The Cosmic Perspective (9th Edition)
The Cosmic Perspective (9th Edition)
9th Edition
ISBN: 9780134874364
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Chapter S4, Problem 54EAP
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To Explain:The reason for lifetime of lower mass black hole being shorter than the massive ones.

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The Schwarzschild radius is the distance from an object at which the escape velocity is equal to the speed of light. A black hole is an object that is smaller than its Schwarzschild radius, so not even light itself can escape a black hole. The Schwarzschild radius r depends on the mass m of the black hole according to the equation (See image.) where G = 6.673 × 10-11 (Nm2)/(kg2) is the gravitational constant and c = 2.998 × 108 m/s is the speed of light.   1. Consider a black hole with a mass of 3.70 × 107M.. Use the given equation to find the Schwarzschild radius for this black hole. Remember that 1 M = 1.989 × 1030 kg and 1 N = 1 kg * m/s2   2. What is this radius in units of the solar radius? Remember that 1 R = 6.955 × 108 m.
In 1999, scientists discovered a new class of black holes with masses 100 to 10000 times the mass of our sun, but occupying less space than our moon. Suppose that one of these black holes has a mass of 1x10^3 suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in g/cm^3? The radius of our sun is 7.0x10^5km and it has an average density of 1.4x10^3kg/m^3. The diameter of the moon is 2.16x10^3 miles. Note: the volume of a sphere is V=4/3 pie r^3
The following quotation is taken from the article “Quantum Black Holes”, by Bernard J. Carr and Steven B. Giddings, in the May 2005 issue of Scientific American. "The total time for a black hole to evaporate away is proportional to the cube of its initial mass. For a solar-mass hole, the lifetime is an unobservably long 1064 years." a. Recall that the solar mass is 2 × 10³0 kilograms. Write a formula for the lifetime, L, of a black hole as a function of its mass, m. Start by finding the value of the constant k, then write your function using the letter k (rather than its value in scientific notation). For example, for a direct variation you would write “L(m) = km”. k = a × 10¹ where a = L(m) = b. The present age mass = c × 10ª kg, where c = A and b = = of the universe is about 10¹0 years. What would be the mass of a black hole as old as the universe? ID and d = J
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