The Meaning Behind the Black Hole Equation | Physics Made Easy

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The Schwarzschild Metric is very often used to describe nonrotating, uncharged, black holes (as well as other gravitational bodies) and the effect that they have on the spacetime around them.
Hey guys, I'm back with a video that I kinda threw together, because I'm on holiday at the moment lol. But I wanted to make a (serious) video about black holes, and the equation most commonly used to describe them. In this video, I try to explain what the Schwarzschild Metric means, and where it comes from.
So we can build all the information we need in order to understand the equation that gives the proper time interval between two events in 4 dimensional spacetime (jargon alert lol) just by starting from Pythagoras' theorem. We can see how it can be used to find the distance between two points on a 2 dimensional grid, and we can even extend this theorem into 3d and 4d.
It's the 4d version that's most useful for us - after all, according to relativity, we live in a 4 dimensional spacetime. However, the equation we find by using Pythagoras' theorem and extending it to 4d only applies if the spacetime itself is flat, or non-warped, or non-wibbly-wobbly-timey-wimey'd. So we need to modify it further, using the equations of general relativity (specifically "Einstein's Field Equations") which tell us just how mass, and therefore gravity, ends up warping spacetime.
One such solution of the Einstein Field Equations is the Schwarzschild Metric - which is the equation that Brian Greene, legendary physicist, posted on his FaceBook page as a response to the announcement that humans had finally imaged a black hole. However, I reckon Brian got something slightly wrong... stick around until the end to find out what lol.
By the way, yes I've been a bit inconsistent in this video regarding a couple of things - firstly, I've said "point" instead of "event" and "distance" instead of "interval" a few too many times (but hopefully not when it actually matters). Secondly, in some of the equations I've left in powers of the speed of light, c, whereas in others I've used the form of the equation when we set c = 1. Hopefully this isn't a massive issue though.
Also, some of the stuff in this video is quite complicated and takes a while to wrap your head around (or it did for me at least), so if you have any questions then let me know down in the comments. As well as this, if you spot a mistake I've made, then let me know too.
Thanks so much for watching! Subscribe for fun physics videos every Tuesday! Follow me on Instagram @parthvlogs where I post 1 minute long physics content, and on Twitter @parthvlogs where I occasionally post some very bad physics jokes.

Опубликовано:

22 апр 2019

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Комментарии : 257

@tatjanagobold2810 5 лет назад

You are honestly doing a great job on bringing "complicated" concepts closer to non-physics students or people who claim to not understand physics! I want to study physics in the future as well and you have always been an inspiration for me :) wouldn't mind some more physics-maths related videos!😂😉

@_kantor_ 4 года назад

@@ParthGChannel i would love more like in depth videos... great content man! quality education

@Best_yet_is_2_come 2 года назад

@Arthur r=R

@Best_yet_is_2_come 2 года назад

@Arthur Landau & Liftshitz used it in 1975

@Best_yet_is_2_come 2 года назад

@Arthur In the physicist book Gallileo Unbound it does show R sub s. Like you said. I understand what you mean. However, it appears a lot of people are using R sub s and r sub s interchangeably. Which is not what was initially said. Is r sub s = event horizon size?

@Arkamfrz 5 лет назад

Now I understand the meaning of " If you can't explain it simply, you don't understand it well" Great job pal. Very clear explanation of this complex equation

@ThisisProgrammer-xi7qt Год назад

- Einstein

@jones1351 4 года назад

Great stuff. For me physics/math is the the beautiful woman who said, "...but we can still be friends."

@AstroB7 4 года назад

jones1351 good one :)

@globaldigitaldirectsubsidi4493 4 года назад

you just have to try harder

@pranayranjan3777 3 года назад

So it's one sided love means u love Physics but physics doesn't love u

@jones1351 3 года назад

@@pranayranjan3777 Precisely. I came from somewhere back in her long ago. A sentimental fool don't see trying hard to recreate what had yet to be ...😎

@Godakuri 3 года назад

@@globaldigitaldirectsubsidi4493 trying harder has nothing to do with anything

@inderjitsingh4588 3 года назад

This is the guy we all need an hour before exam.. ☺

@saftheartist6137 4 дня назад

Excellent video! 👍 You simplified such a complex topic and kept it concise, without unnecessary jargon.

