A Critical Analysis of LIGO's Recent Detection of Gravitational Waves Caused by Merging Black Holes,
This document is a review of the article:
"A Critical Analysis of LIGO's Recent Detection of Gravitational Waves Caused by Merging Black Holes, by Stephen J. Crothers".
The article performs a critical analysis of the LIGO results, but this analysis itself also requires a critical investigation.
In the last paragraph I explain my own opinion.
- The text in italics is copied from that url
- Immediate followed by some comments
The document starts with the following text:
"the two black holes that merged are reported to have been of ~29
solar masses and ~36 solar masses respectively, the newly formed
black hole at ~62 solar masses, radiating away ~3 solar masses as
Einstein gravitational waves."
The question is how do they now these exact numbers?
The issue is that the whole process of BH merging is a very time consuming
process which takes ages and in which the two BH's over a long period spiral
together and loose energy (mass?) in the form of gravitational radiation.
The actual merging is almost an instantaneous process during which the
two BH's also can loose mass, but that is not in the form of gravitational
radiation. IMO the numbers in the text give a wrong impression.
In any case after the merging the BH emits almost the same gravitational
radiation as before, combined.
At page 3 we read:
"Presumably the gravitational waves reported by LIGO-Virgo
are present inside some Big Bang expanding universe as there has been no
report that Big Bang cosmology has been abandoned."
At page 4 we read:
"Let X be some black hole universe and Y be some Big Bang universe."
At page 4 we read:
"It is clearly evident that black holes and Big Bang
universes cannot coexist by their very definitions."
Why mention all of this?
The first problem is the concept "BB Universes".
There exist only one Universe (mainstream physics) and there once was a BB.
The second problem is the concept "BH Universe". A BH is not a Universe.
A BH is like a star an object with a small size (and large density)
compared with a star of the same size. The major difference is that a
star emits light and a BH not.
At page 6 we read:
"Propagation speed of Einstein's gravitational waves is
arbitrary, because it is coordinate dependent."
Propagation speed of gr waves is not arbitrary. The same applies for
the speed of light. The importance is that both are a representation of
a physical phenomena i.e. the speed of gravitons versus photons. Both values
are considered the same but the physical processes involved are very different.
At page 7 we read:
"All types of black hole universes are spatially infinite
and eternal, and are either asymptotically flat or, in more esoteric cases,
Thus etc; bearing in mind also that each different type of black hole
universe pertains to a different set of Einstein field equations and
therefore have nothing to do with one another."
IMO nothing of this makes much sense. When more BH's are considered the
physical behaviour of each is influenced by the behaviour of all the others.
To be more specific: the gravitational fields (waves) of all the BH's
should be considered.
As such all the Einstein equations (each of which describes one object)
should be considered in total in order to calculate the evolution of each
At page 8 we read:
"Although they have been construed as such by cosmology, singularities
are not in fact physical entities."
I agree. Singularities (infinities) are purely mathematical constructs.
"A singularity also occurs in Newton's theory; it is called the
centre of gravity."
I do not agree. A singularity in Newton's Theory only occurs when the
distance r between two objects is zero, which is physical impossible.
At page 11 we read:
"Einstein's field equations 'in the absence of matter' are,
Rµv = 0" This is equation (6.1)
IMO it does not make much sense to study astronomy without matter. Equation
(6.1) only makes sense with the remark that in reality Rµv is always
larger than 0.
At page 16 we read:
De Sitter’s universe contains no matter:
“This is not a model of relativistic cosmology because it is devoid
of matter.” d'Inverno 
The text is from page 337 of d'Inverno in paragraph 23.4 "The de Sitter model"
In that chapter many different models with contain matter are discussed.
At page 339 of d'Inverno we read:
"The de Sitter model was the only
in existance at that time which could explain expansion"
This is a valid explanation to study "The de Sitter model" at the same time
you have to be carefull about the results of such a study based on a
universe which does not exist in reality.
