Intrinsic Curvature and Singularities 

Italian subtitles please !

Thanks.

Thanks for that really great compliment.

@@EugeneKhutoryansky Werner Music is right, for someone who tried to wrap their head around curvatures and parallel transports to get an intuitive understanding of general relativity, this video is invaluable. Thanks for making this.

I'll have to take your word for it. I'm totally Homer Simpson watching this. My doofus brain is so out of its depths that it can only think about pizza, donuts, and party hats. So my question is this: If black hole singularities are party hats, what are they celebrating?

@@EugeneKhutoryansky What about extrinsic curvature?

@@Sapientiaa this really is extrinsic curvature as we are seeing curvature outside of the objects surface and its embedding to a higher dimension

Thanks. I am glad that my videos have been helpful.

Salvador Guzman exactly u are true they are really helpful

Thanks for the compliment. More videos are on their way. I make all the animations for my videos myself. In many cases, it takes me several months of work to create the animations for a single video, so please be patient.

@@EugeneKhutoryansky may I ask what softaware/language+libraries/modules you're using to create the animations? Keep up your excellent work!!

I make the 3D animations with "Poser." Also, I sometimes create some of the 3D models in "Wings3D", and then import them into Poser as ".obj" files. Also, although Poser has a built in physics simulator called "Bullet Physics", I also have an add-on to Poser called "Poser Physics" which works better for certain types of simulations.

I would rather they take their time, that's how we get gems like this!

@@EugeneKhutoryansky I much prefer quality over quantity. Unfortunately the RU-vid algorithms currently do not properly reward your style of work, but I hope and expect that your material will have a "long tail", providing value long into the future. In other words, take all the time you need, and please keep a copy of the original models and code. I suspect that they will be used in the future to extend your videos into interactive and/or AI-assisted learning environments. This work will last.

I watched that one! 😃

V L indeed, I had the same thought, re parallel transport. Or as Professor Susskind says in his videos in his endearing accent, “parallelly transport” :-)

Wondering what you were referring to, I found 1:02:15 of the YT vid 'Einstein's General Theory of Relativity | Lecture 6' by Leonard Susskind & Stanford

@@alwaysdisputin9930 I strongly recommend all of his lectures (there's a 193 videos playlist), unfortunately some are in low quality

Thanks for the compliments.

Thats heavy man, heavy enough to bend some dimensions.

Black holes probably have both intrinsic and extrinsic infinite curvature. They might just be the only objects in the universe with that property.

@@NikolaosSkordilis Mass is composed of micro black holes.

It also (kind of) explains how gravity affects time, since its one of the four dimensional vector components

The larger the radius of a circle, the more the outside of the circle will look like a straight line.

@@EugeneKhutoryansky Isn't it possible in theory that earth is the largest object in the universe it is in?

@@ME-ru4hv That which contains the largest thing... is the largest thing. :)

@@Reach3DPrinters Theoretical things like gravity and it's relation to time (which is just a transient-blip construct and not a fabric) can make all kinds of sense in our minds or on paper and even have some natural characteristics as well but doesn't necessarily mean they are reality. Take for instance these vector laws; do you think if you traveled a 1000 km square over the surface of earth, you would not return to your original location? I asked my original question because E.K. should be amply intelligent to apply all the things that limit vision and how they contribute to the theoretical "horizon" we see, instead of the common mistake of seeing it as a literal drop off point of a curved earth. So indeed, the earth is the biggest object and somehow contains the stars and sun and moon in it's sky, and not the other way around. At the very least, we now know for a fact that earth is not spherical, and great minds should be working out some theories that support these yet-to-be-understood realities instead of the fantasies that are getting old.

In reality, radii does not apply. but in theoretical mind ^#$%ery a straight line has INFINITE radius! (i will re-watch to see if there was practicality to giving a straight line infinite radii)

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Thanks for the compliments.

Glad my video was helpful. Thanks.

Thanks.

thanks lol

Do it on ACID :) 150-200ug IT ALL MAKE SENSE

It's also time consuming. I watched it, and then with a drooling mouth I started thinking and Google'd some things, watched more videos, and went on a Wikipedia adventure and there we are, just wasted the whole day.

