ABlackHolerepresentsaperfectequilibriumbetweentheElectricForces,MagneticForcesandGravitationalForces.term1+term2+term3+term4+term5+term6=0
term1=-term2=(∇. )term3=−×(∇×)term4=∇. term5=−×∇×term6=-μ . ε .
1
2
c
∂×
¯
E
¯
Η
∂t
ε
0
¯
E
¯
E
ε
0
¯
E
¯
E
μ
0
¯
Η
¯
Η
μ
0
¯
Η
¯
Η
1
2
2
ε
¯
E
¯
E
+
2
μ
¯
H
¯
H
¯
g
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
r=.
In[]:=
θ=.
In[]:=
φ=.
In[]:=
t=.
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Needs["DifferentialEquations`NDSolveProblems`"]
In[]:=
Needs["DifferentialEquations`NDSolveUtilities`"]
In[]:=
Needs["DifferentialEquations`InterpolatingFunctionAnatomy`"]
In[]:=
InverseFunctions->True
Out[]=
InverseFunctionsTrue
In[]:=
Get["VectorAnalysis`"]
In[]:=
r=.
In[]:=
SetCoordinates[Spherical[r,θ,φ]]
Out[]=
Spherical[r,θ,φ]
In[]:=
{Coordinates[Spherical],CoordinateRanges[Spherical]}
Out[]=
{{r,θ,φ},{0≤r<∞,0≤θ≤π,-π<φ≤π}}
In[]:=
CoordinatesToCartesian[Coordinates[Spherical],Spherical]
Out[]=
{rCos[φ]Sin[θ],rSin[θ]Sin[φ],rCos[θ]}
In[]:=
f[r]=.
In[]:=
n=.
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
Q1=.
In[]:=
G1=6.67408
-11
10
Out[]=
6.67408×
-11
10
In[]:=
Q1=1.6021765
-19
10
Out[]=
1.60218×
-19
10
In[]:=
ϵ0=8.85
-12
10
Out[]=
8.85×
-12
10
In[]:=
μ0=4π//N
-7
10
Out[]=
1.25664×
-6
10
In[]:=
G1=.
In[]:=
Q1=.
In[]:=
ϵ0=.
In[]:=
μ0=.
In[]:=
f[r]=K1
-
-+8πLog[r]
G1ϵ0μ0
r
8π
Out[]=
-
-+8πLog[r]
G1ϵ0μ0
r
8π
In[]:=
ev={0,f[r]Sin[ωt],-f[r]Cos[tω]}
Out[]=
0,K1Sin[tω],-K1Cos[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
8π
-
-+8πLog[r]
G1ϵ0μ0
r
8π
In[]:=
mv=(1/Sqrt[μ0])Sqrt[ϵ0]{0,f[r]Cos[tω],f[r]Sin[tω]}
Out[]=
0,K1,K1
-
-+8πLog[r]
G1ϵ0μ0
r
8π
ϵ0
Cos[tω]μ0
-
-+8πLog[r]
G1ϵ0μ0
r
8π
ϵ0
Sin[tω]μ0
In[]:=
gv=,0,0
G1
4π
2
r
Out[]=
,0,0
G1
4π
2
r
In[]:=
ev
Out[]=
0,K1Sin[tω],-K1Cos[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
8π
-
-+8πLog[r]
G1ϵ0μ0
r
8π
In[]:=
Div[ev]
Out[]=
-
-+8πLog[r]
G1ϵ0μ0
r
8π
r
In[]:=
Div[mv]
Out[]=
-
-+8πLog[r]
G1ϵ0μ0
r
8π
ϵ0
Cos[tω]Cot[θ]r
μ0
In[]:=
FullSimplify[%]
Out[]=
G1ϵ0μ0
8πr
ϵ0
Cos[tω]Cot[θ]2
r
μ0
In[]:=
term1a=D[Cross[ev,mv],t]
Out[]=
{0,0,0}
In[]:=
term1=((-ϵ0)*μ0)*D[Cross[ev,mv],t]
Out[]=
{0,0,0}
In[]:=
term2=ϵ0*ev*Div[ev]
Out[]=
0,ϵ0Cot[θ],-ϵ0Cos[tω]Cot[θ]Sin[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
r
In[]:=
term3=(-ϵ0)*Cross[ev,Curl[ev]]
Out[]=
-ϵ0-G1ϵ0μ0-G1ϵ0μ0,-ϵ0Cot[θ],-ϵ0Cos[tω]Cot[θ]Sin[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
8π
2
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
8π
2
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
r
In[]:=
term4=μ0*mv*Div[mv]
Out[]=
0,ϵ0Cot[θ],ϵ0Cos[tω]Cot[θ]Sin[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
r
In[]:=
term5=(-μ0)*Cross[mv,Curl[mv]]
Out[]=
-μ0-G1-G1,-ϵ0Cot[θ],ϵ0Cos[tω]Cot[θ]Sin[tω]
G1ϵ0μ0
4πr
2
K1
2
ϵ0
2
Cos[tω]
8π
4
r
G1ϵ0μ0
4πr
2
K1
2
ϵ0
2
Sin[tω]
8π
4
