flaws in black hole theory and general relativity - Indico
https://indico.cern.ch/event/211539/.../Crothers-Protvino-2013.pdf
SJ Crothers 著 - 引用元 3 - 関連記事
2013/06/28 - (Foster, J. and Nightingale, J.D., A Short Course in General. Relativity ... according to general relativity, there must be a singularity of infinite density, within .... These quantities are undefined since division by zero is undefined.
FLAWS IN BLACK HOLE THEORY AND GENERAL RELATIVITY
STEPHEN J. CROTHERS
Alpha Institute for Advanced Study
PO Box 1546, Sunshine Plaza, 4558, QLD, Australia
∗E-mail: thenarmis@gmail.com
www.sjcrothers.plasmaresources.com/index.html
All alleged black hole models pertain to a universe that is spatially infinite, is eternal,
contains only one mass, is not expanding, and is asymptotically flat or asymptotically
not flat. But the alleged big bang cosmology pertains to a universe that is spatially finite
(one case) or spatially infinite (two different cases), is of finite age, contains radiation and
many masses including multiple black holes (some of which are primordial), is expanding,
and is not asymptotically anything. Thus the black hole and the big bang contradict
one another - they are mutually exclusive. It is surprisingly easy to prove that neither
General Relativity nor Newton’s theory predicts the black hole. Despite numerous claims
for discovery of black holes in their millions, nobody has ever actually found one. It is also
not difficult to prove that General Relativity violates the usual conservation of energy
and momentum. Fundamentally there are contradictions contained in black hole theory,
big bang cosmology, and General Relativity. Numerical methods are therefore to no avail.
Keywords: Black Hole, Big Bang, Superposition
1. INTRODUCTION
General Relativity has long been the theoretical basis for gravitation and the structure
of the Universe. It is used to predict and characterise black holes, although it is
also frequently claimed that Newton’s theory predicts black holes as well. There is
now a vast literature on the theory and discovery of black holes and their features,
despite the fact that nobody has ever found one. It is not difficult to prove that the
black hole and big bang cosmology actually contradict one another; in other words
they are mutually exclusive.
2. BLACK HOLE AND BIG BANG CONTRADICTORY
All alleged solutions to Einstein’s field equations for the black hole pertain to a
universe that is spatially infinite, is eternal, contains only one mass, is not expanding,
and is asymptotically flat or asymptotically not flat (e.g. are asymptotically
de Sitter or anti de Sitter space). But the alleged big bang models pertain to a
universe that is spatially finite (one case) or spatially infinite (two different cases),
of finite age, contains radiation and many masses including multiple black holes
(some of which are said to be primordial), is expanding, and is not asymptotically
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
2
anything. Thus the black hole and big bang cosmology contradict one another; they
are mutually exclusive. Furthermore, Einstein’s field equations are nonlinear and so
the Principle of Superposition does not hold in General Relativity; but it does hold
in Newton’s theory.
“The Einstein equations are nonlinear. Therefore for gravitational fields the
principle of superposition is not valid.” Landau and Lifshitz1
Thus, if X and Y are two different solutions to Einstein’s field equations then
the linear combination aX + bY, where a and b are scalars, is not a solution.
Physically this means that one cannot simply pile up masses and radiation in any
given spacetime to obtain multiple masses and radiation. Additionally, there are
no known solutions to Einstein’s field equations for two or more masses and there
is no existence theorem by which it can even be asserted that the field equations
contain latent solutions for two or more masses.2–6 Consequently it is not possible
to insert a black hole universe into a big bang universe or into another black hole
universe, or to insert a big bang universe into a black hole universe or another big
bang universe. Nonetheless astrophysical scientists routinely and incorrectly claim
the existence of multiple black holes and the formation of black holes from objects
such as stars by means of irresistible gravitational collapse.
3. THE SCHWARZSCHILD RADIUS IS NEITHER A RADIUS
NOR A DISTANCE
The Schwarzschild radius, sometimes called the gravitational radius, features prominently
in black hole theory. This radius is just that of the so-called event horizon
of the black hole. Consider Hilbert’s solution7,8 usually given as,
ds2 =
1 －
2m
r
dt2 －
1 －
2m
r
－1
dr2 － r
2
dθ2 + sin2
θ dϕ2
(1)
0 ≤ r
According to Penrose,9
“The quantity m is the mass of the body. . . ”
Schwarzschild’s10 actual solution is different to Hilbert’s and contains no black hole.
