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# [Phys-l] Bekenstein Bound and the Davies-Hawking-Unruh effect

Bekenstein Bound and the Davies-Hawking-Unruh effect

From the Bekenstein bound we have;

E= hbar*c*S/(2*pi*R)

Where S is entropy, c is the speed of light, hbar is the reduced Planck
constant and R is the radius of the volume being modeled.

From the second law of thermodynamics we have

dE/dS=k*T

Where k is Boltzmann's constant and T is temperature.

dE/dS= hbar*c/(2*pi*R)

Incorporating the Horizon generated by acceleration;

R=c^2/a

Where a is acceleration.

dE/dS=k*T=a*hbar/(2*pi*c)

k*T =a*hbar/(2*pi*c)

Which is the Davies-Unruh equation.

This should hold for horizons generated by mass energy concentration per
the equivalence principle, therefore;

a=G*M/R^2

Where G is the gravity constant, M is the mass and R is the Radius.

L=KE +PE =0

Where L is the Lagrangian in its ground state, KE is kinetic energy and PE
is the negative gravitational potential energy, therefore

m*v^^2/2-G*m*M/R=0

Where m is the mass of a gravity bound body (m <<<< M)

For a black hole

v=c

Therefore

R=2*G*M/c^2

Therefore

a= c^4/[(2*GM)^2]

k*T=a*hbar/(2*pii*c)= hbar*c^3/(8*pi*G*M)

Putting this in the more common form;

T=h*c^3/(16*pi^2*G*k*M)

This is the Hawking temperature equation for Schwarzchild black holes.

Bob Zannelli