1.1)
One may use any reasonable equation to obtain the dimension of the questioned
quantities.
I) The Planck relation is
1
2
1
]
][
[
]
[
]
[
]
][
[


=
=
⇒
=
⇒
=
T
ML
E
h
E
h
E
h
ν
ν
ν
(0.2)
II)
1
]
[

=
LT
c
(0.2)
III)
2
3
1
2
2
2
]
][
][
[
]
[



=
=
⇒
=
T
L
M
m
r
F
G
r
m
m
G
F
(0.2)
IV)
1
2
2
1
]
[
]
[
]
[



=
=
⇒
=
K
T
ML
E
K
K
E
B
B
θ
θ
(0.2)
1.2) Using the StefanBoltzmann's law,
4
θ
σ
=
Area
Power
, or any equivalent relation, one obtains:
(0.3)
.
]
[
]
[
]
[
4
3
1
2
4




=
⇒
=
K
MT
T
L
E
K
σ
σ
(0.2)
1.3)
The StefanBoltzmann's constant, up to a numerical coefficient, equals
,
δ
γ
β
α
σ
B
k
G
c
h
=
where
δ
γ
β
α
,
,
,
can be determined by dimensional analysis. Indeed,
,
]
[
]
[
]
[
]
[
]
[
δ
γ
β
α
σ
B
k
G
c
h
=
where e.g.
.
]
[
4
3


=
K
MT
σ
(
) (
) (
) (
)
,
2
2
2
3
2
1
2
2
2
3
1
1
1
2
4
3
δ
δ
γ
β
α
δ
γ
β
α
δ
γ
α
δ
γ
β
α





+
+
+
+









=
=
K
T
L
M
K
T
ML
T
L
M
LT
T
ML
K
MT
(0.2)
The above equality is satisfied if,

=


=




=
+
+
+
=
+

⇒
,
4
,
3
2
2
,
0
2
3
2
,
1
δ
δ
γ
β
α
δ
γ
β
α
δ
γ
α
(Each one (0.1))
⇒
=
=

=

=
.
4
,
0
,
2
,
3
δ
γ
β
α
(Each one (0.1))
⇒
.
3
2
4
h
c
k
B
=
σ
2.1) Since
A
, the area of the event horizon, is to be calculated in terms of
m
from a
classical theory of relativistic gravity, e.g. the General Relativity, it is a combination of
c
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 Spring '11
 NA
 Thermodynamics, Energy, Black hole, dt, Black body, Hawking radiation

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