@fortunehacking 3 года назад

I've literally watched 50+ hours of lectures on GR on YT. The way YOU say it in your videos...makes related concepts come together very nicely. For example: You said..."We're no longer measuring coordinates in space-time... we're measuring events..." It's like an observation that causes 10,000 languishing superpositions to collapse instantly into coherent thought. I go.... "ohhhhh, so that means..." Idk..bad analogy maybe... Either way. Thank you.

@davidwright8432 Год назад

What you do here is very valuable, particularly for people who haven't gone beyond high school math or physics. Without showing how to derive, or solve, the equation, you make clear what it's about and how the individual terms contribute to the overall picture. You show what we need to know to solve the equation, and how the overall meaning of the equation is built up. By comparison, solving for particular situations is grunt work! Without the ideas - no equations.

@arunjanarthanan6380 4 года назад

its beautiful how you present so much so humble! the beauty of what we do not know prevails at the end :)

@jenromeave4793 3 года назад

hey! i’ve been loving your videos which are very informative and concise! but, if ever, would you create a video detaling how exactly physicists are able to come up with a theory? including the mathematical formulae? thank you!

@michaeledwardharris Год назад

Parth, I've had some awesome teachers in my life. You are notable among them! Really learning a lot from your videos. Thanks 😊.

@adityapandey9639 4 года назад

You are doing a great job😍... Thanks from India 🇮🇳

@rgriffsf 3 года назад

Wow!! I previously thought I would never understand Mathematics under the complex physics equations I have seen numerous times in the past. Thank you for explaining from Pythagoras (2D) to 4D. I get it now. Great job!

@Li.Siyuan 4 года назад

Beautifully explained, thank you.

@bhuvaneshs.k638 4 года назад

Dude this channel is so amazing

@lol-rw7yd 4 года назад

Extraordinary man love it

@SabrinaXe 4 года назад

You're good at this, you should make A level CIE videos for students struggling in a levels

@AgentWD40x 10 месяцев назад

Thanks for your explanation. As an amateur trying to solve these types of equations, I always thought at some point that I was supposed to integrate it. I had no idea I was actually looking at a coordinate system.

@satyamkumar567 4 года назад

U r the most amazing person on u tube I have ever seen

@ehsanullahhassani5102 4 года назад

Nice video. I had difficulty understanding this equation in my college. It was confusing to me till this day. Now after watching your video it completely makes sense.👍👍👍

@immortalsofar5314 4 года назад

I did something similar to the 3d Pythagoras problem to set 3 angles (shoulder horizontal, shoulder vertical and elbow) to move the tip of a robot arm to a given x,y,z co-ordinate. Just use the result of 2d xy into 2d (xy)z.

@MsDilan2009 4 года назад

Awesome. After watching your Vedio. I understood it .

@ganeshikhar 4 года назад

Parth Sir ...u explain nicely up to the equation ...but it will be very nice if u focus more on that equation itself. May be create a separate video. I also saw ur couple of other videos. There also u did the same.😌

@calimaulud5708 4 года назад

Man, because of you I gained courage to pursue astrophysics. Thank you

@soumikdas3909 4 года назад

Hey can you help me i want to study astrophysics

@everythingpossible8185 4 года назад

Dude u are doing a great job and im feeling bad for u cause u have so much less subscribers I'll tell my buddies to see it too. Keep it up . I'm a great fan of physics and maths and I'm in the 10 class I m much interested in quantum physics and I learned calculus in 9 .

@LivingWaterEternal 2 года назад

Amazing presentation.

@Dan__S 6 месяцев назад

Thank you. So many other videos are dumbed down and they totally omit accounting for the difference in time as you approach a massive body and further time difference due to relative velocities. Over millions or billions of light years that kind of thing tends to add up.

