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A Black Hole has an event horizon, located at the Schwartzschild radius from the center of...

A Black Hole has an event horizon, located at the Schwartzschild radius from the center of the black hole. The Schwartzschild radius of a black hole is proportional to its mass. We can write a handy version of this equation for stars in terms of Solar Masses as follows: R = 3M

Where R is measured in kilometers and M in Solar Masses. So a 1 solar mass object (the Sun for example) if turned into a black hole would have a Schwartzschild radius of 3km. We believe galaxies have supermassive black holes at their centers with masses that can be a million, or even a billion times the mass of the Sun.

a) How large is the Schwartzschild radius for a black hole of a million solar masses?

b) What about a billion (109 ) solar masses?

c) How do these sizes compare with the radius of the sun (the actual sun, not the sun as a black hole), and the size of our solar system?

Remember you must compare the sizes in kilometers. The radius of the solar system is about 100 AU. 1 AU is about 150 million kilometers.

Solutions

Expert Solution

a) Schwartzschild radius is given by the relation, in km ---------(1)

Mass of the black hole, MB1 = 1 million solar masses

Therefore according to equation (1) Schwartzschild radius,

b) Mass of the black hole,

Therefore Schwartzschild radius,

c) Radius of Sun,

Radius of solar system,

Comparison of first Black hole with sun,

Comparison of second Black hole with sun,

Comparison of first Black hole with solar system,

Comparison of second Black hole with solar system,

genius_generous answered 1 year ago

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