Your Daily Equation #31: BLACK HOLES: And Why Time Slows Down When You Are Near One

Episode 31 #YourDailyEquation: Shortly after Einstein wrote down his new equations for gravity--his general theory of relativity--a German mathematician found the first exact solution. And within that solution physicists realized that a strange new entity was lurking: black holes. Join Brian Greene for a visual exploration of black holes and some of the mathematics that underlies them.

Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.

The World Science Festival (WSF) is an innovative multi-media organization that produces original live and digital content straddling the arenas of science, technology, the arts, media, performance and education. With the goal of radically transforming public perceptions of science, WSF creates world-class programming, both live on stage and televised, featuring inspired collaborations, outstanding talent and novel production techniques that bring scientific discovery, insight and perspective to a broad general audience.

[zstrizzel]

Daily equation idea: i^2=j^2=k^2=ijk=-1.

Btw Brian, these 'intermediate' level math/physics videos are a uniquely precious resource! it is a pleasure to hear ur perspectives! Thank you!

[greaper]

Thank you Prof. Greene - I find ALL of your Daily Equation videos SO fascinating! I am SUCH a fan of black hole theory; however, I have so many questions (in no particular order):

1. What are the physical properties of a black hole after its collapse (ie: what is it "eventually" made of)?
Does it change over time, and if so, what effect does that have?

2. Since protons are mass-less, what do black holes "work-on" to change their trajectory? (I'm assuming that the answer is, "they don't work on the mass of the proton - they bend space-time around them - which then becomes their trajectory" .. but I want to be sure...

3. Black holes are often portrayed in 2-dimensions (like a funnel); however, in reality, they have a 3-dimensional effect on everything around them in all 3-dimensions). Is this to say that the event horizon is at a given circumference at a given distance around the black hole? If so, how is the event horizon distance calculated? Does it vary? If so, why? (if I missed this, please forgive me in advance...)

4. Gravity is considered a "weak force"; however, in the case of a black hole, the gravitational force can be so strong that it bends spacetime. Doesn't this conflict with the idea of it being a "weak force"?

5. We can measure LARGE gravitational waves (as experienced a few years ago with LIGO) - leading you conclude that gravity is a wave... so can we measure SMALL gravitational waves? If so, to what level? Why are we unable to find/identify a particle (ie: graviton) in play?

6. Assuming the universal speed limit (aka: the speed of light), wouldn't you expect protons to "pick-up-speed" after crossing the event horizon and heading towards the singularity? (this "might" go back to my question #2...)

7. What are your thoughts on the "completeness" of Einstein's General Relativity? I've always felt that it's missing something, but I'm not savvy enough to pinpoint why...

Thanks, and I look forward to future videos!

[borntoosoon]

Thank you Professor Greene (btw greetings from Italy). Thanks for all the effort you do to clarify these wonderful concepts, I really appreciate it. About black holes, could you please explain (maybe in the next Q&A session) what underlies in the "information paradox" of black holes? Because I didn't understand where is the paradox....thank you very much, Sir.
Take care

[ruineves]

Hi, I have a question which is making my brain go around.
So, the attraction between earth and the sun ( for example) depends on both their masses, and the distance. However if that attraction comes from space time curvature then say if the sun was bigger smaller but much more dense ( the mass would stay the same) wouldn’t the space time be curved in a different way? And therefore gravitacional force would depend not only on the mass and distance as newton shows in the equation right?

[nishatiwari]

Does anyone see his enthusiasm.
Amazing

[smartlythando]

Hi Brian,

My name is Luthando Mayatula and I am an aeronautical engineering student at the University of the Witwatersrand, Johannesburg. I have been studying for so long that I thought I would never touch another book after I graduate at the end of 2024. I am happy to tell you that your videos and lectures have inspired me to go further still. I am now so inspired to go into the study of nuclear physics that it is almost a guaranteed next step after I graduate engineering.

Thank you so much for all the hard work you do!!

[Valdagast]

I will say this about professor Greene, he has some of the neatest handwriting I've ever seen in a professional scientist.

[macify]

Here I am having zero experience with such equations yet watched the entire video in awe. Thank you!

[_John_Sean_Walker]

The advantage of channels like this is that we can thank our professor for the many times he was on TV shows and YouTube videos like with Janna Levin and the very nice talk on the Commonwealth Club channel two months ago for example.
Thank you professor Greene.

[createtheengineerinyou]

I see a lot of space videos but only Prof Greene breaks down complex math and phy for me with simple visuals. Thank you for being a great educator Prof.

[tomrobbins]

This is awesome it's exactly what I was looking for thank you Brian!

[richiethesailor]

Does the stars core collapse initially do to the core cooling rapidly? Fun to follow even a glimpse of gleaning the meaning! Thanks Doctor

[stevenyee]

Thanks Brian for explaining the black hole equation. Using the mass of the Universe the Schwarzschild radius is within the observable Universe. Is it because of the density of the Universe is defused and crossing the horizon would be much less than the speed of light? Between the Big Bang and about 3 BLY after the Big Bang the Schwarzschild radius is bigger than Universe radius then what is your idea about the conditions that kept the Universe from collapsing into a singularity? Thanks for your reply?

[kharanshu]

Professor Greene.... you're an absolute Genius! Thanks a lot for this mathematical preliminary on black holes.

[DrJeeps]

I could listen to Brian Greene for hours. His ability to provide intuitive images that roughly approximate complex phenomena is amazing. As a fellow professor (psychology for me), I can do nothing else but tip my hat to him. I'm sure going to miss these daily equations when we all go back into the classroom.

[michaeljmorrison]

Enjoying your lectures....we are so lucky that corona seems to have you with us -a very real silver lining! So.... my question....Is gravity emergent and if so can it be manipulated by affecting entropy in a particular volume of space or specifically here on Earth?

[gpcrawford]

Excellent explanation of black holes for those maths dumbos like me . From this I gather that closer to a black hole you get your future is directed to the singularity until you can’t escape is that correct Brian?

[cesarmoya]

Omg I'm so excited!!! Been waiting for this one for a while!!! Thank you professor Greene!!

[MyWissam]

The achievement of Schwarzschild in the WW I, in the trenches and being bombed, is what anthropologists call "situational logic"...a concrete sense of singularity.

[StaticBlaster]

Thanks for these great videos, Brian. I really appreciate you taking the time to explain these physics and mathematical concepts to the layman. Your book, The Elegant Universe, piqued my interest and was the gateway for me wanting to learn more about theoretical physics.