The Schwarzschild radius, RS, of a black hole depends on its mass m, the speed of light c, and the gravitational constant G (with units m3/(kg s2 )). Find a dimensionally correct expression for RS in terms of these quantities. Assuming that you found a dimensionally correct expression, can you be sure that this expression is, in fact, the correct expression for calculating the Schwarzschild radius? Explain your answer.

The Schwarzschild radius, RS, of a black hole depends on its mass m, the speed of light c, and the gravitational constant G (with units m3/(kg s2 )). Find a dimensionally correct expression for RS in terms of these quantities. Assuming that you found a dimensionally correct expression, can you be sure that this expression is, in fact, the correct expression for calculating the Schwarzschild radius? Explain your answer.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 59AP: A neutron star is a cold, collapsed star with nuclear density. A particular neutron star has a mass...

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Schwarzschild radius RS of a black hole is the maximum distance from the black hole’s center at which light cannot escape its gravitational field. The quantity RS (with dimensions of length) is dependent on the mass of the black hole M, the speed of light c, and the gravitational constant G. Based on the dimensions of these four parameters, predict an equation for the Schwarzschild radius. Hint: G has dimensions of [L3/MT2]
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That did answer a lot of questions. Thank you. But where do you derive the equation E=(K|q|)/r? My book says E=(K|q|)/r^2. I tried re-arranging some equations to get your equation, but I can't figure it out. Thanks.
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