In expression (1) the speed of light c and Newton’s gravitational constant G are
both set equal to unity. This practice is misleading and so with c and G written
explicitly so that nothing is hidden, expression (1) becomes,
ds2 =
1 －
2Gm
c
2r
dt2 －
1 －
2Gm
c
2r
－1
dr2 － r
2
dθ2 + sin2
θ dϕ2
(2)
0 ≤ r
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
3
The quantity r in Hilbert’s solution has never been correctly identified by astrophysical
scientists. It has been variously and vaguely called a distance, the radius,
the radius of a 2-sphere, the coordinate radius, the radial coordinate, the radial
space coordinate, the areal radius, the reduced circumference, the Schwarzschild rcoordinate,
the shortest distance a ray of light must travel to reach the centre, and
even a gauge choice: it defines the coordinate r. In the particular case of r = 2Gm/c2
it is invariably referred to by proponents of the black hole as the Schwarzschild radius
or the gravitational radius. Dirac11 calls r = 2m “the critical radius” and
also says, “It would seem that r = 2m gives a minimum radius for a body of mass
m.” Penrose9
says, “The radius r = 2m is referred to as the Schwarzschild radius
of the body.” To correctly identify the quantity r consider the First Fundamental
Quadratic Form3,4,12 for the surface in Hilbert’s solution,
ds2 = r
2
dθ2 + sin2
θ dϕ2
(3)
One of the most important geometric features of a surface is its Gaussian curvature
K, which is an intrinsic property of a surfacea
. For a two dimensional surface this
can be calculated by,
K =
R1212
g
(4)
R1212 is a component of the Riemann tensor. Applying (4) to (3) gives,
K =
1
r
2
r =
1
√
K
(5)
This now fully determines r as the inverse square root of the Gaussian curvature of
the spherically symmetric geodesic surface in the spatial section of Hilbert’s metric,
and so it is neither a radius nor a distance therein. Consequently the Schwarzschild
radius is the radius of nothing in Hilbert’s solution; it is not even a distance therein.
The radius Rp
in the spatial section of Hilbert’s solution is given elsewhere.3,4,13
Consider the first two components of the metric tensor of expression (2),
g00 =
1 －
2Gm
c
2r
g11 = －
1 －
2Gm
c
2r
－1
(6)
When r = 2Gm/c2
it is routinely asserted (e.g. Dirac11) that,
g00 = (1 － 1) = 0 g11 =
－1
(1 － 1) =
－1
0
= －∞ (7)
and that a trapped surface is produced in the course of gravitational collapse,2,15
and that the quantity r = 2Gm/c2
is the Schwarzschild radius of the black hole.
However, in expressions (7) there is division by zero in the case of g11; which is
undefined in mathematics. It is also noted that not only is division by zero permitted
to generate the Schwarzschild radius for the event horizon of the black hole, division
aTheorema Egregium - Gauss’ Most Excellent Theorem
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
4
by zero is also alleged to produce －∞. This too is incorrect. Since g11 is undefined
at r = 2Gm/c2
expression (2) is undefined at this value, and so no physical entity
can be assigned to this value of r. In the case of r = 0 expressions (6) give,
g00 =
1 －
2Gm
0
g11 =
－1
1 －
2Gm
0
(8)
Once again division by zero results, not once but twice. In this case both g00 and
g11 are undefined and so expressions (1) and (2) are undefined. Nonetheless, the
proponents of the black hole again permit division by zero and assign to this value
of r an infinitely dense point-mass singularity.
“Once a body of matter, of any mass m, lies inside its Schwarzschild radius
2m it undergoes gravitational collapse . . . and the singularity becomes
physical, not a limiting fiction.” Dodson and Poston14
4. THE BLACK HOLE HAS NO ESCAPE VELOCITY
Consider the expression for the Schwarzschild radius of the black hole event horizon,
r =
2Gm
c
2
(9)
Solving for c gives,
c =
r
2Gm
r
(10)
which is Newton’s escape velocity. In the Collins Encyclopaedia of the Universe,15
“black hole A massive object so dense that no light or any other radiation
can escape from it; its escape velocity exceeds the speed of light.”
