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January 19, 2018

ARTICLE: Black Holes: Paradox Regained [back to article]
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Cristi Stoica wrote on Mar. 18, 2012 @ 18:53 GMT
In fact, spacetime behaves very well at singularities, in the old framework of General Relativity. Singularities occur, indeed, as Penrose and Hawking proved long time ago. But physics and differential geometry can be done there. Equivalent versions of Einstein's equation can be written. They give the same result as the standard Einstein equation where there are not singularities, but apply also where there are singularities. The singularities don't destroy information.

The stationary black holes admit coordinate systems which makes the singularity of the metric to be "benign", i.e. smooth and without infinities:

Schwarzschild Singularity is Semi-Regularizable

Analytic Reissner-Nordstrom Singularity

Kerr-Newman Solutions with Analytic Singularity and no Closed Timelike Curves

The FLRW Big Bang singularity is already benign:

Big Bang singularity in the Friedmann-Lemaitre-Robertson-Walker spacetime

Beyond the Friedmann-Lemaitre-Robertson-Walker Big Bang singularity

For benign singularities one can do differential geometry

On Singular Semi-Riemannian Manifolds

Warped Products of Singular Semi-Riemannian Manifolds

Cartan's Structural Equations for Degenerate Metric

and write equivalent to Einstein's equation

Einstein equation at singularities

A large class of benign singularities also answer one big puzzle of Penrose:

On the Weyl Curvature Hypothesis

The singularities are compatible with global hyperbolicity and don't destroy information, if we know how to continue the equations beyond the singularities:

Globally Hyperbolic Spacetimes With Singularities

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Steve Dufourny replied on Mar. 20, 2012 @ 00:51 GMT
Hi Christi,

Hope you are well. I am also intriged by these singularities.What are the productions and radiations of these BH also ? The spherical volume is important and its mass also.

But what is this puzzle ?


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Cristi Stoica replied on Mar. 20, 2012 @ 09:24 GMT
Hi Steve,

It was believed that nothing can escape the black holes, and then in 1974 Hawking realized that they can emit particles. The particles are not emitted from inside the black hole's event horizon, but from the outside, through a quantum process. Simplifying, the virtual pairs particle-antiparticle are separated, so that one of them falls in the black hole, the other escapes. So the virtual pair becomes real, but without violating the energy conservation, If you account for the potential energy of the particles, the black hole looses weight, although it swallowed a particle. Hawking calculated that after a long time, black holes evaporate and eventually explode. So what's happening with all the information which fell into the black hole and reached the singularity? Will it be recovered, or is it lost forever? If it is lost, then this raises some problems to the physics, especially to the unitary evolution, which is very important for quantum mechanics. This is the puzzle. If it is not lost, then how can it escape? You can read more about this in Hawking's "A brief history of time", but since then, many new things were understood. You may find interesting the links in the Wikipedia article. As you may have seen from my previous comment, my viewpoint is that the Einstein equations can be reformulated so that they can be continued through the singularities, and nothing is in fact lost. Many people don't like this, because they want to promote their new theories by saying that general relativity fails because of the singularities. But one should not confound general relativity with our limited understanding of general relativity, because it is in fact the latter which fails.

Best regards,


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Wilhelmus de Wilde replied on Mar. 20, 2012 @ 16:40 GMT
Congratulations Christie with your latest works. I understand that you make singulairities workable with SR. You use a lot of mathematics that I cannot follow, but thet is not the problem, I was thinking that singulairities are only a mathematical way of expressing a non existing entity, in mathematics we can count with it but in "reality" that is materialistically limited they just cannot "exist" (also with the BB), so in my opinion (maybe wrong) mathematics can not always explain "reality". It is our mind ,consciousness that can easily think about infinities, singulairities the root of -1 etc. This of course is a great gift and indicates that there is more ...

think free (sorry Steve)


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Cristi Stoica wrote on Mar. 21, 2012 @ 05:56 GMT
Hi Steve,

Probably you know that there are physicists who proposed that eventually there will be a remnant, and you may find their solutions more on your taste.

