# Schwarzschild Radius: Calculating V(esc.) & R

• I
• SD das
In summary, the conversation discusses the Schwarzschild radius, which can be calculated using the classical formula for escape velocity by setting it equal to the speed of light and solving for the radius. However, this calculation may not accurately represent black holes, as they are not like classical bodies. To fully understand black holes, one must use the Schwarzschild solution to the Einstein field equations. There are many posts and articles on PF about the Schwarzschild radius, including a calculation for objects the mass of our sun and a proton.
SD das
Correct if I'm wrong.

V(esc.)=(2GM/R)^1/2 that is equal to R=2GM/V^2 putting v=c,we get R=2GM/c^2 by putting the value of G,M,C we get schwarzschild radius=1.46*10^-27 m/kg

Yes, you will get the Schwarzschild radius if you start with the classical formula for escape velocity as a function of mass and radius, set the escape velocity to ##c##, and solve for ##r##. However, a black hole is nothing like a classical body whose escape velocity is ##c##, so it is not clear that this result is telling us anything important.

To properly understand black holes and why the Schwarzschild radius is what is, you have to start with the Schwarzschild solution to the Einstein field equations. You'll find many threads here if you search for "black hole escape velocity".

I've found hundreds of posts on PF about the Schwarzschild radius, which you might look for as well. Simply use the search functionality at the top right in the frame of this side. Especially a couple of recently written Insight articles might be of your interest: https://www.physicsforums.com/insights/schwarzschild-geometry-part-1/#toggle-id-1

I've also found a funny calculation of the corresponding radii for objects the mass of our sun and a proton which you can compare your result to:

Unfortunately the book quotation doesn't show how to assess these results, as it's not for free.

## 1. What is the Schwarzschild radius?

The Schwarzschild radius is a theoretical concept in physics that represents the distance from the center of a non-rotating, uncharged black hole at which the escape velocity exceeds the speed of light.

## 2. How is the Schwarzschild radius calculated?

The Schwarzschild radius (R) can be calculated using the formula R = 2GM/c^2, where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

## 3. What is the significance of the Schwarzschild radius?

The Schwarzschild radius is significant because it defines the event horizon of a black hole. Anything that crosses this radius will be unable to escape the gravitational pull of the black hole.

## 4. How does the Schwarzschild radius relate to escape velocity?

The Schwarzschild radius is directly related to the escape velocity of a black hole. As the radius decreases, the escape velocity increases, making it more difficult for anything to escape from the black hole's gravitational pull.

## 5. Can the Schwarzschild radius be measured?

The Schwarzschild radius cannot be directly measured since it is a theoretical concept. However, it can be estimated based on the mass of the black hole and its distance from other objects, such as stars or gas clouds, using the equation mentioned in question 2.

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