But it is also claimed that nothing can even leave the black hole. Hawking16 says,
“I had already discussed with Roger Penrose the idea of defining a black hole
as a set of events from which it is not possible to escape to a large distance.
It means that the boundary of the black hole, the event horizon, is formed
by rays of light that just fail to get away from the black hole. Instead, they
stay forever hovering on the edge of the black hole.”
Thus, the black hole is alleged to have an escape velocity and to have no escape
velocity at one and the same time. Contra hype! Furthermore, if the black hole has
an escape velocity c, then, by definition, light can escape. If the escape velocity of
the black hole is greater than c then light cannot escape, but that does not mean
that nothing can leave, only that nothing can escape. The idea of black hole escape
velocity is just a play on the words “escape velocity”.2 This fact also invalidates the
Hawking-Penrose Singularity Theorem.17
Equations (9) and (10) have nothing to do with the black hole whatsoever; they
are related only to Newton’s theory of gravitation, and equation (9) is the critical
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
5
radius for the formation of the theoretical Michell-Laplace dark body, which is not
a black hole. The theoretical Michell-Laplace dark body forms when,
r <
2Gm
c
2
5. NEWTON’S THEORY DOES NOT PREDICT THE BLACK
HOLE
It is incorrectly claimed that the Michell-Laplace dark body is a black hole. Hawking
and Ellis18 say,
“Laplace essentially predicted the black hole. . . ”
Chandrasekhar19 says,
“By a curious coincidence, the limit Rs discovered by Laplace is exactly the
same that general relativity gives for the occurrence of the trapped surface
around a spherical mass.”
Chandrasekhars’ Rs
is the Schwarzschild radius. But it is not surprising that General
Relativity gives the same Rs “discovered by Laplace” because the Newtonian
expression for escape velocity is deliberately inserted post hoc into Hilbert’s solution
in order to arbitrarily make a massive source appear therein.
The Michell-Laplace dark body possesses an escape velocity, but the black hole
has no escape velocity; masses and light can leave the Michell-Laplace dark body,
but nothing can leave the black hole; it does not require irresistible gravitational
collapse, whereas the black hole does; it has no infinitely dense singularity, but the
black hole does; it has no event horizon, but the black hole does; there is always a
class of observers that can see the Michell-Laplace dark body, but there is no class
of observers that can see the black hole;2
the Michell-Laplace dark body persists
in a space which by consistent theory contains other Michell-Laplace dark bodies
and other matter and they can interact with themselves and other matter, but the
spacetime of all types of black hole pertain to a universe that contains only one mass
and so cannot interact with any other masses; the space of the Michell-Laplace dark
body is 3-dimensional and Euclidean, but the black hole is in a 4-dimensional nonEuclidean
spacetime; the space of the Michell-Laplace dark body is flat whereas the
curved spacetime of the black hole is asymptotically flat or asymptotically curved.
Therefore, the Michell-Laplace dark body does not possess the characteristics of the
black hole and so it is not a black hole.