As for the singularities, they are usually presented as boogie man. As someone who invested many years in the study of the sphere, you probably know than whenever you try to parametrize the sphere - to cover the entire sphere with a coordinate system - you get singularities. For example, the latitude and longitude coordinates have singularities at the North and South poles. In these coordinates, it seems that you can't go beyond the North pole, since the latitude coordinate ends there. But you can always use an additional coordinate system, which is not singular at the poles, and switch between the two. Believe it or not, something similar happens when you get the singularities. But in this case the things are more complex than in the case of the sphere, because there are coordinate singularities both in the standard representations of the black hole solutions, and in the way we choose the parameters to write Einstein's equations. But the point is that my parametrizations remain smooth even in the cases when the standard parametrizations are singular.

Best regards,


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Cristi Stoica replied on Mar. 21, 2012 @ 05:58 GMT
Sorry, this post was intended for the previous thread, I did not intend to open a new one.

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Steve Dufourny replied on Mar. 21, 2012 @ 13:02 GMT
Hi Christi,

It is interesting.

Have you already thought about the main singularities, these main central spheres in all.Their volumes are the secret like their rotations spinal and orbital. Now we must assume that these main central spheres are coded.

These codes are far of us Christi, very far. The parametrizations must be realistic respecting the 3D and 4D evolutive space time.

It is logic to have singularities in all in fact becauser all is composed by spheres with their main central spheres, the volumes seem the key for the steps of stability of analyzes.The volumes of an entanglement of uniqueness answer if we calculate the correct series, their corrletaed volumes, the rotations and the mass. Now considering a different sense of rotation for the bosons and the fermions, so we have a kind of gauge for the classment of singularities and their codes of evolution in 3D.


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Steve Dufourny replied on Mar. 21, 2012 @ 23:12 GMT
If we take our Universal Sphere and a volume, evolutive V.

We can consider a main BH, the main central sphere and a Volume evolutive V2.

The adds of mass inside an universal sphere implies a continuous SPHERICAL space Time. The variations of V is important for V1 and V2.The rotations talke all their meanings.The mass and the Swartz.R0 can be inserted. But for a correct serie of analyzes of these volumes. We must insert the serie of Uniqueness becoming from the main central sphere, the number 1.The Volume of the universal sphere can be linked with the entropical arrow of time. The curvatures appear with an universal spherical logic due to an increase of mass. If the expansion, spherical is the first step towards a maximum volume, so we can see a contraction after the expansion due to an increasing of density.The gravity is balanced with the rotations and the volumes. The space is curved by thi mass and more this mass increase more this spherization increases proportional with density, gravitational.If a singularity is a reality, so it is the main code, and so when the Swartz R is reached , so the mass is under its relativity.2 GM/c²=R. Now imagine that we consider the 3 motions of c, c linear, o orbital, s spinal velocity. So we have an entanglement, a photon with its uniquenss serie , so a specific serie, so a specific group. Now imagine that the serie is relativistically the same that the serie cited above about the volum V , the main central sphere. So we can consider the singularity like this ultim serie, the photon. If c is a gauge, so we have c maximum and o maximum and s maximum. If a BH becomes a singularity, so it becomes this serie, so the energy liberated is eneormous considering the steps of fractalization of this Entropy. Ther maximum is so correlated with the volumes Christi. The balance with mass can be made for an evolutive point of Vue.

We can class these BH with their volumes and furthermore we have a link with the fractalized entropy. The maximums can be seen if we take my equations ,E=m(c³o³s³) so we have this maximum entropy considering the walls at this singularities of extrapolations. The gravity in my line of reasoning turns in the other sense but has the same number of serie of uniqueness.

See that the Universal sphere possesses the same number.The radiations of emission and absorption of BH respect this logic.


