimensions. It can be more than that also depending on the number of dimensions thry cater to. For Einstein Field Equations irnaojls be four as it deals with the four dimensions of spacetime

[@thevegg3275]

OK I think I can clarify this imagine as skewed system acute not obtuse. Now I will define the coordinates FaceTime to systems the parallel projection which creates contra variant components. Those values are 6 and 40. No, I will be fine. Perpendicular projection components otherwise called covariant components, the values of which are two and -12. OK we have an actual graph of a coordinate system with a vector and the components of the vector and two systems. Now here’s where the connection gets lost for me. I have no idea how this data gets into a tensor in the indices. Can you simply go from knowing these phone numbers to creating a tensor? If not, what is the value of these four numbers because the indices do say they are covariant or contravariant, and I understand that Christoffel symbols have certain meanings along with the certain meanings of tensors, but I just don’t know where these numbers fit in if in fact they do fit in at all , if they don’t why are they call covariant Encontrar variant. Thank u

[@gpcrawford8353]

Trying to understand general relativity from a layman’s view so pictures and diagrams to me are more understandable what I would like to know is the shape of the curvature of ie a picture of this .

[@physicsforstudents]

Thank you for watching this. That is the reason I put up figures which are easy to understand and visualize. Please SUBSCRIBE to my channel and I am posting interesting videos. I hope you will like it.

[@pradeepmachara4724]

Thanks sir

[@physicsforstudents]

Welcome. It seems you are into the study of general relativity.

[@pradeepmachara4724]

@@physicsforstudents Yes sir i am a student of physics at iit guwahati

[@physicsforstudents]

@@pradeepmachara4724 That is wonderful to know...... I am coming up with a new video (may be you won't be interested) where I will be explaining on the possible career opportunities in mathematics.... You can also watch out my videos on Topology.

[@pradeepmachara4724]

@@physicsforstudents Yes sir i will watch your video on topology

[@ionmurgu783]

yes, is a beauty presentation , but can I to ask if you sir thought any times in mod critic about? There is a lot of geniality included and then any times fall in stasis . Are you any times aware this is about a Spherical Universe?? And we are in the front maybe of a Eliptical one?

[@physicsforstudents]

Yes. That is true. This is just an introductory video on general theory of relativity which has been perceived by Einstein. Thank you for watching. Please do subscribe and like. Thanks.

[@skkuedu]

I thought 'relativistic mass' has become obsolete. The mass of an object (= its rest mass) is an invariant property of the object....

[@derciferreira2523]

Hilbert´s Field Equations.

[@user-ug6zi2gg4m]

可以新增討論題

[@physicsforstudents]

English, please

[@ScienceAspect]

these lecture are not well arrange, sequence is unable to determined, because of not clearly mentioned like lec 1 or lec 2.

[@physicsforstudents]

I have numerically numbered the lectures as 1,2,3,4... Please look into the thumbnails. Those which are not numbered are independent concepts. For example, this one, Metric Tensor is an independent concept which crops up everywhere. I think if you check the thumbnails you will find the chronology.

[@ScienceAspect]

@@physicsforstudents ohh ok thankyou. And by the way your effort is really very helpful for us, in general theoretical physics field for research is a very vast field usually sometimes it is very difficult to get help and instruction, guide in this field.

[@physicsforstudents]

@@ScienceAspect You are welcome....

[@taiucnguyenvo3115]

You should speak fluently and clearly

[@physicsforstudents]

Oh yes !! Thanks for the comment. I am learning to speak .

[@taiucnguyenvo3115]

@@physicsforstudents good luck !