A \"black hole\" is created when a star collapses to such a smallradius that the

Question

A "black hole" is created when a star collapses to such a smallradius that the gravitational force at its surface becomes sostrong that not even light can escape. This radius is called theSchwarzchild radius in honor of Karl Schwarzchild whofirst solved the equations of General Relativity and showed thatblack holes could exist, at least in theory. Although the propercalculation requires knowledge of General Relativity, interestinglywe can derive the correct Schwarzchild radius by doing acalculation using classical physics*. That is, you'lluse the equation we derived in class and solve for the Schwarzchildradius assuming that the escape velocity equals the speed oflight.

What is the Schwarzchild radius for a star of mass M =1.10 x 1030kg? (this star iscomparable in mass to our Sun).
1 m
Find the density of such a black hole
2 kg/m3

* The reason the classical calculation yields thecorrect answer is there are are two errors that are made that"cancel" each other out and fortuitously give the same answer asthe full, proper calculation using general relativity.

Explanation / Answer

Assuming speed of light : c = 3*108 m/s Escape velocity for the black hole is : v = c such that : GMm/R = 0.5*m*v2 So, v = [2GM/R] = c So, R = 2GM/c2 = 2*6.67*10-11*1.1*1030 /[3*108]2 = 1.63044*103 m So, density of the black hole would be : M / [(4/3)*(R3)] = 6.0588*1019 kg/m3 = 1.63044*103 m So, density of the black hole would be : M / [(4/3)*(R3)] = 6.0588*1019 kg/m3

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