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Steve Dufourny wrote on Mar. 22, 2012 @ 23:28 GMT
The informations are conserved , it is sure. The laws of thermodynamics and mecanics are universal at all scales. So it is not a paradox when we consider the complementarity of the BH considering an evolutive point of vue. If they are evaporated, or destroyed, so they became an other proportional reality.And so the informations also are conserved considering the rotations and thje volumes of entangled spheres. The cosmological spheres are in the same relativistic logic. Humbly the rotating spheres answer to all proportions if and only if the continuity is respected for the evolution of states. If we consider this evolution of mass, so these spheres.The ultim code is far. But in theory, if we change the ultim code, so we have a paradox, but we are not Gods at my humble opinion. It is bizare. I beleive that never we could change this ultim code.

I am insiting about the volumes of the serie of uniqueness!These volumes , these rotations, these velocities, these mass, they turn they are...they build ...

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Juan Ramón González Álvarez wrote on Mar. 30, 2012 @ 10:10 GMT
The literature in black holes is open to many objections.

In section 8 of Non-redundant and natural variables definition of heat valid for open systems bogus claims done in black hole 'thermodynamics' are corrected. It is not true that black holes violate the second law of thermodynamics. The so-named generalized second law is unneeded, apart from confounding the production term (proportional to volume) with a flow term (proportional to area)!

It is not true that "black holes also destroy information as they munch on matter, violating the laws of quantum mechanics". In the first place, as shown recently in General relativity as geometrical approximation to a field theory of gravity the metric formulation associated to general relativity is valid only when one avoids higher order corrections due to gravitons. This is somewhat similar to geometrical optics arising as an approximation to physical optics.

The spacetime singularities associated to general relativity are only apparent and results from applying general relativity beyond its field of validity. General relativity is obtained when (i) one ignores the contribution of gravitons to the source of the gravitational field and approximates it by Tab (the right-hand-side of Einstein equations) and (ii) one approximates the field-theoretic effective metric by the general-relativistic metric.

In the second place, it can be shown that the correct field theory of gravity can be quantized as other ordinary field theory.

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Steve Dufourny replied on Mar. 30, 2012 @ 11:08 GMT
Hello Juan,

I agree totally about your words. Indeed we cannot violate our second law. It is the same for the QM and the relativity, they are rational those extrapolations. Indeed we cannot destroy a BH and still less the informations, ultim. Now it exists a lot of informations, and thus a pure classment of these informations become an universal essential. The encodings, the synchronizations, the sortings are very complexs and this taxonomy can be correlated witht the volumes of the pure serie of uniqueness.

The continuous metric and the finite groups also are essential at my humble opinion.

The bosonic fields can be axiomatized with the fermions and their encoding of evolution respecting the sortings and the synchro.

My equations help when we consider a different sense of rot.for the bosons and the fermions. So we can correlate the fields, the entropy and the mass.

mcosV=Constant and E=(c³o³s³)m.with a serie of uniquenss and with m mass,c linear velocity,o orbital speed,s spinal speed,V Volume of a physical 3D sphere.The generality can be analyzed for a number of spheres with the same universal logic. For the respect of all proportions, we must accept the 3D and this scales in meter.


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J. C. N. Smith wrote on Apr. 26, 2012 @ 18:22 GMT
But Giddings has identified a key, and debatable, assumption in those locality arguments: "All of that assumes that there is some pre-existing spacetime that defines what it means for things to travel faster than the speed of light or not."

While people are being open minded about reexamining fundamental assumptions, I'd like to suggest that a reexamination of key assumptions about the fundamental nature of time is in order, and in fact long overdue. Some hopefully cogent thoughts on the topic will be found in a recent essay titled 'Toward a Helpful Paradigm for the Nature of Time,' which will be found here.

