# What is Schwarzchild radius: Definition and 17 Discussions

The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a physical parameter that appears in the Schwarzschild solution to Einstein's field equations, corresponding to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916.
The Schwarzschild radius is given as

r

s

=

2
G
M

c

2

,

{\displaystyle r_{s}={\frac {2GM}{c^{2}}},}
where G is the gravitational constant, M is the object mass, and c is the speed of light.

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1. ### I If time doesn't pass at the event horizon, how is it crossed?

So when an object is falling towards a black hole, it's clock relative to us, outside observers, is slowing down. Until said object reaches the Schwarzschild radius and it stops completely. So how can that object ever cross the event horizon, if it is frozen in time?
2. ### I Is the Schwarzchild Radius Relativistic or Newtonian?

I noticed that the Schwarzschild Radius Formula and the Escape Velocity Formula are actually identical. The Schwarzschild Radius is supposed to be one of the great equations generated from Relativity, while the Escape Velocity is something that was generated just using Newtonian gravity. All you...
3. ### I Can someone fact check my speech about BH?

Hey everyone, is anyone able to check the facts of this speech I wrote? I have 3 minutes max to say this, I might cut out tiny parts to save seconds. What do you guys think, is this correct? Should I change anything? Thanks! How Black Holes work Stars are massive collections of mostly hydrogen...
4. ### B Schwarzschild Radius: Compression Inside Black Holes

Learning about Schwarzschild radius from Wikipedia: Is it accurate to say any object of mass crossing the event horizon of a black hole is compressed sufficiently to have its own Schwarzschild radius, becoming a black hole itside of a black hole?
5. ### Schwarzschild radius calculation

Is this the proper formula for calculating the Schwarzschild radius of a black hole? rs = 2GM / c2 If it is not, or if anyone has one that might work better, could you refer it to me?
6. ### Black hole calculations, the "Event Horizon Telescope"

Homework Statement Soon astronomers will be imaging the “shadow” of light from the event horizons of black holes. Since black holes are very small, this achievement seems impossible. Nevertheless, it is possible for three reasons: 1. Supermassive black holes have large event horizons. 2. Radio...
7. ### B Smallest Schwarzschild Radius: Theory & Facts

Is there theoretically a smallest possible Schwarzschild radius?
8. ### Minimum Orbital Radius Around Black Holes

Hi there, I was reading one of my textbooks and I had a thought. For a black hole, there is minimum orbiting radius of ##R_{min}=3R_s## where ##R_s## is the Schwarzschild Radius. This minimum orbit is created by the fact that in order to obtain an orbit of that radius around a black hole, you...
9. ### Sean Carroll's Spacetime and Geometry Chapter 5. Questions 3

Homework Statement I'm not in grad school but I've been trying to teach myself some GR and I asked a professor what problems he thought would be good to study. He mentioned this one. I'd ask him for help, but he's out of town this week. I've also attached a picture to this problem. (It seems...
10. ### BH to Sun, back of the napkin calculation of solar mass

Yesterday I had a bizarre idea. I supposed that a black hole (which I assumed to be a sufficiently dense sphere) became our sun. I know this is completely wrong, but please humor me and see what I've done. Suppose we have a sphere sufficiently dense, so that the Schwarzschild radius, r_s, is...
11. ### Deriving the Schwarzchild radius?

I'm a bit confused about the derivation of the Schwarzschild radius. I can do it quite easily using Newton's Law of gravitation, but this law is only an approximation, so I am wondering whether the result I obtain, r_{s}=\frac{2GM}{c^{2}}, is an approximation or not. It seems to me that it...
12. ### Schwarzchild Radius: By definition must be dependent on distance.

The Schwarzschild Radius of an object is the length such that if the object is shrunk down that small, the escape velocity becomes equal to the speed of light. That being said, however, the escape velocity of any gravitational body matters where it is measured relative to the center of mass...
13. ### Schwarzchild radius and escape velocity?

We know that the escape velocity at the schwarzchild radius is c. Since the escape velocity is defined as the velocity needed to escape from the gravitational field, to reach a total energy of 0 at infinity: Doesn't this mean that an object falling from infinity starting at rest, to the...
14. ### Escaping the Schwarzchild Radius

There's something bothering me about the event horizons of black holes. The Schwarzschild radius (as I see it) is basically the distance from a center of mass at which the escape velocity is the speed of light. The way escape velocity is defined though is the speed a body must have to "reach...
15. ### Electron schwarzchild radius problem

The schwarszchild radius of an electron=1.353*10^-57m, and to work out the volume of a particle assuming it is spherical is 4/3*pi*radius^3 so the volume of an electron at its schwarzchild radius is 4/3*pi*1.353*10^-57^3 = 0??! WHAT DOES THIS MEAN :S
16. ### Calculating mass and Schwarzchild radius of Black Hole

Homework Statement The temperature of a black hole is given by T = \frac{\hbar c^3}{8 \pi k G M} where h is Planck's constant, k is Boltzmann constant, G is the universal gravitation constant, and M is mass. Calculate (A) the mass, and (B) the Schwarzschild radius of a black hole at room...
17. ### Is the schwarzchild radius a radius of curvature?

EDIT: Is the Schwarzschild coordinate a radius of curvature in the geodesic? And also, in physics, what do I make of a negative radius of curvature?