Aferin bir türk, türkçeye çevir lütfen diğer videolarıda

Ya milleti böyle korkutup ne eline geçiyor cesaretlendireceğine

Thanks. I am glad you like my videos.

Thanks. I am glad you like my videos.

Thanks for the compliment about my video.

Thanks.

Thanks.

Thanks for the compliments.

Thanks. I am glad my videos are helpful.

Glad you liked my video. Thanks.

Thanks. I am glad my video was helpful.

Thanks for the compliments.

Thanks.

Thanks for that really great compliment.

Thanks.

Спасибо.

Thanks. I am glad you liked my video that much.

Thanks.

Thanks.

Thanks. I am glad you like my videos.

Thanks. I am glad you like my videos.

Thanks for the compliment. More videos are on the way.

@@EugeneKhutoryansky Thank you for the reply!

More videos are on their way. I make all the animations for my videos myself. In many cases, it takes me several months of work to create the animations for a single video, so please be patient.

Thanks.

Thanks.

Thanks for the compliment. I am glad you like my videos.

Thanks. I am glad you like my videos.

Thanks.

Thanks for the compliment. More videos are on the way.

Glad you liked my video. Thanks.

@@EugeneKhutoryansky In fact, not just this one. All of your videos I have watched are wonderful! :D It is always nice to visualize the abstract mathematical concepts. Particularly when these have to do with geometry!!

Glad you liked my explanation. Thanks.

Thanks. I am glad you liked my explanation.

Thanks. I am glad you liked my explanation and my animation.

May the Force be negatively curved...

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Ok i will translate in urdu very soon.

Please make videos regularly because your explanation is unique. No one in this world can explain like you

@@gurejalectures if you become pateron, it will be more often.

Please help me Which software used for the animation video

Kawser, I make my 3D animations with the software "Poser." Poser is expensive, but there are also free 3D animation programs available such as "Blender" and "Daz Studio."

Thanks. Glad my videos have been helpful.

Thanks for the compliment. I already have a video about Quantum Chromodynamics at the following link. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-FoR3hq5b5yE.html

Glad you liked my video. More videos are on their way. Thanks.

I am glad you liked my explanation. Thanks.

Thanks. I am glad you liked my video and my explanation.

Thanks. I am glad you liked my visualization.

Thanks for the compliment.

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Glad you liked my video.

Glad to hear that. Thanks.

Thanks for the really great compliment.

Instead of a regular sphere, you have a 4 dimensional hypersphere with time as the 4th dimension. Time gets stretched to infinity as well as the curvature of space the closer you get to a singularity. It's hard to visualize, but lookup Penrose diagrams and watch PBS spacetime for more examples.

In the 3-dimensional case of gravity, imagine a large lattice of dots representing points in 3D space. Now place a spherical object in the middle and imagine each point around it being pulled in from all sides. I think a black hole would just be a place where those points are really densely packed together so that all geodesics lead toward the center.

A hypercone seems to be a good representation of a black hole. The tip of the cone is in the center of the spherical cone.

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Thanks.

Thanks.

Thanks for the compliment.

Glad you enjoyed my video.

Thanks. I am glad you liked my video.

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Thanks. Glad you liked my video.

Thanks for the compliment. I plan to make a video about solid state physics (semiconductors). Thanks.

@@EugeneKhutoryansky Thank you.

Thanks. I will add that to my list of topics for future videos.

I don't know what a NFT is, but thanks for the compliment.

@@EugeneKhutoryansky NFTs are a way of packaging and selling digital art. It's an easy and fast growing new industry... it may be worth your time to look into it... Best wishes!

You are welcome and thanks.

@Leo Yohansen thank you for taking the time to answer. I am confused by your answer. In the first part you say you need equal energy to slow down as you do to speed up. But in the second part you say there is a resistance one way and not the other, implying that there would be unequal amounts of energy.

@Leo Yohansen thank you for a wonderful explanation. It fits exactly how I envisioned the universe working and confirmed some suspicions I had about other aspects.

@Leo Yohansen not to mention they have experimentally proven that the acceleration of a rotating body has been shown to drag spacetime with it. This tells me that spacetime has almost what could be described as a viscosity against acceleration and velocity.

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Thanks for the compliment. Glad you liked my animation and explanation.

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