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Collector
Posts: 4114
Joined: August 21st, 2001, 12:37 pm

### Re: RIP

RIP on $\pi$-day

One of several equations where Stephen Hawking used $\pi$, Hawking temperature

$T=\frac{\hbar c^3}{8\pi GM k_B}$

and time slows down at the Black hole surface area $16\pi N^2l_p^2$
I'm with Wittgenstein on this one; this formula is a description, not an explanation.

Are black holes also black bodies? I am missing an entry for emissivity somewhere...The Stefan-Boltzman law AFAIR is $\varepsilon\sigma T^4,$  where $0 < \varepsilon < 1$.
Even humble soot - the closest thing to a black body - has a value of 0.97. (I used to simulate (black and white) TV CRTs using FEM at a Dutch company so I know a little bit and even phosphor was not a perfect absorbers).

Does anyone have a step-by-step derivation?

Not my area, but do perfect absorbers exist far away (or in people's heads) but not on planet Earth? Just wondering.

Hawking used π
When does it appear?
"Does anyone have a step-by-step derivation?"

It is in his famous 1974 paper, on page 30 Hawking says"

"one would expect if the black hole was a body with temperature of $(\kappa/2\pi)(\hbar/2k)$..."

And yes he says $\kappa$ is the surface gravity of the Black hole. If we for simplicity assume Newton surface gravity at the Karl radius (better known as the Schwarzschild radius)  we have the following Newtonian Schwarzschild gravitational acceleration field (Newton where only radius is replaced by Schwarzschild radius $r_s$ :

$g=\frac{GM}{r_s^2}$

(after sleeping on it) I am quite sure we must divide this by c, then replace the k and we get

\begin{eqnarray*}
T&=& \frac{\frac{\frac{GM}{r_s^2}}{c}}{2\pi}\frac{\hbar}{2k}  \\
T&=&\frac{ \frac{\frac{GM} { \left( \frac{2GM}{c^2}\right)^2 }}{c}} {2\pi}\frac{\hbar}{2k}  \\
T&=&\frac{\frac{\frac{GM}{\frac{4G^2M^2}{c^4}}}{c}}{2\pi}\frac{\hbar}{2k}  \\
T&=&\frac{c^3}{8\pi GM}\frac{\hbar}{2k}
\end{eqnarray*}

off by a factor of $\frac{1}{2}$   . The formula  $T=\frac{\hbar c^3}{8\pi GM k_B}$  is based on different method for surface gravity taking into account the bending of space-time, the Schwarzschild metric solution of GR that is known to be different in strong gravitational fields than Newton.

I guess similar to also GR bending of light twice as Newton.

Anyway I am on Cuch on Wittgenstein on this one; this formula is a description, not an explanation.

Ohh yes Cuch, I now understand you for years have wondered about the temperature of Einstein in the Black Hole Hedge Fund ? It was a 10 solar masses Black Hole, so looks like the Hawking temperature is approx $6.17 \times 10^{-9}$ kelvin (I assume he moved his space station down to the surface of the bh). Ohh that explain why so few Black Hole hedge funds, I always wondered. Their assets have been frozen so to say!!!.

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

### Re: RIP

mathematician Philip J. Davis who wrote large chunks of Abramowitz & Stegun, including the section on Gamma functions, died March 14, 2018 aged 95

Cuchulainn
Posts: 58390
Joined: July 16th, 2004, 7:38 am
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### Re: RIP

mathematician Philip J. Davis who wrote large chunks of Abramowitz & Stegun, including the section on Gamma functions, died March 14, 2018 aged 95
RIP.
A top numerical analyst. His "Interpolation and Approximation" is a classic.
95! A good innings.

//
I see that Cathleen Morawitz Synge also passed last year
https://en.wikipedia.org/wiki/Cathleen_Synge_Morawetz

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

### Re: RIP

RIP  Cathleen Morawitz Synge

Cuchulainn
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### Re: RIP

One began to hear it said that World War I was the chemists’ war, World War II was the physicists’ war, World War III (may it never come) will be the mathematicians’ war.

Philip J. Davis

katastrofa
Posts: 7235
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Location: Alpha Centauri

### Re: RIP

Daphne Sheldrick, 86, Kenyan-British environmentalist and elephant conservationist

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

### Re: RIP

Daphne Sheldrick, 86, Kenyan-British environmentalist and elephant conservationist
RIP

tw
Posts: 951
Joined: May 10th, 2002, 3:30 pm

### Re: RIP

six horses at Cheltenham festival

Hopefully Aintree is more benign today but the soft running doesn't bode well.

ppauper
Posts: 70239
Joined: November 15th, 2001, 1:29 pm

### Re: RIP

six horses at Cheltenham festival

Hopefully Aintree is more benign today but the soft running doesn't bode well.
RIP horsies

tw
Posts: 951
Joined: May 10th, 2002, 3:30 pm

### Re: RIP

Well that is the UK for you; all buttoned up repression, demureness and inhibition.
six horses at Cheltenham festival

Hopefully Aintree is more benign today but the soft running doesn't bode well.
RIP horsies

katastrofa
Posts: 7235
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: RIP

Milos Forman

ppauper
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### Re: RIP

RIP

rmax
Posts: 6060
Joined: December 8th, 2005, 9:31 am

### Re: RIP

RIP

Cuchulainn
Posts: 58390
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### Re: RIP

RIP
"I can't take it no more. I gotta get outta here. "

Cuchulainn
Posts: 58390
Joined: July 16th, 2004, 7:38 am
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### Re: RIP

RIP Big Tom McBride

https://www.rte.ie/entertainment/2018/0 ... ride-dies/

Oh we're going out the same way we came in
Don't matter who you know or where you've been
Makes no difference who you are Skid Row Joe or superstar
You're going out the same way you came in

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