@shivamSharma-ml5xg 4 года назад

I really liked how you described it. i would like to see more of your videos. love from india

@aniket1090 4 года назад

Thanks for simplification .

@kenantahir 5 лет назад

thanks for the explanation

@Govstuff137 4 месяца назад

Ok Thank you. It's 5am i should be asleep. But I enjoyed this video. I'm looking forward to seeing the rest of your videos. Do you realize how fast you talk? I am hoping you might do a video on Time Compression. Unless you have already and I just haven't gotten there yet. Thank you for your time. 🖖Live long and prosper!

@kartikeysharma 3 года назад

Honestly this is one of the simplest explanations of the phenomena that one could come up with without losing a lot of the mathematical essence. A job well done. Although, I have to point out a small error, which many of us tend to overlook even on a good day. At 5:28 you specify the Polar angle to be phi (φ) but at 6:28 you write the metric with theta (θ) being the polar angle. It doesn't impact the rest of the explanation, as you started with a mathematician's definition and changed to a physicist's definition, but I felt like it should be put out there for anyone who also spotted the typo.

@kartikeysharma 2 года назад

@Arthur Bruh

@BillySugger1965 4 года назад

Parth that’s a superb intro to the mathematical concepts underlying GR. If you haven’t already, could you post a video taking us a step further along the road, without doing a full undergrad maths/physics course, in the vein of your superb series on Maxwell’s Equations? Maybe take the equation Brian Greene posted and show what the terms represent? Thanks for all you do!

@andrewevans5761 3 года назад

It would be so nice if you gave us a numerical example in any such video.

@jishnun4537 3 года назад

just beautiful !!

@cmtro 4 года назад

Excellent !

@anjalishekhar1 4 года назад

Very good!

@MrLethalShots 3 года назад

Very educational video! :) Bit of trivia: a rotating black hole actually has two event horizons and a singularity shaped like a ring. If you navigate through it properly you can even come back out of the event horizons or go through the ring singularity and possibly come out at a parallel universe. Closed time like curves are even possible inside the inner event horizon so you can potentially meet your past self. If you get sufficiently close to the outer event horizon (a region called the ergosphere) of the rotating black hole and throw a mass in the opposite direction of the rotation you can even leave the ergosphere with more energy than you had originally going in. This extra energy comes at the expense of the black hole's rotation. So rotating black holes are a potential source of (limited) energy :) Edit: btw this last thing is called the penrose process

@dimitrispapadimitriou5622 Год назад

Actually this is the Kerr solution, that describes an eternal , unperturbed rotating black hole . Realistic rotating black holes, that originate from collapsed matter and are not isolated, are similar to what you describe, but with the important difference that their inner region, in the vicinity of the internal "Cauchy" horizon , is actually unstable: It doesn't probably contain a ring singularity, or closed time like curves etc. There is a " weak null ( light like) singularity there ( or even a strong spacelike singularity, or both; it depends on the details), as all the calculations have shown. Interestingly, it was R. Penrose the first who pointed out this kind of instability ( initially for charged black holes, that have also two horizons).

@acatisfinetoo3018 5 лет назад

This is actually really interesting. Even Blackhole Chan would be pleased:)😂

@harshittiwari4487 4 года назад

Blackhole chan is kawaii 😊

@jayjayf9699 4 года назад

Parth can you do a video on what a tensor is and tensor calculus?

@rafaelgarciamoheno4938 3 года назад

great video! Im wondering, does this equation change when talking about the mathematical concept of white holes?

@mmmk6322 4 года назад

When spacetime becomes timelike. Oh yea that will be a very interesting video!

@solapowsj25 2 года назад

Thanks for making physics interesting.

@inboccaallupo14 4 года назад

Please make a video about differentiation and integration

@bacakomen6019 4 года назад

Please explain charge density in 3d dimension calculation,and cosmology

@achmadrizaldanisya9517 4 года назад

the first of your videos that i need to rewind

@rubentamang1050 3 года назад

This helps a lot.. Thanks

@curvebal 4 года назад

Great job explaining a mathematically tough concept. According to biographies on Einstein, even he had to seek help with the math of his field equations. Would a rotating black hole’ s effect on space-time be in any way analogous to the effect of negative mass on space-time ? I think you see where I’m going with this( Alcubierre’s geometric manipulation of the field equations) Great topics for future videos are his equations, Casimir Effect and York time. Thanks for bringing science down to earth.

