Stephen Hawking's Epitaph

His formula for the temperature of a Black Holeby Tony Heyes

Stephen Hawking'sformula for the temperature of a Black Hole is inscribed on his tombstone in Westminster Abbey and also on one of my tee shirts. My tribute to an old friend.Stephen was never afraid of an arument and never shy of a controvesy. When in 1972

Jacob Bekensteinsuggested that there should be thermodynamics of black holes Stephen was one of his detractors. Subsequent anslysis led to a change of mind after which Stephen persued the subject with enthusiasm.Stepehen's temperature formula is most remarkable. It is the only formula I know which incorporates both Classical Constants and Quantum Constants.

Actually, Hawking's somewhat similar formula for the Entropy of a Black Hole also does this.

I had always understood that it was this latter formula that Stephen wished to have as his epitaph!

For more information as to the significance of this formula listen to my radio interview

Those, like me, who enjoy doing calculations will need to know the values of the various constants; so here they are:On Stephen Hawking's EpitaphOr watch a video: Deriving Hawking's most famous equation:

The Temperature of a Black Hole

c Velocity of light = 299,792,458 m s-1Given that the above are all constants the temperature equation may be reduced to:h bar Planck's concstant/2pi = 1.05 x 10^-34 kg m2 s-1

pi = 3.14

G Newton's Gravitational constant = 6.67 x 10^-11 m3 kg-1 s-2

kb Boltzmann's constant = 1.38 x 10^-23 m2 kg s-2 K-1

T = (6 x 10^-8)/Ms deg K where Ms = the number of solar masses.

Note: the mass of the sun = 1.989 X 10^30 kg

the mass of the moon = 7.347 X 10^22 kg

the Cosmic Microwave Background radiation temperature = 2.725 deg K

the diameter of a Black Hole = 2 X the Schwarzschild radius = 4GM/c^2 mNow it is easy to work out the mass of tbe Black Hole whose temperature equals that of tbe Cosmic Background Radiation.

Notice that it is approximately equal to the mass of our Moon and has the diameter of a human hair!

In 2019 the Royal Mint produced a commemorative 50 pence coin to celebrate Stephen's life. The obverse of the coin shows an artist's impressionof a black hole. With tbe aid of a magnifying glass one may also see the Hawking formula for the entropy of a black hole. what a pity the artist did not choose to have a hole in the middle of the coin surrounded by an accretion disk. To avoid making a mess of the Queen's face on the other side the hole could have been a dimple.

Somewhat 'tounge-in-cheek' the Mint published a list of the atributes of a Black Hole with the same mass as their coin.

And now the man himself....

In 2015 Stephen delivered the

BBC Reith lectures.Iwhy Stephen,Do Black Holes have no hair?like me, was grateful for Britain'sNational Health Service

of