The problem of the text is the overall claimed importance of equation (6.1)
At page 17 we read:
"Note that in Eq.(6.1) and Eq.(7.1), Tµv = 0. Thus, according to Einstein
and the cosmologists, material sources are both present and absent by the
very same mathematical constraint, which is a violation of the rules of
logic. Since de Sitter’s universe is devoid of material sources by virtue
of Tµv = 0, the ‘Schwarzschild solution’ must also be devoid of material
sources by the very same constraint. Thus, Eq.(6.1) contains no matter
and its solution physically meaningless. But it is upon Eq.(6.1) that
black hole theory relies."
The same type of logis is also followed at page 21:
"Hence, if there are no material sources (i.e. Tµv = 0) then there is no
gravitational field, and no universe."
At page 23 we read:
Recall that according to Einstein, everything except his gravitational
field is matter and that matter is the cause of his gravitational field.
More or less the same is written at page 170 in d'Inverno,
"that is to say, the gravitational field is coupled to itself"
"This non-linearity means that the equations are very difficult to solve"
In the document the details of these difficulties are not discussed,
In d'Inverno in the chapters 16, 18 and 19 mainly individually BH's are
discussed. In chapter 20 gravitational waves are discussed, however Binary
BH's are not discussed.
At page 23 we read:
"Numerical analysis of merging black holes and perturbation of black
holes are ill-posed procedures for the simple fact that such mathematical
means cannot validate a demonstrable fallacy."
The problem is that no analytical solutions exists of merging BH's or
of the behaviour of a binary BH system which meets a third large object.
The only way is to use numerical solutions.
One hugh problem of the Ligo experiment are the initial conditions and (a sequence of) events that
took place 1.3 billion years ago which resulted in a collision
Reflection part 1
The startegy of the document "A Critical Analysis of Ligo" etc is explained in page 3:
Only theoretical considerations are considered herein, as there is no need to analyse the LIGO app
aratus and its signal data to understand that the claim for detection of Einstein gravitational
waves and black holes is built upon theoretical fallacies and conformational
The most important argument that their are problems with BH's etc i.e. do not exist is equation (6.1). This equation is a reflection of a "Universe" without matter. IMO to understand GR such a system is too simple. In fact that is the major problem, also of the book by d'Inverno. The examples studied are too simple . A point in case is the numerical study of the simulation of the planet Mercury, as explanained in the document VB Mercury numerical.htm .
To understand GR at least two objects (BH's) must be considered and in the case of Mercury both the Sun and Mercury must have mass and the Sun should move through space. If GR can not handle such a situation let it be known. Be open.
The same problem exists if you want to understand the evolution of the Universe using GR. When you use GR you should make your predictions strictly using GR. The introduction of a cosmological constant is "wrong".
Reflection part 2
To solve the equations of GR is a difficult task.
The solution depents very much of the full gravitational field of each object. When you calculate such a field for one object this is relatif simple assuming this is stationary. The calculation of a second gravitational field of an identical stationary object is of the same complexity. IMO you can add these two fields in order to describe the behaviour of a third point mass object.
The problem starts when the two objects are a binary pair and rotate around each other. In that case the behaviour of each gravitational field becomes much more complex. The same with the combined gravitational field. When the third object also has mass the whole combined gravitational field becomes even more intricate. This is the situation discussed in the document VB BHmerger operation.htm using Newton's Law,
What makes this whole issue so complicated that in order to do any simulation correct you must make a clear distinction between the speed of light and the speed of the gravitational field (gravitons).
- The speed of light is only important when observations are involved and to test the results of the predictions. This is also the case when the objects studied are electrical or magnetical charged, which introduces extra forces.
- To study the actual movement (trajectory) of the objects gravitational forces or the gravitational field has to be considered. The importance if objects are visible or not visible disappears.
For me it is a big question how important the density is assuming that the objects studied have the same mass. This reflects itself in a different size. This size is only important to establish the moment (if) when two objects collide.
- These calculations are specific difficult if the time base for all calculations is not the same. This difficulty arises from the denial of the concept simultaneous.
Original 20 September 2016
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