@julioalvear1641 4 года назад

Ah! Warp drive.....moving (warping) space-time to travel...yes that would be nice explanation videos.

@Prometheus7272 4 года назад

To your first question no negative energy is not yet known to exist and the Casemir. Effect is not negative energy.

@curvebal 4 года назад

Prometheus Yes the Casimir Effect is not negative energy but rather on the quantum level negative energy density. There is another theory that the attractive force between 2 plates is nothing more than caused. by van der Waals attraction.

@The_dead-guy 7 месяцев назад

I wanted to understand the equation at the end which you said was required for rotating spherical objects

@casualinfoguy 3 года назад

That was a brilliant explanation. I knew where you were going with it at around 1:57. Anyways, where were you when I was an undergraduate? I would have become a physicist, instead of a computer scientist. Btw, I like your haircut.

@omekafalconburn9202 4 года назад

Cool videos, I not convinced on stars not having charge it seems that stars and whole galaxies are linked by plasma filaments with massive magnetic fields, would be good if you could have a look at the physics of electric currents in a plasma ie cosmic z- pinch

@martin-hollingsworth 2 года назад

I thought algebra was always my strong suit, but you sir have just blown my mind ..

@wulphstein 3 года назад

It would be important to try to connect the geometry of black holes to wave functions. Wave functions have all of the properties you need to be "building blocks" of spacetime. If you could do that, then you could use quantum entanglements for analogues of wave functions. If quantum entanglements are the building blocks of spacetime, then theoretically you could create artificial gravity fields using quantum entanglements.

@singhanianilesh 2 года назад

can you show how equation for wormhole connects two distant points close at certain conditions. help visualize in lower dimensions

@alijoueizadeh8477 4 года назад

Thank you.

@69erthx1138 Год назад

Using S_2 as a standard sphere, the projections onto the surface can be arbitrary combinations of polygons, that would be animated with angular restriction for the surface (boundary). Going to S_3 the projections are polyhedrons, with the animating coordinate (aka, degree of freedom that no one seems to understand).

@aman-bd2ub 4 года назад

so well made. so sad to this not spark up 😭

@user-vr4ud8go2c 16 дней назад

THANKS SO MUCH

@KritikX 3 года назад

you are good teacher

@seyencho 3 года назад

So is the ds in the Schwarzchild Metric a geodesic? And, more interestingly, is it invariant like SR's spacetime interval and the Pythagorean Theorem is between reference frames? Is it invariant when an observer is experiencing different amounts of gravity relative to another? If so, does this mean that we can use this formula to find coordinate values between reference frames--for example, Time Dilation?

@ratnakarahuja4409 4 года назад

Tell me something about the prospects of Physics Masters or PhD

@RAJESHSK-ch9uc 4 года назад

Sir please make videos about calculus integration derivatives

@wRICKyRIZZ 2 года назад

It seems since space and time is on multiple curvatures, (causing gravity right?),like waves in an ocean, a black hole seems to be like a horizontal underwater hurricane in a sense going through those waves aka space time curvatures instantaneously or it seems to be proof that we could theoretically create a wormhole to instantaneously go through these curvatures of space and time and visit the future, past, or different moments of the present

@kayeassy 5 лет назад

Well there is a slight mistake if I may point out ... The choice of your theta and phi coordinates is inconsistent with the formula of the ds ... It's really very minute mistake... You're doing a great job ... I really enjoy your videos

@thewhizkid3937 4 года назад

How so, explain

@eeshanghosh1605 3 года назад

please do more of it

@Spontaneouscomp 4 года назад

Can you explain how this spacetime curvature makes things fall when released from rest? (and this is applicable to point particles since they also fall in), so can you explain it via considering the thing as electron in this curvature.

