# Recent papers on self-dual loop quantum black holes

1. Nov 30, 2015

### kodama

self-dual loop quantum gravity results when the immirizi parameter y=i has been the subject of many recent research papers here is a partial list

Gravitational axial perturbations and quasinormal modes of loop quantum black holes

M.B. Cruz, C.A.S. Silva, F.A. Brito
(Submitted on 26 Nov 2015)
Gravitational waves can be used as a way to investigate the structure of spacetime. Loop Quantum Gravity is a theory that propose a way to model the behavior of spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole's singularity. A recent prediction of loop quantum gravity is the existence of sub-Planckian black holes called loop quantum black holes (LQBH) or self-dual black holes which correspond to a quantized version of Schwarzschild black hole. In this work, we study the gravitational waves spectrum emitted by a LQBH through the analysis of its the quasinormal modes. From the results obtained, loop quantum black holes have been shown stable under axial gravitational perturbations.
Comments: 9 pages, 4 figures, 2 tables
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1511.08263 [gr-qc]
(or arXiv:1511.08263v1 [gr-qc] for this version)

Near-Horizon Radiation and Self-Dual Loop Quantum Gravity
Marc Geiller, Karim Noui
(Submitted on 17 Feb 2014)
We compute the near-horizon radiation of quantum black holes in the context of self-dual loop quantum gravity. For this, we first use the unitary spinor basis of SL(2,C) to decompose states of Lorentzian spin foam models into their self-dual and anti self-dual parts, and show that the reduced density matrix obtained by tracing over one chiral component describes a thermal state at Unruh temperature. Then, we show that the analytically-continued dimension of the SU(2) Chern-Simons Hilbert space, which reproduces the Bekenstein-Hawking entropy in the large spin limit in agreement with the large spin effective action, takes the form of a partition function for states thermalized at Unruh temperature, with discrete energy levels given by the near-horizon energy of Frodden-Gosh-Perez, and with a degenerate ground state which is holographic and responsible for the entropy.
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Europhys. Lett. 105 (2014) 60001
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1209%2F0295-5075%2F105%2F60001&v=3fe43976 [Broken]
Cite as: arXiv:1402.4138 [gr-qc]
(or arXiv:1402.4138v1 [gr-qc] for this version)

Quasinormal frequencies of self-dual black holes
Victor Santos, R. V. Maluf, C. A. S. Almeida
(Submitted on 14 Sep 2015)
Considering the emission of gravitational waves within the framework of Loop Quantum Gravity, we compute the quasinormal frequencies of a scalar field in a spherically symmetric black hole, described in the semiclassical limit by an effective metric called self-dual metric. We compute the frequencies using a sixth order WKB method and compare them with numerical solutions of the Regge-Wheeler equation.
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1509.04306 [gr-qc]
(or arXiv:1509.04306v1 [gr-qc] for this version)

Gravitational Lensing by Self-Dual Black Holes in Loop Quantum Gravity
Satyabrata Sahu, Kinjalk Lochan, D. Narasimha
(Submitted on 19 Feb 2015 (v1), last revised 13 Mar 2015 (this version, v2))
We study gravitational lensing by a recently proposed black hole solution in Loop Quantum Gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the mass suppression' effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter. Gravitational lensing in the strong and weak deflection regimes is studied and a sample consistency relation is presented which could serve as a test of this model. We discuss that though the consistency relation for this model is qualitatively similar to what would have been in Brans-Dicke, in general it can be a good discriminator between many alternative theories. Although the observational prospects do not seem to be very optimistic even for a galactic supermassive black hole case, time delay between relativistic images for billion solar mass black holes in other galaxies might be within reach of future relativistic lensing observations.
Comments: 13 pages; 4 figures; minor revisions to match published version + a reference added
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: Phys. Rev. D 91, 063001 (2015)

