I'm having no end of trouble with this seemingly simple problem:(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

What's the minimum mass of a black hole for which you could survive a fall through the event horizon without being ripped to shreds? Why would you be ripped to shreds for smaller black holes?

2. Relevant equations

[tex] \textbf{F} = -G\frac{mM}{r^2}\hat{\textbf{r}} [/tex](Schwarzschild radius)

[tex] R_s = \frac{2GM}{c^2} [/tex]

3. The attempt at a solution

Assume person of height h (= 2 m) can survive a tidal stretching force of 5mg over the length of his body (g being the acceleration due to gravity on Earth). Assume further that he is to be just barely surviving when his feet touch the event horizon. Then, the difference between the gravitational acceleration on his head and his feet should be:

[tex] \Delta a = -GM\left[\frac{1}{R_s^2} - \frac{1}{(R_s + h)^2} \right] = 5g [/tex]

When I try and solve this, I get some cubic equation:

[tex] \frac{c^2 h^2}{10g} = R_s^3 + 2R_s^2h + R_s\left[h^2 -c^2 \frac{h}{5g}\right] [/tex]

I spoke to other people who said they solved this easily and got something on the order of 10^{4}solar masses as the lower limit. Have I done something wrong with my algebra (or worse yet, with the physics)?

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# Homework Help: Minimum black hole mass to survive fall to event horizon

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