Parth G's video: Why Black Holes MUST Be Disordered - Entropy of a Black Hole Thermodynamics Physics

The first 1000 people to use the link will get a free trial of Skillshare Premium Membership: https://skl.sh/parthg10201 How can a black hole have entropy? Well, if it didn't have entropy, then it would be breaking one of the most fundamental laws of the universe - the Second Law of Thermodynamics. Hi everyone, in this video I wanted to talk about black holes - because it's always fun to do so! Specifically, I wanted to explain the equation describing the entropy of a black hole. Black hole thermodynamics is a very interesting topic to talk about, so let me know if you want more videos on this! First, let's begin with some timestamps! 0:00 - Hey there! 0:29 - Black Hole and its Event Horizon, Radius of the Black Hole 1:13 - Escape Velocity of a Black Hole 2:04 - The Shape of... Black Hole (Schwarzschild Metric) 2:38 - Surface Area of a Black Hole('s Event Horizon) 3:28 - Please Check Out the Link in the Description Below for a Free Skillshare Premium Trial 4:39 - Entropy: A Measure of Disorder 5:12 - What If Black Holes Did NOT Have Entropy? 5:49 - Entropy Equation of a Black Hole, and its Dependence on Surface Area 6:56 - Schwarzschild Radius of a Black Hole 7:37 - Very Few Variables... Let's understand that black holes are highly dense bodies in outer space. They are so dense, i.e. they have so much mass squished into a small region of space, that not even light can escape their gravitational pull. Specifically, their event horizon is the boundary past which not even light will be able to escape the black hole. The event horizon can be thought of as the boundary at which the escape velocity from the black hole becomes the speed of light. Anything closer to the center of the black hole than this, even light, is doomed to fall in. We have no way of finding out what happens here unless we fall into a black hole ourselves - but this would be quite disastrous, as you'd expect. The interesting thing about the event horizon of a stationary (non-rotating) black hole is that it's shaped like a sphere. This is based on the Schwarzschild metric in general relativity, which is currently our best mathematical model for the description of a black hole. And the metric tells us the event horizon is spherical. We can also define the radius of the black hole (from the centre to the event horizon) as the Schwarzschild radius. This radius depends on the mass of the black hole, and is specifically the largest possible radius a black hole with a given mass can have. Now using the usual equation for the surface area of a sphere, we can say that the surface area of a black hole is equal to 4pi multiplied by the square of the (Schwarzschild) radius. This is important, because this surface area is useful in calculating the entropy, or disorder, of a black hole. Specifically, the entropy of a black hole is directly proportional to this surface area, linked by universal constants such as the Boltzmann constant, and the Planck length (itself made up of the universal gravitational constant, the reduced Planck constant, and the speed of light). The point is that the entropy of a black hole solely depends on the surface area of the black hole. As we've already seen, the surface area is solely dependent on the radius of the black hole, and in turn the radius is solely dependent on the mass of the black hole. Therefore in order to find the entropy of a black hole, we only need to know its mass! No other quantities are needed. Again, this is assuming the black hole is stationary (non-rotating). Things get a teeny bit more tricky when black holes rotate - but surprisingly, not that much more tricky! A couple of videos of mine that you may find useful to watch, in order to understand this video better: 1) Black Hole Equation Explained: https://www.youtube.com/watch?v=ci06S-jNn8U 2) Entropy Explained: https://www.youtube.com/watch?v=mg0hueOyoAw Thanks so much for watching! Please hit the like button and subscribe to my channel for more fun physics content. Check out my socials! Second YouTube Channel: Parth G's Shenanigans Instagram: parthvlogs Patreon: parthg Disclaimer: This video was sponsored by Skillshare - big thanks to them! :)