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
r
In[]:=
term6=-Dot[mv,mv]+μ0Dot[ev,ev]gv
ϵ0
2
μ0
2
2
ϵ0
2
Out[]=
,0,0
G1-μ0+-ϵ0ϵ0+ϵ0
1
2
2
ϵ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
1
2
2
μ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
μ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
μ0
4π
2
r
In[]:=
vergelijking=term1+term2+term3+term4+term5+term6
Out[]=
-μ0-G1-G1-ϵ0-G1ϵ0μ0-G1ϵ0μ0+,0,0
G1ϵ0μ0
4πr
2
K1
2
ϵ0
2
Cos[tω]
8π
4
r
G1ϵ0μ0
4πr
2
K1
2
ϵ0
2
Sin[tω]
8π
4
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
8π
2
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
8π
2
r
G1-μ0+-ϵ0ϵ0+ϵ0
1
2
2
ϵ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
1
2
2
μ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
μ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
μ0
4π
2
r
In[]:=
rvergelijking=term1[[1]]+term2[[1]]+term3[[1]]+term4[[1]]+term5[[1]]+term6[[1]]
Out[]=
-μ0-G1-G1-ϵ0-G1ϵ0μ0-G1ϵ0μ0+
G1ϵ0μ0
4πr
2
K1
2
ϵ0
2
Cos[tω]
8π
4
r
G1ϵ0μ0
4πr
2
K1
2
ϵ0
2
Sin[tω]
8π
4
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
8π
2
r
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
8π
2
r
G1-μ0+-ϵ0ϵ0+ϵ0
1
2
2
ϵ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
1
2
2
μ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Cos[tω]
μ0
-
-+8πLog[r]
G1ϵ0μ0
r
4π
2
K1
2
Sin[tω]
μ0
4π
2
r
In[]:=
FullSimplify[%]
Out[]=
0
In[]:=
rvergelijking1=%
Out[]=
0
In[]:=
θvergelijking=term1[[2]]+term2[[2]]+term3[[2]]+term4[[2]]+term5[[2]]+term6[[2]]
Out[]=
0
In[]:=
FullSimplify[%]
Out[]=
0
In[]:=
θvergelijking1=%
Out[]=
0
In[]:=
φvergelijking=term1[[3]]+term2[[3]]+term3[[3]]+term4[[3]]+term5[[3]]+term6[[3]]
Out[]=
0
In[]:=
FullSimplify[%]
Out[]=
0
In[]:=
φvergelijking1=%
Out[]=
0
Results force densities in resp r-direction, θ-direction, φ-direction
In[]:=
rvergelijking1
Out[]=
0
In[]:=
θvergelijking1
Out[]=
0
In[]:=
φvergelijking1
Out[]=
0
In[]:=
Theradialfunction'f[r]'fortheelectromagnetic-gravitationalconfinement(GEON)equals:f[r]=K1Inthebook:'
-
-+8πLog[r]
G1ϵ0μ0
r
8π
RisingoftheJamesWebbSpaceTelescopeanditsFundamentalBlindness
',page104,Figure4,agraphicPlothasbeenpresentedfortheGEONwiththechosenvalueforK1=6.67408-11
10
-
Times[5]+Times[3]
8π
′
function
′
K1
-
Times[5]+Times[3]
8π
Out[]=
-
-+8πLog[r]
G1ϵ0μ0
r
8π
In[]:=
ϵ0=8.85
-12
10
Out[]=
8.85×
-12
10
In[]:=
μ0=4π
-7
10
Out[]=
π
2500000
In[]:=
Out[]=
In[]:=
G1=6.67408
-11
10
Out[]=
6.67408×
-11
10
In[]:=
ϵ0=8.85
-12
10
Out[]=
8.85×
-12
10
In[]:=
μ0=4π
-7
10
Out[]=
π
2500000
TheMassfortheBlackHolehasbeenchosen:Mass=[kg]
35
10
Out[]=
In[]:=
Mass=
35
10
Out[]=
100000000000000000000000000000000000
In[]:=
Plot,{r,,}
-
-+8πLog[r]
MassG1ϵ0μ0
r
8π
7
10
4
10
Out[]=
In[]:=
Plot,{r,,}
-
-+8πLog[r]
MassG1ϵ0μ0
r
8π
5
10
4
10
Out[]=
TheMassfortheBlackHolehasbeenchosen:Mass=[kg].TheradiusoftheBlackHoleequalsabout25[km].
35
10