Bojowald sets up for black hole

[marcus]

Earlier, back around 2001, Martin Bojowald got rid of the Big Bang singularity and since then many authors have repeated this using quantum gravity methods, their results confirming Bojowald's: there was no singularity, it goes away when the classical equations are quantized.

Classical Gen Rel had two famous singularities: the Big Bang and the Black Hole. the first of these seems to have been cured by the work subsequent to the 2001 paper.

Now it looks like Bojowald is preparing to look at the second, the black hole singularity.

he and another person at Albert Einstein Institute (MPI Potsdam) have
diagonalized the volume operator in the spherically symmetric case and gotten the volume spectrum

it looks like energy levels of an atom
the homogeneous/isotropic case volume spectrum was calculated some years back and this what they show now looks like "line splitting"

it refines the homogeneous/isotropic case

gravity is geometry so the quantities you measure, instead of being quantities like energy, can be geometric quantities like curvature and area and volume

so not so unlike Bohr studying the energy spectrum of the hydrogen atom a century ago, Bojo and co-worker have to study the volume spectrum of a black hole---it is their atom

and the spectrum looks sort of nice, I will get a page reference for it.

I don't get any feeling that they are near to removing the singularity, just that they are setting up to consider it----doing ground work to get ready to look at LQG black holes

http://arxiv.org/abs/gr-qc/0407018
"The Volume Operator in Spherically Symmetric Quantum Geometry"

 

[marcus]

"...though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger spherically symmetric volume spectrum adds fine structure to the homogeneous spectrum. The formulas of this paper complete the derivation of an explicit calculus for spherically symmetric models which is needed for future physical investigations.

1 Introduction
In complicated theories such as general relativity or its possible quantization, loop quantum gravity[1], much information can usually be gleaned by studying simpler situations in symmetric contexts.

Classically one thus obtains special exact solutions, which are relevant if perturbations around them are stable. In the quantum theory, symmetric models always present an approximation, whose relevance can be investigated by comparison with less symmetric situations. Examples for exact symmetric solutions were found early on, with applications in cosmology (isotropic space, [2, 3]) and black holes (spherical symmetry, [4]). Quantum gravity in the Wheeler–DeWitt form has, similarly, first been studied in isotropic models[5] followed later by inhomogeneous ones[6]..."



"In loop quantum gravity there is a systematic procedure to derive symmetric models and to relate them to the full theory[7, 8]. Alsohere, applications were first done in the simplest, isotropic context followed by anisotropic models. Applications include a general non-singular behavior in those models[9, 10, 11, 12], new information about initial conditions[13], and several phenomenological scenarios[14, 15, 16]. Spherical symmetry presents an inhomogeneous model with infinitely many kinematical degrees of freedom, but also interesting physical applications for black holes..."

for the "level splitting" see Figure 1, on page 11.

 

[marcus]

BTW Penrose has made an interesting critique of LQG
(at this point challenges help the theory grow I think and this is a tough one----involving second law----so should have interesting repercussions)

Bojowald has shown that within LQG context one can reduce the theory by symmetry and get a LQ cosmology and in LQC the bigbang singularity goes away.

Penrose says this is possibly a bad sign because of the second law.
Maybe a good theory SHOULD have a bigbang singularity

because the state right at bigbang should be one of very low entropy----which he gets from the uniformity of the gravitational field
(a uniform gravitational field is low entropy and normally things like to clump together so the field evolves from a smooth even field to a bumpy clumpy one)

now suppose Bojowald removes the singularity so there is a collapsing stage right before the beginning of expansion

what can this collapsing "pre-universe" look like so that it has even LESS entropy!

(BTW bojo also discovered that the volume element turns inside out at the moment of bounce----maybe there is some other kind of reversal that Penrose did not hear about that will make it OK)

Penrose's lectures at princeton October 2003 are online
they are the "Fashion, Faith and Fantasy" talks

 

[Olias]

Great Paper Marcus, I give it a thorough reading last night/yesterday, I had to do some family housesitting today, so I took the paper with me, I find it a very..very interesting paper, first class!

Just incase he has two new papers, your link and this:

http://uk.arxiv.org/abs/gr-qc/0407017

 

[meteor]

He introduces new terminology (at least for me): The Bohr Hilbert space and the Schroedinger Hilbert space.
Would be interesting to know what's the triad spectrum (I guess that he refers to the spectrum of the densitized triad)
My bet is that black hole singularities will be quantized before 5 years from now

 

[marcus]

Hi meteor, best wishes on your birthday!
I agree with you about the BH singularity getting quantized---5 years
looks like a safe bet to me and I would take it if I liked the stake and odds.

 

[jeff]

My bet is that black hole singularities will be quantized before 5 years from now

Betting on a horse simply because it's the only one you know isn't the best idea.