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

[Spinozalens@aol.com]

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