The Geometry of a Black Hole

Gravity is said to be the curvature of space and time, but what does such curvature actually look like? In this video we explore the foremost solution to Einstein's equations -- the Schwarzschild solution -- in order to construct a concrete visualization of the spacetime manifold. Will this visualization grant us new insight into our higher-dimensional reality? The secrets of gravity are locked away... in The Geometry of a Black Hole.

Contents:
00:00 - Intro
00:50 - The Schwarzschild Metric
02:03 - The Schwarzschild Coordinates
06:30 - Resizing Space and Time
10:48 - Visualizing the Manifold
12:07 - Motion on the Manifold
14:14 - Reconstructing the Classical Gravitational Field
15:02 - The Geometry of a Black Hole
17:22 - Conclusion

[RecoilTechno]

As a regular PBS Spacetime et al. viewer I am glad to find this channel. I really like the more in-depth explanations and enjoy the way the animation is executed - helps me wrap my brain around these mind-melting subjects.

[Diaming]

Every new video I watch about how the geometry of spacetime is constructed, I'm blown away for how Einstein came up with it!

[rhythmguild]

I always struggled with maths yet I’m obsessed with physics. These videos are great. 🙂

[miinyoo]

This is a brilliant visualization. The toughest thing to get your head around (which on its own isn't) is the transformation from Inertial coords to Accelerated coords and back again to demonstrate what's really going on. Otherwise, this makes perfect sense.

[taramarielmt]

I followed immediately after watching! This is the most meaningful information I've found so far on youtube! I didn't have the opportunity to realize my dream of becoming an astrophysicist, but my obsession with learning about it has never gone away. I'm so grateful for science communicators who give others the opportunity to understand and learn!

[ScienceClicEN]

Fantastic video as always ! It left me eager to see you tackle the inside of a black hole, maybe in a next video ? I was thinking about how the scaling terms of the spacetime slices become imaginary under the horizon, and how this could be related to a rotation maybe ?

[caveman]

Each episode ends in a cliffhanger, getting you closer to but not quite there to the full picture. Absolutely amazing videos and the progression allows you to actually grasp the concepts easily.

[Bitzy]

i’m watching this at 2am with barely a highschool understanding of math and i just wanted to say that the way you describe things is perfect! particularly the diagram with the hill. i felt that “aha” moment and this video is constructed in a way that i can actually understand the basics of what’s going on! fantastic job

[drottercat]

If there were a Nobel Prize for methodical explanation, you would get it. Speaking slowly and clearly is a big par tof it.

[abcde_fz]

. FINALLY !!! THIS IS THE FIRST TIME, in all the videos I've ever seen, where the 'rubber sheet' analogy was effectively replaced with an understandable 3D representation, using the 'multiple cone' model you used.
It's about time someone did this. I've been waiting years for it...

[mastershooter]

An absolutely brilliant deconstruction of the ideas of Riemannian Geometry and General Relativity, this should be shown in every GR class in the world. Beautiful visuals and wonderful explanations! You sir, have gained a like and a subscriber!

[maujo]

This video needs a sequel where you offer a visualization of the Spacetime of a black hole past its event horizon.

[darrennew]

This is probably the best explanation of spacetime curvature I've ever seen, as a layman.

[nlee]

Thank you for the new video! Your team always does a great job balancing visual aids with careful explanations. It is hard to be so clear about a topic as nuanced as general relativity, so I appreciate the time and research you all put into the videos. Looking forward to the next ones!

[PSG_Mobile]

Each one of your videos adds a new piece of a big puzzle. It is very satisfying to realize how they link together to tell the same story. Really great work!

[genericjoe]

Absolutely amazed by the fact that this channel still doesn't have a 100k subscribers. The visuals and explanations are simply wonderful.

[csimet]

Probably the best visual explanation I've ever seen of this topic. Relatively easy to understand. Good job!

[realcygnus]

Superb content ! As usual. I've never seen an explanation quite like this.

[northernalberta]

I don’t even want to imagine how much work went into making the graphics for a video like this, well done!

[thetinkerist]

I know this is from a year ago, but this video shows one of the best visual constructions of how gravity emerges. I love this! Everyone slightly interested in physics should watch this.