Subject: Globally naked and effective naked singularities
Date: Mon, 01 Mar 2004 16:19:58 +0200
From: Dimi Chakalov <>
To: Tomohiro Harada <>
BCC: [snip]


It seems to me that globally naked and effective naked singularities [Ref. 1] are effectively indistinguishable. If so, I wonder why we're still alive to discuss this issue.

Since you mentioned that we need quantum gravity to settle this crucial question [Ref. 2], and have explored the possibility of naked singularities as a possible central engine of gamma-ray bursts [Ibid.], may I draw your attention to a fundamental paper by Daniel Terno,

As to your latest gr-qc/0310079 of March 1st [Ref. 3], I wonder how you would modify the equation of state for quark matter if the future direct observational data on gravitational waves turn out to be zero, as predicted by Angelo Loinger,

It seems to me that we have to get back to the roots of quantum gravity, as explained by Karel Kuchar,

Otherwise we're fishing in murky waters, aren't we?

I will appreciate the opinion of your colleagues as well. Will keep it strictly private and confidential.

Kindest regards,

D. Chakalov


[Ref. 1] Tomohiro Harada, Gravitational Collapse and Naked Singularities, a plenary talk in the 5th International Conference on Gravitation and Cosmology, Jan 5-10, 2004, Cochin, India,

[the so-called effective naked singularities, in which the curvature strength outside horizons is beyond some cut-off scale,

appear with non-zero probability for physically reasonable matter fields,

[Ref. 2] Tomohiro Harada, Hideo Iguchi and Ken-Ichi Nakao, Physical Processes in Naked Singularity Formation, gr-qc/0204008

pp. 64-65: "3.4. Naked singularities and quantum gravity

"The above discussions are based on quantum field theory in curved spacetime. (...) It follows that the further evolution of the star will depend on quantum gravitational effects, and without invoking quantum gravity it is not possible to say whether the star radiates away on a short time or settles down into a black hole state."

"(S)everal authors have speculated naked singularities as a possible central engine of gamma-ray bursts. 110); 117) Any way, to answer the question may be out of scope of a semiclassical theory of quantum fields in curved space."
110) T. Harada, H. Iguchi and K. Nakao, Naked Singularity Explosion, Phys. Rev. D 62 (2000), 084037,

117) P.S. Joshi, N.K. Dadhich and R. Maartens, Why do naked singularities form in gravitational collapse? Mod. Phys. Lett. A 15 (2000), 991,

[Ref. 3] Hajime Sotani, Kazunori Kohri, and Tomohiro Harada (March 1, 2004), Restricting quark matter models by gravitational wave observation, gr-qc/0310079, to appear in Phys. Rev. D

Note: I spotted typos in my note above, I should have written "effectively naked singularities". Sorry about that. If nobody replies to my note above, I would say that the reason is my typos, and certainly not the lack of professional dedication to their fields of expertise.

I mean, if I was collecting post stamps, and they were doing bottle labels, then I wouldn't expect to hear from them: nobody would agree to change his hobby.

Here the case is different. None of the recipients of my email above has treated GR as some hobby. Never ever. They all are professionals. But with those typos, ... well, I don't know, I might not get any feedback!

D. Chakalov
March 2, 2004


Subject: A simple and natural discussion on quantum effects of gravity
Date: Fri, 09 Jul 2004 17:00:42 +0300
From: Dimi Chakalov <>
To: Tomohiro Harada <>
CC: Ken-ichi Nakao <>,,,,,,,,,,,,,,

Dear Professor Harada,

I hope my email of Mon, 01 Mar 2004 16:19:58 +0200 has been safely

I read with great interest your "Border of Spacetime" [Ref. 4], in which
you and Dr. Ken-ichi Nakao speculated on the limitations of general
relativity and mentioned some "simple and natural discussion on quantum
effects of gravity".

This latter phrase reminded me of the famous Murphy's Law No. 15: Complex problems have simple, easy-to-understand wrong answers.

I believe the limitations of general relativity are known since 1917,

Now we have to address the tug-of-war of "dark matter" & "dark energy"
[Ref. 5],

You and Dr. Ken-ichi Nakao wrote that the energy scale of the curved spacetime "can be measured by the curvature through Einstein's field equations."

I agree, but only after we understand the limitations of general relativity, which show up in the notorious, and highly misleading, notion of 'spacetime curvature',

I suggest we go back to the 1917 paper by Tito Levi-Civita,

and find out where we went wrong.

My speculations can be read at


D. Chakalov


[Ref. 4] Tomohiro Harada, Ken-ichi Nakao, Border of Spacetime, gr-qc/0407034. Accepted for publication in Physical Review D.

"We have already known that general relativity will have the limitation of its applicable scale in a high-energy side. A simple and natural discussion on quantum effects of gravity yields the Planck energy E_pl ~ 10^19GeV as a cut-off scale [lambda]. (...) The energy scale of the curved spacetime can be measured by the curvature through Einstein's field equations. Then if the above expectation is true, general relativity is not applicable to the spacetime region whose curvature strength exceeds [XXX]. This consideration naturally leads to the notion of the border of spacetime as follows.

"The appearance of visible borders with non-zero probability implies not only the limitation of general relativity but also a new window into extremely high-curvature spacetime physics in principle observable."

[Ref. 5] Wayne Hu and Martin White, The Cosmic Symphony, Sci American, February 2004, pp. 44-53,

"Last, further observations of the CMB could shed some light on the physical nature of dark energy. This entity might be a form of vacuum energy, as Einstein had hypothesized, but its value would have to be at least 60 and perhaps as much as 120 orders of magnitude as small as that predicted from particle physics. And why is dark energy comparable to dark matter in density now and apparently only now? To answer these questions, researchers can take advantage of the fact that CMB photons illuminate structures across the entire observable universe. By showing the amplitude of density fluctuations at different points in cosmic history, the CMB can reveal the tug-of-war between matter and dark energy."

Note 2: Tomohiro Harada published a new paper, "Gravitational collapse and naked singularities", gr-qc/0407109:

"Therefore, it is still uncertain whether or not naked singularities are censored in physically reasonable gravitational collapse. However, these modern examples of naked singularities strongly suggest that effective naked singularities appear with nonzero (maybe not too small) probability for physically reasonable matter fields. Therefore, naked singularities are within a scope of physics."

Let's first sort out the issue about the energy of the gravitational field. Then perhaps we'll understand why we are still alive to discuss naked singularities. In the case of a spherically symmetric homogeneous scalar field (the work on the inhomogeneous generalization is in progress, see gr-qc/0410144), the formation of naked singularity depends on the initial distribution of matter fields and the geometry of trapped surfaces which may subsequently form as the "collapse" evolves, so we should have already encountered at least one naked singularity in the past 13.7 billion years. Another catastrophe that hasn't happened is with the so-called exotic matter, as explained by Matt Visser.

All this reminds me of the famous ultraviolet catastrophe of 1900, which hasn't happened either, so maybe we should check out the textbook lore of general relativity and work out a complete theory of quantum gravity.

D. Chakalov
July 30, 2004
Last update: October 29, 2004