http://vixra.org/pdf/1308.0073v1.pdf
再生核研究所声明297(2016.05.19) 豊かなゼロ、空の世界、隠れた未知の世界
ゼロ除算の研究を進めているが、微分方程式のある項を落とした場合の解と落とす前の解を結び付ける具体的な方法として、ゼロ除算の解析の具体的な応用がある事が分かった。この事実は、広く世の現象として、面白い視点に気づかせたので、普遍的な現象として、生きた形で表現したい。
ある項を落とした微分方程式とは、逆に言えば、与えられた微分方程式はさらに 複雑な微分方程式において、沢山の項を落として考えられた簡略の微分方程式であると考えられる。どのくらいの項を落としたかと考えれば、限りない項が存在して、殆どがゼロとして消された微分方程式であると見なせる。この意味で、ゼロの世界は限りなく広がっていると考えられる。
消された見えない世界は ゼロの世界、空、ある隠された世界として、無限に存在していると考えられる。たまたま、現れた項が 表現する物理現象を記述していると言える。
これは、地球に繁茂する動植物が、大海や大地から、生まれては、それらに回帰する現象と同様と言える。大量に発生した卵の極一部がそれぞれの生物に成長して、やがて元の世界に戻り、豊かな大海や大地は生命の存在の元、隠れた存在の大いなる世界であると考えられる。無数の生命の発生と回帰した世界の様は 生物、生体の様の変化は捉えられても、人間の精神活用や生命の生命活動の様の精しい様などは 殆ど何も分からない存在であると言える。我々の認知した世界と発生して来た世界と消えて行った認知できない世界である。
このような視点で、人間にとって最も大事なことは 何だろうか。それは、個々の人間も、人類も 大きな存在の中の小さな存在であることを先ず自覚して、背後に存在する大いなる基礎、環境に畏敬の念を抱き、謙虚さを保つことではないだろうか。この視点では日本古来の神道の精神こそ、宗教の原点として大事では ないだろうか。未知なる自然に対する畏敬の念である。実際、日本でも、世界各地でも人工物を建設するとき、神事を行い、神の許しを求めてきたものである。その心は大いなる存在と人間の調和を志向する意味で人間存在の原理ではないだろうか。それはそもそも 原罪の概念そのものであると言える。
しかしながら、人類が好きなように生きたいも道理であり、巨大都市を建設して、環境を汚染して生存を享受したいも道理であるから、それらの一面も否定できず、それは結局全体的な有り様の中でのバランスの問題ではないだろうか。人類の進化の面には必然的に人類絶滅の要素が内在していると考えられる：
再生核研究所声明 144（2013.12.12） 人類滅亡の概念 － 進化とは 滅亡への過程である
そこで、結局は全体的な調和、バランスの問題である：
再生核研究所声明 56： アースデイ の理念
発想における最も大事なことに触れたが、表現したかった元を回想したい。― それは存在と非存在の間の微妙な有り様と非存在の認知できない限りない世界に想いを致す心情そのものであった。無数とも言える人間の想いはどこに消えて行ったのだろうか。先も分からず、由来も分からない。世の中は雲のような存在であると言える。
以 上
https://indico.cern.ch/event/211539/.../Crothers-Protvino-2013.pdf
SJ Crothers 著 - 引用元 3 - 関連記事
2013/06/28 - (Foster, J. and Nightingale, J.D., A Short Course in General. Relativity ... according to general relativity, there must be a singularity of infinite density, within .... These quantities are undefined since division by zero is undefined.
FLAWS IN BLACK HOLE THEORY AND GENERAL RELATIVITY
STEPHEN J. CROTHERS
Alpha Institute for Advanced Study
PO Box 1546, Sunshine Plaza, 4558, QLD, Australia
∗E-mail: thenarmis@gmail.com
www.sjcrothers.plasmaresources.com/index.html
All alleged black hole models pertain to a universe that is spatially infinite, is eternal,
contains only one mass, is not expanding, and is asymptotically flat or asymptotically
not flat. But the alleged big bang cosmology pertains to a universe that is spatially finite
(one case) or spatially infinite (two different cases), is of finite age, contains radiation and
many masses including multiple black holes (some of which are primordial), is expanding,
and is not asymptotically anything. Thus the black hole and the big bang contradict
one another - they are mutually exclusive. It is surprisingly easy to prove that neither
General Relativity nor Newton’s theory predicts the black hole. Despite numerous claims
for discovery of black holes in their millions, nobody has ever actually found one. It is also
not difficult to prove that General Relativity violates the usual conservation of energy
and momentum. Fundamentally there are contradictions contained in black hole theory,
big bang cosmology, and General Relativity. Numerical methods are therefore to no avail.
Keywords: Black Hole, Big Bang, Superposition
1. INTRODUCTION
General Relativity has long been the theoretical basis for gravitation and the structure
of the Universe. It is used to predict and characterise black holes, although it is
also frequently claimed that Newton’s theory predicts black holes as well. There is
now a vast literature on the theory and discovery of black holes and their features,
despite the fact that nobody has ever found one. It is not difficult to prove that the
black hole and big bang cosmology actually contradict one another; in other words
they are mutually exclusive.
