• [deleted]

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

    • [deleted]

    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 ?

    Regards

    • [deleted]

    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,

    Cristi

    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)

    Wilhelmus

    • [deleted]

    Dear Wilhelmus,

    Interesting thoughts on existence and mathematics. Well, I don't see any contradiction in the existence of singularities in the real world, but I can't say if they really exist or not. Since our limited understanding of mathematics grows permanently, I also cannot say if there are regions of reality which mathematics will never be able to describe. Maybe there are, or maybe not.

    Best regards,

    Cristi

    • [deleted]

    Hi Christi,

    I see the singularities like the ultim informations.

    So they exist indeed and they are inside the physicality at these planck walls if I can say.

    The works of Hawking are relevant about the emissions, that said I don't agree about the explosion and evaporations. The Spheres, central to galaxies have proporties and rules.But I don't see why they shall disappear. In fact when we extrapolate mathematically a serie like an evolutive BH for example, so we must insert limits about the equilibriums between mass.

    So in your line of reasoning, you are right because the ultim informations(main central sphere, the biggest volume) are conserved like the entropy.So Hawking has just forgotten these limits in the calculations of the serie of evolution with the correlated mass.

    That said I d like insist on the fact that we cannot analyze beyond these singularities , because we are beyond the physicality.These singularities are just at these walls separating the unknown and this physicality. So why beyond Christi ? The best analyzes are when they take into account the rationalism and the determinism of this physicality, this 3D universal sphere and its cosmological and quantum spheres.So why beyond the walls of these particules or why beyond our Universal sphere and its limits.You know if the physicality exists, there are reasons. The secerats are inside this physicality, at these walls and we are very far at this moment.We cannot see these singularities , these ultim codes. It is like desiring seeing the central spheres of the quantum world and for the cosmological world and the central universal sphere of the universal sphere in evolution. We cannot see these codes at this moment.But we can see the steps before...

    I beleive strongly Christi that the codes are precise about the general evolution, so I don't see a necessity for a degenerescence of BH.

    the mass curves space GR and the light speed is constant SR .I see the relativity just like this.

    Regards

    • [deleted]

    you are comic Whilhelmus :) don't say sorry, you are free you know to say what you want. I am free to critic like I want also :)

    peace my friend.:)

    ps the -, the 0, the infinities must be analyzed with the biggest rationality. In fact it exists a lot of laws about these meanings. Do you know the alephs of Cantor ? The - and the 0 in fact do not really exist, and the infinity also. But we can class them and utilize them also like tools.

    Regards

    • [deleted]

    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,

    Cristi

      • [deleted]

      Sorry, this post was intended for the previous thread, I did not intend to open a new one.

      • [deleted]

      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.

      Regards

      • [deleted]

      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.

      regards

      • [deleted]

      considering a sphere like a BH you have also my other equation considering that all spheres are under this constant.

      m mass of the sphere, c linear velocity, o orbital velocity, s spinal velocity and V Volume.

      so mcosV=Constant and we can insert a lot of parameters and derivations in this equation. Furthermoere you can also correlate with the F=G m1m2/r² with the rotations and the volumes so we have a force between all spheres, quant or cosmol.

      Regards

      • [deleted]

      I was planning to write about one of your papers here and this general blog entry. However, it is getting a bit too late. I have been working on similar extensions, but with the intention of looking at singularities as dual to the holographic horizon.

      Cheers LC

      • [deleted]

      3 real equations about the improvement of the relativity and about the entropy, maximum in all. This maximum is paradoxal when we add it.So this maximum is not really a possible reaching way. We need just a small fractal. It is sufficient.

      • [deleted]

      Hi Lawrence,

      Thank you for your interest, I would like to hear your viewpoint.

      Best regards,

      Cristi

      • [deleted]

      Hi Lawrence, me also I d like hear your point of vue, I am sad that one of 2 mavericks is not with us.

      Regards

      • [deleted]

      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 ....so they are...they build ...

      • [deleted]

      Cristi,

      The extensions you are making are analytic. In this must then be some aspect of complex variable. What I can't help but think is there is some underlying quantum mechanical aspect to this. The quantization of singularities is necessary in order to determine if there is some dualism between the QFT configuration of the stretched horizon in holography and the field state of the singularity. So I have been playing around with similar ideas in order to generalize the Hawking radiation theory.

      I am again posting late and do not have quite the energy to type out a lot of stuff. I will maybe try to write something here that is longer this weekend. The analytic smoothing of physical singularity in a black hole provides a way in which post selected states due to Hawking radiation can demolish states on the stretched horizon which correspond to the pre-selected states. If there is a duality then this should mean the quantum information which enters the BH is encrypted in another form as the post selected states. This follows the weak measurement approach to quantum mechanics by Ahrahonov and Vaidman.

      Steve,

      It is too bad about Ray Munroe. He was to say the least adventurist about all of this, where I am a bit more cautious. Some of his work on the 5-fold symmetries I did with him, and we published a paper together. He was a few years older than me, but not by too much. I had a friend a few years ago die of a heart attack as well. I had a full check up last year and everything checked out alright. I hope it stays that way.

      Cheers LC

      • [deleted]

      Hi Lawrence,

      Interesting observations.

      Indeed, if the fields can evolve through the singularity, the unitarity is restored. Interesting the explanation with pre-selected and post-selected states.

      I discussed a few months ago with a physicist the possibility of counting the states of the singularities to account for the entropy of the black hole, but I did not advance yet in this direction. My hope is that this will follow from some global conditions, because locally they seem not to be present. Speaking of the duality you mention between singularities and horizon, I see it somehow analogous to the duality between a field and its source, which appears to be a singularity of the field. My view on the stretched horizon is somehow different than Susskind's, in that I don't think it is in conformity with the principle of equivalence to have a special stretched horizon, on which special things happen. But the holographic principle I think doesn't need a fixed stretched horizon. I think there is more freedom, like as we choose a closed surface in Gauss's law for the electric field (to continue the analogy with the duality field-singularity).

      For the moment, I concentrate in pushing the classical GR to understand better what happens at singularities. My guess is that here there are some hints regarding quantum gravity.

      Best regards,

      Cristi Stoica

      • [deleted]

      Hi Lawrence, Christi,

      Take care Lawrence.

      About the singularities and the unitarity, it is intresting to see how the pure mecanical and thermodynamical laws are conserved.

      Regards