Theorems in general relativity
The no-hair theorem states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, electric charge, and angular momentum. Other characteristics (such as geometry and magnetic moment) are uniquely determined by these three parameters, and all other information (for which "hair" is a metaphor) about the matter that formed a black hole or is falling into it "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers after the black hole "settles down" (by emitting gravitational and electromagnetic waves). Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair", which was the origin of the name. In a later interview, Wheeler said that Jacob Bekenstein coined this phrase. Richard Feynman objected to the phrase that seemed to me to best symbolize the finding of one of the graduate students: graduate student Jacob Bekenstein had shown that a black hole reveals nothing outside it of what went in, in the way of spinning electric particles. It might show electric charge, yes; mass, yes; but no other features – or as he put it, "A black hole has no hair". Richard Feynman thought that was an obscene phrase and he didn't want to use it. But that is a phrase now often used to state this feature of black holes, that they don't indicate any other properties other than a charge and angular momentum and mass. The first version of the no-hair theorem for the simplified case of the uniqueness of the Schwarzschild metric was shown by Werner Israel in 1967. The result was quickly generalized to the cases of charged or spinning black holes. There is still no rigorous mathematical proof of a general no-hair theorem, and mathematicians refer to it as the no-hair conjecture. Even in the case of gravity alone (i.e., zero electric fields), the conjecture has only been partially resolved by results of Stephen Hawking, Brandon Carter, and David C. Robinson, under the additional hypothesis of non-degenerate event horizons and the technical, restrictive and difficult-to-justify assumption of real analyticity of the space-time continuum. (Wikipedia).
Brill-Noether part 4: Noether's Theorem
From playlist Brill-Noether
Duality Theorem In this video, I use a neat little trick to show that the limit as n goes to infinity of 2^n is infinity, by using the fact (shown before) that the limit of (1/2)^n is 0. Exponential Limit: https://youtu.be/qxlSclbmh-w Other examples of limits can be seen in the playlis
From playlist Sequences
This video states and investigates the triangle inequality theorem. Complete Video List: http://www.mathispower4u.yolasite.com
From playlist Relationships with Triangles
Set Theory (Part 20): The Complex Numbers are Uncountably Infinite
Please feel free to leave comments/questions on the video and practice problems below! In this video, we will establish a bijection between the complex numbers and the real numbers, showing that the complex numbers are also uncountably infinite. This will eventually mean that the cardinal
From playlist Set Theory by Mathoma
Proof for Square Root of Convergent Sequence | Real Analysis Exercises
We prove if a sequence of nonnegative numbers converges to a limit, then the square root of that sequence converges to the square root of that limit, which we could call the square root limit law or limit law for square roots. #RealAnalysis Put more precisely, if every x_n is at least 0,
From playlist Real Analysis Exercises
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91
There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point
From playlist Math Foundations
You might know that the sequence (-1)^n doesn't converge, but how to you PROVE that it doesn't converge? In this video, I'm using an epsilon-delta style argument (or rather epsilon-N_0 argument) to show that (-1)^n cannot have a limit. Enjoy!
From playlist Calculus
Why Can't I Get Rid of This Cowlick?
You or someone you know may have struggled to get a cowlick to just stay down already, but you can take solace in the fact that these inconvenient hair tufts have a lot to teach us about the world around us. Hosted by: Michael Aranda SciShow has a spinoff podcast! It's called SciShow Tan
From playlist Uploads
Part of the End-to-End Machine Learning School Course 191, Selected Models and Methods at https://e2eml.school/191 A walk through a couple of Bayesian inference examples. The blog: http://brohrer.github.io/how_bayesian_inference_works.html The slides: https://docs.google.com/presentatio
From playlist Talks
How to make Gold Nanowire with Math | Nathan Dalaklis
So you want to make gold nanowire. You have the nanoparticles and some other chemicals, but where do you start? This is where math helps out. The Hairy Ball Theorem remedies some of the difficulties with working with these super small particles. So how does the HBT work and how exactly doe
From playlist The New CHALKboard
Do Black Holes Have Quantum Hair?
We don’t know what happens to stuff when it gets sucked into a black hole, but in the same instance, we don’t know what happens to the black hole. There’s a possibility that sucked up stuff might actually give the black hole “quantum hair”. Hosted By: Reid Reimers ---------- Huge thanks g
From playlist SciShow Space
SAT math Q2 calculator allowed #shorts
Which of the following numbers is NOT a solution of the inequality 3x - 5 ≥ 4x - 3. Take My SAT Quiz Here: https://pythagoreanmath.com/quizzes/sat-quiz/ #shorts #maths #sat #satmath #satprep #mathematics #math #college
From playlist #shorts mathematicsonline
The Black Hole Information Paradox
Viewers like you help make PBS (Thank you 😃) . Support your local PBS Member Station here: https://to.pbs.org/DonateSPACE Thank you to Brilliant for sponsoring this episode! To find out more, visit: https://brilliant.org/SpaceTime We’ve established by now that black holes are weird. The r
From playlist Understanding the Holographic Universe
Beyond linear algebra - Bernd Sturmfels
Bernd Sturmfels University of California, Berkeley December 10, 2014 More videos on http://video.ias.edu
From playlist Mathematics
Multivariate (φ,Γ)-modules by Gergely Zábrádi
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
Stephen Hawking - Quantum Black Holes
In the 1960s Roger Penrose and Stephen Hawking produced their ground-breaking work on Black Holes. In 2017 Stephen gave the first Oxford Mathematics Roger Penrose Public Lecture in honour of his great friend. His subject? Black Holes of course. The full lecture, one of Stephen's last, is n
From playlist Oxford Mathematics Public Lectures
Black Holes - II (Lecture - 05) by G Srinivasan
Summer School on Gravitational-Wave Astronomy DATE: 17 July 2017 to 28 July 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore This school is a part of the annual ICTS summer schools in gravitational wave astronomy. This year’s school will focus on the physics and astrophysics of compact
From playlist Summer School on Gravitational-Wave Astronomy - 2017
Hairy Black Holes in a Box by P. N. Balasubramanian
Bangalore Area String Meeting URL: http://www.icts.res.in/discussion_meeting/BASM2016/ DATES: Monday 25 Jul, 2016 - Wednesday 27 Jul, 2016 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore DESCRIPTION: This meeting is designed to bring together string theorists working in the Bangalore
From playlist Bangalore Area String Meeting
#shorts This video reviews the divisibility rule for 3.
From playlist Math Shorts