2. BLACK HOLE AND BIG BANG CONTRADICTORY
All alleged solutions to Einstein’s field equations for the black hole pertain to a
universe that is spatially infinite, is eternal, contains only one mass, is not expanding,
and is asymptotically flat or asymptotically not flat (e.g. are asymptotically
de Sitter or anti de Sitter space). But the alleged big bang models pertain to a
universe that is spatially finite (one case) or spatially infinite (two different cases),
of finite age, contains radiation and many masses including multiple black holes
(some of which are said to be primordial), is expanding, and is not asymptotically
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
2
anything. Thus the black hole and big bang cosmology contradict one another; they
are mutually exclusive. Furthermore, Einstein’s field equations are nonlinear and so
the Principle of Superposition does not hold in General Relativity; but it does hold
in Newton’s theory.
“The Einstein equations are nonlinear. Therefore for gravitational fields the
principle of superposition is not valid.” Landau and Lifshitz1
Thus, if X and Y are two different solutions to Einstein’s field equations then
the linear combination aX + bY, where a and b are scalars, is not a solution.
Physically this means that one cannot simply pile up masses and radiation in any
given spacetime to obtain multiple masses and radiation. Additionally, there are
no known solutions to Einstein’s field equations for two or more masses and there
is no existence theorem by which it can even be asserted that the field equations
contain latent solutions for two or more masses.2–6 Consequently it is not possible
to insert a black hole universe into a big bang universe or into another black hole
universe, or to insert a big bang universe into a black hole universe or another big
bang universe. Nonetheless astrophysical scientists routinely and incorrectly claim
the existence of multiple black holes and the formation of black holes from objects
such as stars by means of irresistible gravitational collapse.
3. THE SCHWARZSCHILD RADIUS IS NEITHER A RADIUS
NOR A DISTANCE
The Schwarzschild radius, sometimes called the gravitational radius, features prominently
in black hole theory. This radius is just that of the so-called event horizon
of the black hole. Consider Hilbert’s solution7,8 usually given as,
ds2 =
1 －
2m
r
dt2 －
1 －
2m
r
－1
dr2 － r
2
dθ2 + sin2
θ dϕ2
(1)
0 ≤ r
According to Penrose,9
“The quantity m is the mass of the body. . . ”
Schwarzschild’s10 actual solution is different to Hilbert’s and contains no black hole.
In expression (1) the speed of light c and Newton’s gravitational constant G are
both set equal to unity. This practice is misleading and so with c and G written
explicitly so that nothing is hidden, expression (1) becomes,
ds2 =
1 －
2Gm
c
2r
dt2 －
1 －
2Gm
c
2r
－1
dr2 － r
2
dθ2 + sin2
θ dϕ2
(2)
0 ≤ r
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
3
The quantity r in Hilbert’s solution has never been correctly identified by astrophysical
scientists. It has been variously and vaguely called a distance, the radius,
the radius of a 2-sphere, the coordinate radius, the radial coordinate, the radial
space coordinate, the areal radius, the reduced circumference, the Schwarzschild rcoordinate,
the shortest distance a ray of light must travel to reach the centre, and
even a gauge choice: it defines the coordinate r. In the particular case of r = 2Gm/c2
it is invariably referred to by proponents of the black hole as the Schwarzschild radius
or the gravitational radius. Dirac11 calls r = 2m “the critical radius” and
also says, “It would seem that r = 2m gives a minimum radius for a body of mass
m.” Penrose9
says, “The radius r = 2m is referred to as the Schwarzschild radius
of the body.” To correctly identify the quantity r consider the First Fundamental
Quadratic Form3,4,12 for the surface in Hilbert’s solution,
ds2 = r
2
dθ2 + sin2
θ dϕ2
(3)
One of the most important geometric features of a surface is its Gaussian curvature
K, which is an intrinsic property of a surfacea
. For a two dimensional surface this
can be calculated by,
K =
R1212
g
(4)
R1212 is a component of the Riemann tensor. Applying (4) to (3) gives,
K =
1
r
2
r =
1
√
K
(5)
This now fully determines r as the inverse square root of the Gaussian curvature of
the spherically symmetric geodesic surface in the spatial section of Hilbert’s metric,
and so it is neither a radius nor a distance therein. Consequently the Schwarzschild
radius is the radius of nothing in Hilbert’s solution; it is not even a distance therein.
