document as a secondary effect for entropy generation. The idea would be that
we would have, for a quantum level, n, specified for a black hole, due to what Corda
developed the following temperature distribution which would ALSO add into more
entropy. We include it in as a future works project. The first term below comes from
Dyson (1966) and is linkable to a way to also, in addition to the mechanism so
brought up a way to also add more early universe entropy, which is linkable to
gravitons.
T H ¼ m D Á
m D Á n þ 2
ð
Þ
m bh Á 8 Á Γ
nþ3
2
À Á
! 1=nþ1
ð
Þ
Á
n þ 1
4
ffiffiffi
π
p
m D ¼
: 1 TeV 10
12 eV ¼ 1:783 Â 10
À30 g
m bh ¼
: 1:22 Â 10
21 TeV ¼ 2:175 Â 10
À9 g
T H / 1 TeV Á
n þ 2
ð
Þ
1:22 Â 10
21
Á 8 Á Γ
nþ3
2
À Á
! 1=nþ1
ð
Þ
Á
n þ 1
4
ffiffiffi
π
p
ð3:26Þ
We look at the initial state of created gravitons, and use the physics given in
Hawking (1974) with the specified Hawking temperature, as the main physics
phenomenon of interest to our analysis. We then can, if we have this Hawkings
temperature, as given in Eq. (3.7) consider the question of first, if the black holes
have classical or quantum behavior as well as Γ being a gamma function, i.e., look at
what is given in Beckwith (2018), in its conclusion which we will cite here. That is,
the idea is based upon the formation of a finite number of black holes, which decay.
Quoting Beckwith (2018) we have that we will be looking at the following:
Quote, Beckwith (2018)
“Our physics is simplified if we change Planck length to be scaled as 1 and we
look at a ‘unit’ evaluated space-time volume.” Then we can set n of Eq. (3.26) equal
to zero initially and obtain the following from Corda (2018) and Beckwith (2018)
16π
e n qm
4 Â 10
4
Á
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1 À
e n qm À 1
e n qm
s
% 10
6
m bh % 10
2
 m planck 4 À dim
ð
Þ
ΔV total ’ 10
2
 ΔV e n qm À1!e n qm % 10
2
 16π
e n qm
4 Â 10
4
Á
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1 À
e n qm À 1
e n qm
s
% 10
8
ð3:27Þ
This puts a serious restriction on the number of allowed quantization levels e n qm ,
but it also means that within this horizon space we may be seeing mini black holes
created which could release gravitons. We will then discuss what may be pertinent to
characterizing if the black holes are behaving classically or quantum mechanically.
Note, if n in Eqs. (3.26) and (3.31) is set equal to zero, we have that if we literally
32
A. W. Beckwith
we would have, for a quantum level, n, specified for a black hole, due to what Corda
developed the following temperature distribution which would ALSO add into more
entropy. We include it in as a future works project. The first term below comes from
Dyson (1966) and is linkable to a way to also, in addition to the mechanism so
brought up a way to also add more early universe entropy, which is linkable to
gravitons.
T H ¼ m D Á
m D Á n þ 2
ð
Þ
m bh Á 8 Á Γ
nþ3
2
À Á
! 1=nþ1
ð
Þ
Á
n þ 1
4
ffiffiffi
π
p
m D ¼
: 1 TeV 10
12 eV ¼ 1:783 Â 10
À30 g
m bh ¼
: 1:22 Â 10
21 TeV ¼ 2:175 Â 10
À9 g
T H / 1 TeV Á
n þ 2
ð
Þ
1:22 Â 10
21
Á 8 Á Γ
nþ3
2
À Á
! 1=nþ1
ð
Þ
Á
n þ 1
4
ffiffiffi
π
p
ð3:26Þ
We look at the initial state of created gravitons, and use the physics given in
Hawking (1974) with the specified Hawking temperature, as the main physics
phenomenon of interest to our analysis. We then can, if we have this Hawkings
temperature, as given in Eq. (3.7) consider the question of first, if the black holes
have classical or quantum behavior as well as Γ being a gamma function, i.e., look at
what is given in Beckwith (2018), in its conclusion which we will cite here. That is,
the idea is based upon the formation of a finite number of black holes, which decay.
Quoting Beckwith (2018) we have that we will be looking at the following:
Quote, Beckwith (2018)
“Our physics is simplified if we change Planck length to be scaled as 1 and we
look at a ‘unit’ evaluated space-time volume.” Then we can set n of Eq. (3.26) equal
to zero initially and obtain the following from Corda (2018) and Beckwith (2018)
16π
e n qm
4 Â 10
4
Á
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1 À
e n qm À 1
e n qm
s
% 10
6
m bh % 10
2
 m planck 4 À dim
ð
Þ
ΔV total ’ 10
2
 ΔV e n qm À1!e n qm % 10
2
 16π
e n qm
4 Â 10
4
Á
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1 À
e n qm À 1
e n qm
s
% 10
8
ð3:27Þ
This puts a serious restriction on the number of allowed quantization levels e n qm ,
but it also means that within this horizon space we may be seeing mini black holes
created which could release gravitons. We will then discuss what may be pertinent to
characterizing if the black holes are behaving classically or quantum mechanically.
Note, if n in Eqs. (3.26) and (3.31) is set equal to zero, we have that if we literally
32
A. W. Beckwith