Analytic continuation of real Loop Quantum Gravity : Lessons from black hole thermodynamics
Jibril Ben Achour, Karim Noui
(Submitted on 22 Jan 2015)
This contribution is devoted to summarize the recent results obtained in the construction of an "analytic continuation" of Loop Quantum Gravity (LQG). By this, we mean that we construct analytic continuation of physical quantities in LQG from real values of the Barbero-Immirzi parameter γ to the purely imaginary value γ=±i. This should allow us to define a quantization of gravity with self-dual Ashtekar variables. We first realized in [1] that this procedure, when applied to compute the entropy of a spherical black hole in LQG for γ=±i, allows to reproduce exactly the Bekenstein-Hawking area law at the semi-classical limit. The rigorous construction of the analytic continuation of spherical black hole entropy has been done in [2]. Here, we start with a review of the main steps of this construction: we recall that our prescription turns out to be unique (under natural assumptions) and leads to the right semi-classical limit with its logarithmic quantum corrections. Furthermore, the discrete and γ-dependent area spectrum of the black hole horizon becomes continuous and obviously γ-independent. Then, we review how this analytic continuation could be interpreted in terms of an analytic continuation from the compact gauge group SU(2) to the non-compact gauge group SU(1,1) relying on an analysis of three dimensional quantum gravity.
Comments: 8 pages, 1 figure, Proceedings of Frontiers of Fundamental Physics 2014 - Proceedings of Science (PoS)
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1501.05523 [gr-qc]
(or arXiv:1501.05523v1 [gr-qc] for this version)

Near-Horizon Radiation and Self-Dual Loop Quantum Gravity
Marc Geiller, Karim Noui
(Submitted on 17 Feb 2014)
We compute the near-horizon radiation of quantum black holes in the context of self-dual loop quantum gravity. For this, we first use the unitary spinor basis of SL(2,C) to decompose states of Lorentzian spin foam models into their self-dual and anti self-dual parts, and show that the reduced density matrix obtained by tracing over one chiral component describes a thermal state at Unruh temperature. Then, we show that the analytically-continued dimension of the SU(2) Chern-Simons Hilbert space, which reproduces the Bekenstein-Hawking entropy in the large spin limit in agreement with the large spin effective action, takes the form of a partition function for states thermalized at Unruh temperature, with discrete energy levels given by the near-horizon energy of Frodden-Gosh-Perez, and with a degenerate ground state which is holographic and responsible for the entropy.
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Journal reference: Europhys. Lett. 105 (2014) 60001
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1209%2F0295-5075%2F105%2F60001&v=3fe43976 [Broken]
Cite as: arXiv:1402.4138 [gr-qc]
(or arXiv:1402.4138v1 [gr-qc] for this version)

SL(2, C) and SU(2) Connection Variable Formulations of Kerr Isolated Horizon Geometries for Loop Quantum Gravity
Christian Röken
(Submitted on 11 Mar 2013)
A construction of both self-dual SL(2, C) and SU(2) connection variable formulations for the description of the degrees of freedom of classical, rotating Kerr isolated horizon geometries is presented. These descriptions are based on sets of connection Hamiltonian variables instead of the spacetime metric. The analysis is motivated in a concrete, physical manner based on the stationary, axisymmetric Kerr solution of the vacuum Einstein equations, evaluated in a proper, well-defined frame of reference, on which isolated horizon boundary conditions are imposed. Having derived the kinematical part of such an isolated horizon phase space setting, one can set up a conserved presymplectic structure for the study of dynamical aspects of black hole theory. Since black holes play a crucial role in various fields like quantum gravity, mathematical physics, astrophysics and cosmology, or numerical relativity, one has to deal with different models describing these objects. The quasi-local framework studied in this paper is appropriate for covering most of the physical settings involving black hole dynamics. Moreover, the SU(2) connection variable formulation of classical Kerr isolated horizons allows directly for a semiclassical treatment of rotating quantum black holes in the context of loop quantum gravity.
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1303.2548 [gr-qc]
(or arXiv:1303.2548v1 [gr-qc] for this version)
Quantum tunneling radiation from self-dual black holes
C. A. S. Silva
(Submitted on 15 Oct 2012)
We calculate the Hawking temperature for a self-dual black hole in the context of quantum tunneling formalism.
Subjects: General Physics (physics.gen-ph)
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1016%2Fj%252Ephysletb%252E2013%252E07%252E033&v=5f331d80 [Broken]
Cite as: arXiv:1210.4472 [physics.gen-ph]
(or arXiv:1210.4472v1 [physics.gen-ph] for this version)
Submission history
From: Carlos Alex Souza da Silva M.Sc [view email]
[v1] Mon, 15 Oct 2012 05:10:00 GMT (11kb)
Emission spectra of self-dual black holes
Sabine Hossenfelder, Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 2 Feb 2012 (v1), last revised 15 Feb 2012 (this version, v2))
We calculate the particle spectra of evaporating self-dual black holes that are potential dark matter candidates. We first estimate the relevant mass and temperature range and find that the masses are below the Planck mass, and the temperature of the black holes is small compared to their mass. In this limit, we then derive the number-density of the primary emission particles, and, by studying the wave-equation of a scalar field in the background metric of the black hole, show that we can use the low energy approximation for the greybody factors. We finally arrive at the expression for the spectrum of secondary particle emission from a dark matter halo constituted of self-dual black holes.
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Cite as: arXiv:1202.0412 [gr-qc]
(or arXiv:1202.0412v2 [gr-qc] for this version)

Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip
(Submitted on 10 Mar 2015 (v1), last revised 3 Jul 2015 (this version, v3))
At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
Comments: 8 pages; v2: more references, typos fixed, minor rewording; v3: some clearer explanations in response to referees, more references
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: Phys. Rev. Lett. 115, 071302 (2015)
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1103%2FPhysRevLett%252E115%252E071302&v=98cdc36a [Broken]
Cite as: arXiv:1503.02981 [gr-qc]
(or arXiv:1503.02981v3 [gr-qc] for this version)

Self-dual Black Holes in LQG: Theory and Phenomenology
Leonardo Modesto, Isabeau Prémont-Schwarz
(Submitted on 20 May 2009 (v1), last revised 3 Jun 2009 (this version, v2))
In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner-Nordstrom-like metric is self-dual in the sense of T-duality: the form of the metric obtained in Loop quantum Gravity (LQG) is invariant under the exchange "r <-> a0/r" where "a0" is proportional to the minimum area in LQG and "r" is the standard Schwarzschild radial coordinate at asymptotic infinity. Of particular interest, the symmetry imposes that if an observer at "r" close to infinity sees a black hole of mass "m" an observer in the other asymptotic infinity beyond the horizon (at "r" close to "0") sees a dual mass "mp/m" ("mp" is the Planck mass). We then show that small LQBH are stable and could be a component of dark matter. Ultra-light LQBHs created shortly after the Big Bang would now have a mass of approximately "10^(-5) mp" and emit radiation with a typical energy of about 10^(13) - 10^(14) eV but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultra light black holes would be compatible with the observed rate of the Auger detector.
Comments: 18 pages, 32 figures. Extra Plot, Improved Numerical Results and Corrected typos
Subjects: High Energy Physics - Theory (hep-th); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Astrophysical Phenomena (astro-ph.HE); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph)
Journal reference: Phys.Rev.D80:064041,2009
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1103%2FPhysRevD%252E80%252E064041&v=3b61e8cb [Broken]
Cite as: arXiv:0905.3170 [hep-th]
(or arXiv:0905.3170v2 [hep-th] for this version)

Last edited by a moderator: May 7, 2017
2. Nov 30, 2015

### kodama

video
http://www.perimeterinstitute.ca/videos/black-hole-entropy-and-case-self-dual-loop-quantum-gravity

Black hole entropy and the case for self-dual loop quantum gravity

Black hole entropy and the case for self-dual loop quantum gravity

Recording Details
Scientific Areas:
Quantum Gravity
Collection/Series:
Quantum Gravity
PIRSA Number:
14010098
Abstract
By focusing on aspects of black hole thermodynamics, I will present some evidences supporting the unexpected role of the complex self-dual variables in quantum gravity. This will also be the occasion of revisiting some aspects of three-dimensional gravity, and in particular the link between the BTZ black hole and the Turaev-Viro state sum model. Also the information on the website for next week needs to be modified: We will not have a seminar on Thursday (as Thursday is PI day). Instead, we will have the seminar on Wednesday, but actually would prefer a different time, namely 3.30 pm.

Last edited by a moderator: May 7, 2017
3. Dec 1, 2015

### marcus

To me this seems like the start of a valuable select bibliography---or reading list for anyone interested in the self-dual LQG approach.
I want to point out that the speaker/author of the Perimeter talk in post #2 is Marc Geiller
http://inspirehep.net/author/profile/M.Geiller.1
and one thing that stands out about him, for me, is his recent co-authorship with Bianca Dittrich on a different reformulation of LQG.