The radius Rp
in the spatial section of Hilbert’s solution is given elsewhere.3,4,13
Consider the first two components of the metric tensor of expression (2),
g00 =
1 －
2Gm
c
2r
g11 = －
1 －
2Gm
c
2r
－1
(6)
When r = 2Gm/c2
it is routinely asserted (e.g. Dirac11) that,
g00 = (1 － 1) = 0 g11 =
－1
(1 － 1) =
－1
0
= －∞ (7)
and that a trapped surface is produced in the course of gravitational collapse,2,15
and that the quantity r = 2Gm/c2
is the Schwarzschild radius of the black hole.
However, in expressions (7) there is division by zero in the case of g11; which is
undefined in mathematics. It is also noted that not only is division by zero permitted
to generate the Schwarzschild radius for the event horizon of the black hole, division
aTheorema Egregium - Gauss’ Most Excellent Theorem
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
4
by zero is also alleged to produce －∞. This too is incorrect. Since g11 is undefined
at r = 2Gm/c2
expression (2) is undefined at this value, and so no physical entity
can be assigned to this value of r. In the case of r = 0 expressions (6) give,
g00 =
1 －
2Gm
0
g11 =
－1
1 －
2Gm
0
(8)
Once again division by zero results, not once but twice. In this case both g00 and
g11 are undefined and so expressions (1) and (2) are undefined. Nonetheless, the
proponents of the black hole again permit division by zero and assign to this value
of r an infinitely dense point-mass singularity.
“Once a body of matter, of any mass m, lies inside its Schwarzschild radius
2m it undergoes gravitational collapse . . . and the singularity becomes
physical, not a limiting fiction.” Dodson and Poston14
4. THE BLACK HOLE HAS NO ESCAPE VELOCITY
Consider the expression for the Schwarzschild radius of the black hole event horizon,
r =
2Gm
c
2
(9)
Solving for c gives,
c =
r
2Gm
r
(10)
which is Newton’s escape velocity. In the Collins Encyclopaedia of the Universe,15
“black hole A massive object so dense that no light or any other radiation
can escape from it; its escape velocity exceeds the speed of light.”
But it is also claimed that nothing can even leave the black hole. Hawking16 says,
“I had already discussed with Roger Penrose the idea of defining a black hole
as a set of events from which it is not possible to escape to a large distance.
It means that the boundary of the black hole, the event horizon, is formed
by rays of light that just fail to get away from the black hole. Instead, they
stay forever hovering on the edge of the black hole.”
Thus, the black hole is alleged to have an escape velocity and to have no escape
velocity at one and the same time. Contra hype! Furthermore, if the black hole has
an escape velocity c, then, by definition, light can escape. If the escape velocity of
the black hole is greater than c then light cannot escape, but that does not mean
that nothing can leave, only that nothing can escape. The idea of black hole escape
velocity is just a play on the words “escape velocity”.2 This fact also invalidates the
Hawking-Penrose Singularity Theorem.17
Equations (9) and (10) have nothing to do with the black hole whatsoever; they
are related only to Newton’s theory of gravitation, and equation (9) is the critical
July 25, 2013 21:1 WSPC - Proceedings Trim Size: 9.75in x 6.5in Crothers-Proceedings2013
5
radius for the formation of the theoretical Michell-Laplace dark body, which is not
a black hole. The theoretical Michell-Laplace dark body forms when,
r <
2Gm
c
2
5. NEWTON’S THEORY DOES NOT PREDICT THE BLACK
HOLE
It is incorrectly claimed that the Michell-Laplace dark body is a black hole. Hawking
and Ellis18 say,
“Laplace essentially predicted the black hole. . . ”
Chandrasekhar19 says,
“By a curious coincidence, the limit Rs discovered by Laplace is exactly the
same that general relativity gives for the occurrence of the trapped surface
around a spherical mass.”
Chandrasekhars’ Rs
is the Schwarzschild radius. But it is not surprising that General
Relativity gives the same Rs “discovered by Laplace” because the Newtonian
expression for escape velocity is deliberately inserted post hoc into Hilbert’s solution
in order to arbitrarily make a massive source appear therein.