@aldineisampaio 4 года назад

According to Nick Lucid, things fall because the time curvature puts their future at a diferent place on space. He explains it beatifully on this video: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5HKH1ZjGutA.html

@FutureAIDev2015 4 года назад

So the equation relates something about the gravitational field in a region of spacetime to the four-dimensional “distance” between two points in that region?

@materiasacra 4 года назад

In General Relativity gravity IS the warping of spacetime. The fact that the formula for finding the interval between two nearby events is modified compared to the 'pythagorean' recipe is the mathematical expression of this warping. If you want to speak of the 'gravitational field' (which is a perfectly ok thing to do in GR), then it is the collection of coefficients on the right hand side of the equation. For the Schwarzschild case: -(1-2GM/r), 1/(1-2GM/r), r^2, and r^2sin^2(theta). These coefficients are components of what is called the 'metric'. If you know the metric, then you know everything there is to know about the (curved) spacetime. What GR does is describe gravity by making the metric 'come alive' as a dynamic entity, under the influence of the stuff in the universe. There is an equation that connects the metric to the energy and momentum of the stuff in the world: the Einstein equation, not discussed in the video. What Karl Schwarzschild did is solve the Einstein equation for the static case with spherical symmetry, and he obtained the metric shown in the video.

@Spiritualcreator 3 года назад

What is the ramanujan equation for blackholes?

@triptithakur1590 3 года назад

Plz Make some more video about black hole equation....

@The_Shrike Год назад

I’m curious, for determining the interval between two events in space time, what are the units in the final result?

@floydnelson92 Год назад

either use a vector containing the time component and the spatial component or use the fact that the speed of light in a vacuum is the speed limit... and most physicsts will multiply the time component by the speed limit c, so that it transforms into a distance measure, or divide each distance by c to get time measures. Consequently, this is like one second equals 299,792,458 meters, so on a Minkowski spacetime diagram where time moves up, a 45° angle either to the left or right is moving at the speed of light and anywhere in-between is slower than the speed of light.

@humansnotai4912 3 месяца назад

This equation really shines when it comes to black holes - haha...very funny.

@ellenw.lovesyou1740 5 месяцев назад

I like this video. Sean Carroll made a 60 Minutes Video perfectly well explaining every part of the famous Einstein Equation - for people who do not know anything (talking about anything above highschool level) about math or physics. You can learn a lot from his lecture. He is working with 4x4 Tensors, he goes deep into the math but I must say his lecture some levels above yours. It IS possible to send people inside Riemann, Schwarzschild etc. he even added some jokes and talked slowly. I think you have to improve on your didactic. Kind greetings from Germany.

@CapiFlvcko 3 года назад

U the best dude

@ayushikaushik5587 3 года назад

Please make more videos on general relativity

@sriharshaboddu2362 2 года назад

The question of human should never stop , after seeing this I realize this is still alive

@georgelopera6290 4 года назад

Please make the equation easier, my head is aching!

@thevibe8065 4 года назад

Where can I get some physics formula sheets?

@prathamkardam6442 3 года назад

oh well I am a biology student still I could understand it this just proves how well you explained it...

@_John_Sean_Walker 4 года назад

In the equation at the beginning of the video, you can also divide both sides by d.

@Kumar-oe9jm 4 года назад

No u can't.If u took calculus, u would know what it means.

@_John_Sean_Walker 4 года назад

I was joking. But it is a well known shortcoming in physics. We ran out of letters. Little 'm' cancels out all the time. 😂

@HimanshuSingh-ho1xh 4 года назад

10:40...🙌, True...😅

@rajdipbandopadhyay1291 3 года назад

2:20 take AB as a VECTOR AND FIND ITS MAGNITUDE,this will be the ans. For ex. Vector AB = X i^ + Y j^ + Zk^ then the length |AB| = rt(X^2+Y2+Z^2)

@Nikos10 3 года назад

Does spacetime bend towards a fifth dimension?