1. arXiv:1506.08571 [pdf, other]
A new realization of quantum geometry
Benjamin Bahr, Bianca Dittrich, Marc Geiller

3. arXiv:1412.3752 [pdf, other]
Flux formulation of loop quantum gravity: Classical framework
Bianca Dittrich, Marc Geiller
Comments: 60 pages, 13 figures, published version
Journal-ref: Class. Quantum Grav. 32 (2015) 135016

5. arXiv:1401.6441 [pdf, other]
A new vacuum for Loop Quantum Gravity
Bianca Dittrich, Marc Geiller
Journal-ref: Class. Quantum Grav. 32 (2015) 112001

The fact that Geiller is involved in both this and the self-dual approach makes me wonder if there might be a potential connection that could appear further on.

Last edited: Dec 1, 2015
4. Dec 1, 2015

### kodama

yes Marc Geiller wrote several papers on self-dual LQG. the Kodama wavefunction requires y=i. Marc Geiler views self-dual LQG is the way forward for LQG. his and other papers attempt to drive BH entropy when y=i

whats worth noting is several papers attempt to make real predictions such as dark matter LQBH, gamma ray production, hawking radiation etc.

since self-dual lqg is complex i wonder if it can be reformulated in twistor theory.

5. Dec 1, 2015

### marcus

Wolfgang Wieland made some forays in that direction, as I recall. He gave a Perimeter talk about it some time back.
http://pirsa.org/12020129/
and there is also the video that goes with the slides.
Here's a paper that goes with it.
http://arxiv.org/abs/1207.6348

Last edited: Dec 1, 2015
6. Dec 1, 2015

### kodama

yes i ask since one challenge of complex self-dual LQG is imposing reality conditions to get real physics. if QFT and other physics is re-written on complex space, perhaps twistor formalism, that would make self-dual LQG easier.

Black Hole Entropy from complex Ashtekar variables
Ernesto Frodden, Marc Geiller, Karim Noui, Alejandro Perez
(Submitted on 17 Dec 2012 (v1), last revised 28 Dec 2013 (this version, v2))
In loop quantum gravity, the number NΓ(A,γ) of microstates of a black hole for a given discrete geometry Γ depends on the so-called Barbero-Immirzi parameter γ. Using a suitable analytic continuation of γ to complex values, we show that the number NΓ(A,±i) of microstates behaves as exp(A/(4ℓ2Pl)) for large area A in the large spin semiclassical limit. Such a correspondence with the semiclassical Bekenstein-Hawking entropy law points towards an unanticipated and remarkable feature of the original complex Ashtekar variables for quantum gravity.
Comments: 5 pages. New point of view on the analytic continuation, which is now made rigorous by analytically-continuing the SU(2) spins in addition to the Barbero-Immirzi parameter
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: Europhys. Lett. 107 (2014) 10005
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1209%2F0295-5075%2F107%2F10005&v=9358db9b [Broken]
Cite as: arXiv:1212.4060 [gr-qc]
(or arXiv:1212.4060v2 [gr-qc] for this version)

Last edited by a moderator: May 7, 2017
7. Dec 3, 2015

### kodama

worth mentioning that this paper Gravitational Lensing by Self-Dual Black Holes in Loop Quantum Gravity
Satyabrata Sahu, Kinjalk Lochan, D. Narasimha

that if black holes are described by Self-Dual Black Holes in Loop Quantum Gravity it might be possible to distinguish black holes described by Self-Dual Loop Quantum Gravity theory, from black holes described by other gravity theories, although the magnitude of effect is very small.

Self-dual Black Holes in LQG: Theory and Phenomenology

Leonardo Modesto, Isabeau Prémont-Schwarz (Submitted on 20 May 2009 (v1), last revised 3 Jun 2009 (this version, v2) of which other papers in this bibliography have cited, does make predictions.

self-dual loop quantum gravity predicts Self-dual Black Holes
several papers predict Self-dual Black Holes entropy and hawking radiation spectrum.

one class of self-dual loop quantum gravity Self-dual Black Holes are Ultra-light loop quantum black hole
Ultra-light LQBHs.

some Ultra-light LQBHs could give off very high gamma rays that could be observed

some Ultra-light LQBHs are stable. the energy they lose through hawking radiation is exactly balanced by energy they receive from CMB

stable Ultra-light LQBHs have the properties of cold dark matter.

Ultra-light LQBHs could be produced in quantities during big bang that match lambda CM models of dark matter production and could account for some or all of the cold dark matter in the universe.

in conclusion self-dual loop quantum gravity predicts a component of cold dark matter consists of Ultra-light loop quantum self-dual black holes

if this is all correct, then at least one component of cold dark matter is a prediction and evidence of quantum gravity.