The Michell-Laplace dark body possesses an escape velocity, but the black hole
has no escape velocity; masses and light can leave the Michell-Laplace dark body,
but nothing can leave the black hole; it does not require irresistible gravitational
collapse, whereas the black hole does; it has no infinitely dense singularity, but the
black hole does; it has no event horizon, but the black hole does; there is always a
class of observers that can see the Michell-Laplace dark body, but there is no class
of observers that can see the black hole;2
the Michell-Laplace dark body persists
in a space which by consistent theory contains other Michell-Laplace dark bodies
and other matter and they can interact with themselves and other matter, but the
spacetime of all types of black hole pertain to a universe that contains only one mass
and so cannot interact with any other masses; the space of the Michell-Laplace dark
body is 3-dimensional and Euclidean, but the black hole is in a 4-dimensional nonEuclidean
spacetime; the space of the Michell-Laplace dark body is flat whereas the
curved spacetime of the black hole is asymptotically flat or asymptotically curved.
Therefore, the Michell-Laplace dark body does not possess the characteristics of the
black hole and so it is not a black hole.
http://vixra.org/pdf/1308.0073v1.pdf
再生核研究所声明297(2016.05.19) 豊かなゼロ、空の世界、隠れた未知の世界
ゼロ除算の研究を進めているが、微分方程式のある項を落とした場合の解と落とす前の解を結び付ける具体的な方法として、ゼロ除算の解析の具体的な応用がある事が分かった。この事実は、広く世の現象として、面白い視点に気づかせたので、普遍的な現象として、生きた形で表現したい。
ある項を落とした微分方程式とは、逆に言えば、与えられた微分方程式はさらに 複雑な微分方程式において、沢山の項を落として考えられた簡略の微分方程式であると考えられる。どのくらいの項を落としたかと考えれば、限りない項が存在して、殆どがゼロとして消された微分方程式であると見なせる。この意味で、ゼロの世界は限りなく広がっていると考えられる。
消された見えない世界は ゼロの世界、空、ある隠された世界として、無限に存在していると考えられる。たまたま、現れた項が 表現する物理現象を記述していると言える。
これは、地球に繁茂する動植物が、大海や大地から、生まれては、それらに回帰する現象と同様と言える。大量に発生した卵の極一部がそれぞれの生物に成長して、やがて元の世界に戻り、豊かな大海や大地は生命の存在の元、隠れた存在の大いなる世界であると考えられる。無数の生命の発生と回帰した世界の様は 生物、生体の様の変化は捉えられても、人間の精神活用や生命の生命活動の様の精しい様などは 殆ど何も分からない存在であると言える。我々の認知した世界と発生して来た世界と消えて行った認知できない世界である。
このような視点で、人間にとって最も大事なことは 何だろうか。それは、個々の人間も、人類も 大きな存在の中の小さな存在であることを先ず自覚して、背後に存在する大いなる基礎、環境に畏敬の念を抱き、謙虚さを保つことではないだろうか。この視点では日本古来の神道の精神こそ、宗教の原点として大事では ないだろうか。未知なる自然に対する畏敬の念である。実際、日本でも、世界各地でも人工物を建設するとき、神事を行い、神の許しを求めてきたものである。その心は大いなる存在と人間の調和を志向する意味で人間存在の原理ではないだろうか。それはそもそも 原罪の概念そのものであると言える。
しかしながら、人類が好きなように生きたいも道理であり、巨大都市を建設して、環境を汚染して生存を享受したいも道理であるから、それらの一面も否定できず、それは結局全体的な有り様の中でのバランスの問題ではないだろうか。人類の進化の面には必然的に人類絶滅の要素が内在していると考えられる：
再生核研究所声明 144（2013.12.12） 人類滅亡の概念 － 進化とは 滅亡への過程である
そこで、結局は全体的な調和、バランスの問題である：
再生核研究所声明 56： アースデイ の理念
発想における最も大事なことに触れたが、表現したかった元を回想したい。― それは存在と非存在の間の微妙な有り様と非存在の認知できない限りない世界に想いを致す心情そのものであった。無数とも言える人間の想いはどこに消えて行ったのだろうか。先も分からず、由来も分からない。世の中は雲のような存在であると言える。
以 上
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