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Related Pages
Related Symbols
FormulaData
NondimensionalizationTransform
UnitSystem
UnitConvert
Related Categories
Physics
Nondimensional Form of Black Hole Surface Gravity
Example Notebook
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Get the expression for the surface gravity of a charged black hole and the quantity variables present in it:
I
n
[
1
]
:
=
f
o
r
m
u
l
a
=
F
o
r
m
u
l
a
D
a
t
a
[
{
"
B
l
a
c
k
H
o
l
e
S
u
r
f
a
c
e
G
r
a
v
i
t
y
"
,
"
C
h
a
r
g
e
"
}
]
O
u
t
[
1
]
=
k
2
c
2
G
/
4
c
2
M
+
-
1
4
π
G
/
(
ε
0
4
c
)
2
Q
-
1
4
π
G
/
(
ε
0
4
c
)
2
Q
+
2
G
/
2
c
M
G
/
2
c
M
+
2
G
/
4
c
2
M
+
-
1
4
π
G
/
(
ε
0
4
c
)
2
Q
I
n
[
2
]
:
=
v
a
r
i
a
b
l
e
s
=
F
o
r
m
u
l
a
D
a
t
a
[
{
"
B
l
a
c
k
H
o
l
e
S
u
r
f
a
c
e
G
r
a
v
i
t
y
"
,
"
C
h
a
r
g
e
"
}
,
"
Q
u
a
n
t
i
t
y
V
a
r
i
a
b
l
e
s
"
]
O
u
t
[
2
]
=
{
k
,
M
,
Q
}
Replace the quantity variables representing surface gravity, mass and charge with their respective nondimensional variables:
I
n
[
3
]
:
=
N
o
n
d
i
m
e
n
s
i
o
n
a
l
i
z
a
t
i
o
n
T
r
a
n
s
f
o
r
m
[
f
o
r
m
u
l
a
,
v
a
r
i
a
b
l
e
s
,
{
κ
,
m
,
q
}
]
O
u
t
[
3
]
=
2
m
κ
+
2
m
κ
2
K
[
1
]
2
s
2
c
/
m
2
m
1
2
K
[
1
]
4
s
4
c
/
2
m
+
2
q
-
1
4
π
2
K
[
1
]
4
s
4
c
/
2
m
+
2
q
κ
-
1
4
π
K
[
1
]
2
s
2
c
/
m
2
m
1
2
K
[
1
]
4
s
4
c
/
2
m
+
2
q
-
1
4
π
2
K
[
1
]
4
s
4
c
/
2
m
1
Simplify the result further by specifying a natural unit system:
I
n
[
4
]
:
=
e
q
u
a
t
i
o
n
=
N
o
n
d
i
m
e
n
s
i
o
n
a
l
i
z
a
t
i
o
n
T
r
a
n
s
f
o
r
m
[
f
o
r
m
u
l
a
,
v
a
r
i
a
b
l
e
s
,
{
κ
,
m
,
q
}
,
U
n
i
t
S
y
s
t
e
m
"
D
e
S
i
t
t
e
r
U
n
i
t
s
"
]
O
u
t
[
4
]
=
2
m
κ
+
2
q
κ
-
1
/
Λ
2
q
-
1
/
Λ
+
2
m
1
/
Λ
+
2
m
κ
2
/
Λ
2
q
-
1
/
Λ
+
2
m
1
/
Λ
1
Get the transformation rules:
I
n
[
5
]
:
=
r
u
l
e
s
=
N
o
n
d
i
m
e
n
s
i
o
n
a
l
i
z
a
t
i
o
n
T
r
a
n
s
f
o
r
m
[
f
o
r
m
u
l
a
,
v
a
r
i
a
b
l
e
s
,
{
κ
,
m
,
q
}
,
"
N
o
n
d
i
m
e
n
s
i
o
n
a
l
i
z
a
t
i
o
n
R
u
l
e
s
"
,
U
n
i
t
S
y
s
t
e
m
"
D
e
S
i
t
t
e
r
U
n
i
t
s
"
]
O
u
t
[
5
]
=
k
κ
1
Λ
2
c
,
M
m
1
2
c
/
(
Λ
G
)
,
Q
q
2
π
ε
0
2
c
/
(
Λ
G
)
Compare the translation factor for mass to solar masses:
I
n
[
6
]
:
=
U
n
i
t
C
o
n
v
e
r
t
[
(
M
/
.
r
u
l
e
s
)
/
.
m
1
,
"
S
o
l
a
r
M
a
s
s
"
]
O
u
t
[
6
]
=
6
.
4
×
2
2
1
0
M
☉
Related Symbols
FormulaData
NondimensionalizationTransform
UnitSystem
UnitConvert
Publisher Information
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