8. Dec 4, 2015

9. Dec 4, 2015

### kodama

if it interests u u can look it up for each and every paper :)

10. Dec 4, 2015

### marcus

I know :) but this FGNP paper looks especially interesting to me they get the entropy right----A/4 (in Planck units). So I was glad to see that the paper got a good number of cites.

11. Dec 4, 2015

### kodama

Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip
(Submitted on 10 Mar 2015 (v1), last revised 3 Jul 2015 (this version, v3))

also does this using different counting method and complex ashketar

12. Dec 4, 2015

### marcus

Impressive paper! Encouraging to see someone of Carlip's stature working on self-dual LQG. I missed seeing the interest of this paper when it first came out so I'm especially glad you called attention to it. It should have been included in the first quarter 2015 poll. Maybe I should belatedly include it in the fourth quarter poll.
http://arxiv.org/abs/1503.02981
Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip
(Submitted on 10 Mar 2015)
At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
8 pages

Last edited: Dec 4, 2015
13. Dec 4, 2015

### kodama

how many citations does it have? if results hold up then calculation of black hole entropy in self-dual LQG does not require a real immirizi parameter with a specific value.

you are left with complex ashketar values and reality constraint issues. perhaps physics should be done in complex spacetime

14. Dec 4, 2015

### marcus

15. Dec 4, 2015

### kodama

give it time. both papers claim to calculate bh entropy from self-dual lqg using 2 very different approaches.
which do you think is more robust?

http://arxiv.org/abs/1503.02981
Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip
(Submitted on 10 Mar 2015)
At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
8 pages

Black Hole Entropy from complex Ashtekar variables
Ernesto Frodden, Marc Geiller, Karim Noui, Alejandro Perez
(Submitted on 17 Dec 2012 (v1), last revised 28 Dec 2013 (this version, v2))
In loop quantum gravity, the number NΓ(A,γ) of microstates of a black hole for a given discrete geometry Γ depends on the so-called Barbero-Immirzi parameter γ. Using a suitable analytic continuation of γ to complex values, we show that the number NΓ(A,±i) of microstates behaves as exp(A/(4ℓ2Pl)) for large area A in the large spin semiclassical limit. Such a correspondence with the semiclassical Bekenstein-Hawking entropy law points towards an unanticipated and remarkable feature of the original complex Ashtekar variables for quantum gravity.
Comments: 5 pages. New point of view on the analytic continuation, which is now made rigorous by analytically-continuing the SU(2) spins in addition to the Barbero-Immirzi parameter
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: Europhys. Lett. 107 (2014) 10005
DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1209%2F0295-5075%2F107%2F10005&v=9358db9b [Broken]
Cite as: arXiv:1212.4060 [gr-qc]
(or arXiv:1212.4060v2 [gr-qc] for this version)

Last edited by a moderator: May 7, 2017
16. Dec 7, 2015

### kodama

the other papers here, based on complex Ashtekar variables - self-dual black holes make genuine quantum gravity predictions, from thermal emission spectrum to stability of Self-dual Black Holes are Ultra-light loop quantum black hole as cold dark matter candidates. if these predictions are at least in principle falsifiable, although actually detecting them is a major challenge with current technology.

Gravitational Lensing by Self-Dual Black Holes in Loop Quantum Gravity
Satyabrata Sahu, Kinjalk Lochan, D. Narasimha
(Submitted on 19 Feb 2015 (v1), last revised 13 Mar 2015 (this version, v2))
We study gravitational lensing by a recently proposed black hole solution in Loop Quantum Gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the mass suppression' effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter.
....
We discuss that though the consistency relation for this model is qualitatively similar to what would have been in Brans-Dicke, in general it can be a good discriminator between many alternative theories. Although the observational prospects do not seem to be very optimistic even for a galactic supermassive black hole case, time delay between relativistic images for billion solar mass black holes in other galaxies might be within reach of future relativistic lensing observations.
Comments: 13 pages; 4 figures; minor revisions to match published version + a reference added

So self-dual LQG does make falsifiable quantum gravity predictions such that if the prediction is wrong the theory is wrong (well maybe).

the paper suggests the mass of self-dual Black Holes that are Ultra-light loop quantum black hole as cold dark matter is 10^-18 kg, much heavier than any SM particle but light enough to evade current bounds based on gravitational lensing

