General Relativity Lecture 7

(November 5, 2012) Leonard Susskind continues the discussion of black holes in depth using coordinate transformations and diagrams to develop an intuitive understanding of black hole physics.

This series is the fourth installment of a six-quarter series that explore the foundations of modern physics. In this quarter Susskind focuses on Einstein's General Theory of Relativity.

Originally presented in the Stanford Continuing Studies Program.

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[BradleyGao]

11 PM: Just one more video I’ve a long day tomorrow

3 AM:

[patriciaheil]

in the 70s when I was studying Russian language at college, I was enrolled in a specialty of technical articles. the library had Russian physics journals and when I translated an article called Black Holes Have no Hair (U chyornykh dyr nyet volos), my advisor who was non-technical freaked, she had never heard the term before and she hadn't realized that a literal translation of the paper's title was really a thing in physics. I might have picked it up in an Isaac Asimov article for F&SF magazine.

[Abzollo]

Some commenters don’t like the fact that these “dumb” people didn’t instantly get how black holes work. You are talking about probably the most bizarre physical phenomenon that can be seen in the entire universe. Being completely dumbfounded by black holes is the expected thing to do. There is a reason why Professor Susskind took that long to answer questions.

[PetraAxolotl]

At 30:12, Susskind did not explain why lim F(ρ) = 1 as ρ -> 0. It took me a while to derive it. Below are the key steps.

1) In the definition of ρ = Integrate [sqrt(x/(x-1), x={1, r}], replace x by cosh^2(θ). It becomes ρ = Integrate [2 cosh^2(θ), θ={0, arccosh(sqrt(r))}].
2) Since cosh^2(θ) in the integrand is simply r, which is close to 1, the whole integrand is approximately 2. Now ρ ≈ Integrate [2, θ={0, arccosh(sqrt(r))}] = 2 arccosh(sqrt(r)).
3) ρ ≈ 2 arccosh(sqrt(r)) => r ≈ cosh^2(ρ/2) => (r-1)/r ≈ sinh^2(ρ/2) / cosh^2(ρ/2) ≈ (ρ/2)^2.
4) dτ^2 = (r-1)/r dt^2 ... ≈ (ρ/2)^2 * (2 dω)^2 ... = ρ^2 dω^2 ...


Step 3) can also be written as r ≈ cosh^2(ρ/2) = 1 + sinh^2(ρ/2) ≈ 1 + (ρ/2)^2, exactly what Susskind had at 31:32.

[jenniferlaflora]

Compact disc have debris and also 2 syllables for lactose deficiency tides of quarks 1:08:35

[alphaarcva_]

Alice, Bob, and Charlie are the stars for half of the lecture

[randymartin]

Susskind did this whole course of lectures in Jan 2009, and were a lot
easier to understand than this 2012 series. With the integral for Rho (proper distance from Rs to any distance r) at around the 21:00 mark, I was running
into all sorts of weird values using u-substitutions and trig
identities but eventually you get Rho, but it was hard. In the 2009 solution to the integral in Lecture 12 at the 50:43 mark, just use 2MG in the limit and in the integrand which is a constant, and do a square root integral .

[tknuwan]

Love to go back and learn mathematics again.. amazed how physics can calculate what happens in blackhole like this.

[realcygnus]

man some these may not be the best structured lecturers in the world like MIT/Lewin but Lenny is a heavyweight these are CE(continuing education) classes designed for any1.... who wants more then a typical 30min Brian Greene TV show(which I dig is Priceless content & Free mind u....its very cool of Lenny & Stanford to Post such mind candy 4 every1 !

[adamdicken]

So if Bob throws Alice into a black hole he could never get charged for murder since in anyone outsides reference frame she never really dies..

[naimulhaq]

Susskind did say the whole BH is the singularity, along with the point mass. I have a problem with Newtonian 'point mass'. At the center of the earth g=0 and the pressure P=mgh is billions of tons, instead of 0. Thinking the whole BH is the singularity, makes sense, it provides infinite curvature of space and infinite tangent.

[anoopsrana]

Lessons learned :
1) Alice is terminated
2) Bob never knew about it

[jenniferlaflora]

Fake or true: stage mom kardashian is Kaitlyn 55:37 and that’s why he names that ? 55:49

[globaldigitaldirectsubsidi]

49:00 John Wheeler´s conservatism did not extend to social issues. It only resolved around his fear of the soviet union´s nukes. Good to know.

[cheeheifoo]

Videographer zooms too close so can't see rest of the board so he's panning to stay on Leonard Susskind. He should zoom out and as I Lecture 5 and earlier, there isn't this distraction of panning and missing out on the rest of the board

[michaeljorgensen]

36:25 "Where it was space-like out here it becomes time-like in here"
Nothing special is going on here? Yes there is.
This is where Susskind leaves out something important about falling into a Black Hole. In order to fall through the event horizon safely you have to be falling at close to the speed of light when you do. Time dilation causes your clock to run slower but you don't notice it as you are the object that is moving. However you are moving relative to the event horizon and the singularity. Your clock moving slow means that the lines of convergence toward the singularity converge at a faster rate. Or in other words if you thought you would have 40 seconds (Sagittarius A has about a 40 light second Schwarzchild radius) before you hit the singularity...you actually have far less. You probably don't have enough time to notice yourself being spaghettified and compacted.
Another misconception is the concept of a "frozen" image on the surface of the event horizon from someone watching an object fall in. That is just a teaching concept of time moving slower for that object relative to the outside observer. It is NOT what you actually would observe. What you would actually observe is the object image redshifted and fade to black. The reason this is necessarily so is because light is made up of quantized photons...not an imaginary continuous beam. There is not an inexhaustible supply of photons coming from that object. You might see an image long after the object already fell through the horizon...but the image does not sit there frozen forever.

[iiiiii-wh]

49:47 Greetings from Valparaíso, Chile. We do have some nice cafes.

[tobywhite]

Last 2 lectures have been a little < the usual very high standard. Don't blame Susskind or the students. Most probably watch these lectures b/c we're not visual and we do like the math. Maybe using graphics approach is less productive, more confusing, for this audience than field equations would be, however difficult. I'm not physics guy or teacher, so just my $.02.

[billyjean]

I actually have a question... i dont know if leonard looks on here, but what if something was at the point in between the merging black holes if say they were of equal size and create the dumbell shape if one was at the exact point in between where the forces of the horizons were competing with each other could light escape that if it was perpendicular to the two competing forces?

[JaapVersteegh]

Oppositely dragging in one direction, but dragging combined in the other direction. And when the photon is behind the horizon all its energy will be 'dragged' and it won't get out.