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Steve Dufourny replied on May. 10, 2012 @ 22:24 GMT
The time is a constant of evolution, a duration implied by the rotating spheres. The time is the time after all. Is it important to see if this time is reversible? No of course because the time is purely irreversible in its pure generality.The time space evolution is linked but we cannot return in the past ! Perhaps that we can decrease the duration, so our internal clocks, so we can go in the future, but the probelm is that we cannot return at home !It is essential considering the spherization of the spacetime. The time is not a real dimension. But a pure duration implied by the motions, here the rotations of spheres, quantical and cosmological. The time is not reversible. It is a constant of evolution.

I beleive that the bosons cannot pass c, the fermions perhaps considering that they turn in the other sense....


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Douglas Lipp wrote on May. 3, 2012 @ 02:37 GMT

a new interpretation

singularities explained: pure Matter (black hole)

pure Space (100% Dark Chocolate Energy)

One Equation: MTS

Duality resolved. more... see

Experimentally verifiable.

nothing more to offer - out of my thinking stage / please take it from here

website may have to come down soon .... tired.... confused....

THX - doug

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Doug wrote on May. 29, 2012 @ 01:33 GMT
OK - let's have a vote

Raise your hand if you believe in CIG Theory.

OK - hands down

Now, those that don't believe. Higher, I can't see you.

Well, there you have have, Scientific proof!


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Vijay Mohan Gupta wrote on Jul. 12, 2012 @ 15:51 GMT
Good morning Steve,

It is an interesting composition. The statement about black hole, 'The laws we use to describe the rest of space-time no longer apply inside black holes' may not be correct. Some rule of thumb or empirical laws of physics may not be applicable, but universal laws are applicable every where, even inside the black hole or for that mater inside elementary particles. Please advice, if mainstream physicists think otherwise.

May I request your evaluation on my essay on 5-dimensional universe at

I look forward to your comments and evaluation of the essay.

Thanks & Best Regards,

Vijay Gupta

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Sir Issac Newton Jr. wrote on Sep. 5, 2012 @ 04:14 GMT
Well generally speaking no "man's" comprehensibility of thermodynamics and physics don't necessarily apply inside the event horizon.

But we do know that the singularity within a black is so great that EVEN LIGHT cannot escape.

But here is my view and beliefs, for every black hole that exist there is a white hole that exist.

Black holes and white holes are two sides of the same coin In "man's comprehension" a black hole you fall into would actually be a white hole you escaped from in the past.

But WE MUST REALIZE that time is a mere concept and nothing more, time is a measurement system that we use to measure the order in which events and occurrences happen in existence, a mere manmade concept.

So, disregarding time, when your looking at an event horizon you are actually looking at a black hole through a white hole the "event horizon" your seeing is actually light escaping from the white hole.

So if you were to go beyond the "event horizon" and look back you'd see a white hole.

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doug wrote on Dec. 29, 2012 @ 14:17 GMT
Quantum dynamics approaches Classical dynamics as the rate of matter (of traveling particles) approaches stillness (velocity = zero). At zero velocity, the two (quantum & classical theory) are indistinguishable. At velocity = c, matter becomes Space.

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doug wrote on Dec. 29, 2012 @ 15:25 GMT
Final Statement - CIG Theory -

Quantum dynamics approaches Classical dynamics as the rate of matter (of traveling particles) approaches pure stillness (velocity = zero). At zero velocity, the two (quantum & classical theory) are indistinguishable. At velocity = c, Matter becomes Space. In between is everything else [Dark Matter & Dark Energy & other variations of the "dark entities" (that...

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Anonymous wrote on Nov. 8, 2013 @ 23:50 GMT
Baggott[Farewell to Reality: How Fairy-Tale Physics Has Betrayed The Search For Scientific Truth] and even more spot-on Unzicker-Jones[Bankrupting Physics: How Top Scientists Are Gambling Away Their Credibility] critiques shame physics’ shameless rock-star media-hype P.R. spin-doctoring veracity-abandoning touting sci-fi “show-biz” trending viral exacerbated by online social networks...

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