17. Dec 13, 2015

### marcus

http://arxiv.org/abs/1512.03684
Anisotropic loop quantum cosmology with self-dual variables
Edward Wilson-Ewing
(Submitted on 11 Dec 2015)
A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies of the Ashtekar connection and the reality conditions are implemented via the choice of the inner product on the kinematical Hilbert space. The action of the Hamiltonian constraint operator is given explicitly for the case when the matter content is a massless scalar field (in which case the scalar field can be used as a relational clock), and it is shown that the big-bang and big-crunch singularities are resolved in the sense that singular and non-singular states decouple under the action of the Hamiltonian constraint operator.
16 pages

18. Dec 14, 2015

### kodama

marcus paper suggests that LQG research direction is trending back toward self-dual LQG, though this is much more difficult, it appears original LQG is physically incorrect. it also references the paper u liked

19. Dec 14, 2015

### marcus

Indeed! I liked
Frodden et al paper, reference [24] here, that you listed, and also the J.B.ACHOUR et al paper that you spotted, reference [34] which was also about this rising interest in self-dual LQG. The references [24]-[34] include other papers using the self-dual variables, not all perhaps, but some. There are several (many I think) that you have already listed, but maybe also some you have not
[24] E. Frodden, M. Geiller, K. Noui, and A. Perez, “Black Hole Entropy from complex Ashtekar variables,” Europhys. Lett. 107 (2014) 10005, arXiv:1212.4060.
[25] N. Bodendorfer, A. Stottmeister, and A. Thurn, “Loop quantum gravity without the Hamiltonian constraint,” Class. Quant. Grav. 30 (2013) 082001, arXiv:1203.6525.
[26] M. Han, “Black Hole Entropy in Loop Quantum Gravity, Analytic Continuation, and Dual Holography,” arXiv:1402.2084.
[27] J. B. Achour, A. Mouchet, and K. Noui, “Analytic Continuation of Black Hole Entropy in Loop Quantum Gravity,” arXiv:1406.6021.
[28] N. Bodendorfer and Y. Neiman, “Imaginary action, spinfoam asymptotics and the transplanckian regime of loop quantum gravity,” Class. Quant. Grav. 30 (2013) 195018, arXiv:1303.4752.
[29] D. Pranzetti, “Geometric temperature and entropy of quantum isolated horizons,” Phys. Rev. D89 (2014) 104046, arXiv:1305.6714.
[30] M. Geiller and K. Noui, “Near-Horizon Radiation and Self-Dual Loop Quantum Gravity,” Europhys. Lett. 105 (2014) 60001, arXiv:1402.4138.
[31] S. Carlip, “A Note on Black Hole Entropy in Loop Quantum Gravity,” arXiv:1410.5763.
[32] T. Thiemann and H. Kastrup, “Canonical quantization of spherically symmetric gravity in Ashtekar’s selfdual representation,” Nucl. Phys. B399 (1993) 211–258, arXiv:gr-qc/9310012.
[33] E. Wilson-Ewing, “Loop quantum cosmology with self-dual variables,” arXiv:1503.07855.
[34] J. B. Achour, J. Grain, and K. Noui, “Loop Quantum Cosmology with Complex Ashtekar Variables,” Class. Quant. Grav. 32 (2015) 025011, arXiv:1407.3768.

I see that Wilson-Ewing has an earlier paper [33] on LQC using self-dual variables.

Last edited: Dec 14, 2015
20. Dec 14, 2015

### marcus

Here's the previous Wilson-Ewing paper about LQC with self-dual variables.
http://arxiv.org/abs/1503.07855
Loop quantum cosmology with self-dual variables
Edward Wilson-Ewing
(Submitted on 26 Mar 2015 (v1), last revised 14 Oct 2015 (this version, v3))
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well-defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomy-like operators of which some are well-defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived, which provide a good approximation to the full quantum dynamics for sharply-peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a non-singular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
15 pages.

Kodama, you mentioned a trend. There could be a trend in progress, or at least a rising level of interest in self-dual variables LQC and LQG.
I've come to have a high opinion of Wilson-Ewing. It seems significant that he has written two articles this year on this theme. the first was this one, ab out ordinary homogeneous isotropic LQC but with self-dual. the second which just came out is where you relax the requirement that it be isotropic and consider a particular anisotropic case.