@aimeeaveys 3 месяца назад

1:55 imagine that the diagonal line that comes out of point A and goes directly below point B is da^2 so da^2 = dx^2 + dy^2. makes sense? Now, if we add da^2 and dz^2, it get us ds^2 for the same reason da^2 = dx^2 + dy^2. Finally, if we substitute da^2 for dx^2 + dy^2, we get ds^2 = dx^2 + dy^2 + dz^2

@chinmayadhiman3358 4 года назад

Samjha nai jyaada, but sunne me maja aaya😲

@nalamanonixservices3275 4 года назад

It will be different when measured from mars?

@MaesterSilva 3 года назад

can't we change the point of view of the 3d pitagoras theoriam and go back to the 2d one? because in practice when you calculate it you do this you get the hipotenuse of the x and y and used it with z. so can't we calculate the 4d one as a 3d one? or turn it into a 2d one?

@MaesterSilva 2 года назад

@Arthur I was just theorizing... I don' t study physics for real. I just do for fun. So I like to have theorys and see if they are right or wrong.

@s.j.p6394 4 года назад

Taking the shadow of “ds” on the x-y plane. Therefore, we get another right triangle with ds, the shadow of ds(dl) and dz. hence proved [ds^2 = (dl^2) + (dz^2)] Or as taken [dl^2 = (dx^2)+ (dy^2)].....

@rajvikramnema926 3 года назад

Do anybody know how can i use similar text animation and graphics for my videos

@charlieb8735 3 месяца назад

Just wanted to show my appreciation for the “um actually” to Brian green

@andalonds 2 года назад

show off . love it

@richardshelton-dca8810 Год назад

How does the equation take into account that at the event horizon the delta t (the time interval) goes to zero in the inertial frames of particles at the event horizon? To me, this would suggest that the mass of the black hole exists only at the event horizon as with no time there is no 'falling in' (that takes time) to the black hole at that point. There would be no difference in the gravitational effects external to the black hole as a sphere with all the mass at the surface acts as though the total mass was at the center point of the sphere to anything outside the sphere. For rotating black holes, again, no difference in the effect on space-time as the mass would still 'drag' space-time in the same manner. It would also check against the Hawking Radiation as all the quantum information would also exist at the event horizon, meaning that quantum data could easily affect any particle pairs formed near (within a plank-length of) the event horizon.

@cesarjom Год назад

You made a mistake at 5:30 where you label the spherical coordinates. You must switch the theta and phi angles in your coordinate diagram IF they are to match the equation for the interval you defined at 6:24 Also later you state mass results in gravity which results in curvature of spacetime. It is actually in the other direction, mass curves geometry of spacetime which in turn results in what we observe as gravitation (forces of gravity). And yes, that is correct the Kerr metric is the more accurate model/geometry needed to represent a rotating symmetric black hole.

@georgeagonzalez Год назад

On top of that, Schwarsild put a cte =R Later on, people did mistaken for a radius R. So the equation. As it should be maybe diefrent from the Common acceptance

@jojothefrikkenclown 2 года назад

Please just put all relevant equations in the description with comments so we can just dive in on our own time.

@divyanshusahay4148 Год назад

thanks

@cse010shoaibshafi 4 года назад

I found it beautiful

@jenromeave4793 3 года назад

Please do a video about objects falling into a black hole. ✨😭

@aldinhaswari1420 2 года назад

why the sign of time term is negative and space is positive?

@DesertKnight1 3 года назад

Mathematics is the key tool to unlock the mysteries of Nature and Universe with physics it creates an astonishing stuff which blow your mind .

@kingkiller1451 3 года назад

10:02 I disagree on the basis that I understood it as a nod to the initial prediction of black holes, which was the Schwarzschild Metric, rather than to the later math trying to describe a less idealistic version of the same object. Just my own understanding and opinion though. Otherwise love the video though.

@yogeshchauhan74 4 года назад

Please suggest me Quantum physics book for basic to advanced level. Patical physics book, Relativity book, string theory book,Nuclearphysics. Mathematical physics,classical physics.