The schwarzschild radius rbh for an object of mass m is defined as: rbh = (2gm)/(c^2)
where c is the speed of light and g is the universal gravitational constant. rbh gives the radius of the event horizon of a black hole with mass m (in other words, it gives the radius to which some amount of mass m would need to be compressed in order to form a black hole).
1) the mass of the sun is about 1.99 × 1030 kg. what would be the radius of a black hole with this mass?
2)the mass of mars is about 6.42 × 1023 kg. what would be the radius of a black hole with this mass?
3) suppose you want to make a black hole that is roughly the size of an atom (take rbh = 1.30 × 10-10 m). what would be the mass m of such a black hole?

Answers:

1) 2951.39 m

2) 0.000952 m

3)

Explanation:

1) We know the Schwarzschild radius is given by the following equation:

  (1)

Where:

is the Universal Gravitational Constant

the mass of the black hole

is the speed of light

Now, if we have a black hole with the mass of the Sun (), its radius will be:

  (2)

  (3)

  (4) This is the radius of the black hole with the mass of the Sun

2) On the other hand, if the black hole has the mass of Mars (), its radius will be:

  (5)

  (6)

  (7) This is the radius of the black hole with the mass of Mars

3) In this case, we have to isolate from (1):

  (8)

Where

Solving (8) with the known values:

  (9)

  (10) This is the mass of the black hole

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