Ditauonium is a hydrogen atom-like bound state of a tau lepton and an anti-tau lepton, which can come in para- or ortho- varieties depending upon their relative spins. Its properties can be calculated to high precision using quantum electrodynamics and to a lesser extent other Standard Model physics considerations. Its properties are as follows, according to a new paper analyzing the question and doing the calculations:
7 comments:
what do you know of String theory calculation of Extremal black hole entropy
That "fs" stands for femtosecond. Don't plan on doing much chemistry with this thing.
@neo
Almost nothing. There is a huge literature about black holes and honestly, I just don't care much about black holes beyond the basics that I already know.
@Darayvus
Definitely no time for a bathroom break in the middle of your experiments with it.
@andrew
i ask if it is zero or a/4
Extremal limits and black hole entropy
Sean M. Carroll, Matthew C. Johnson, Lisa Randall
Taking the extremal limit of a non-extremal Reissner-Nordström black hole (by externally varying the mass or charge), the region between the inner and outer event horizons experiences an interesting fate -- while this region is absent in the extremal case, it does not disappear in the extremal limit but rather approaches a patch of AdS2×S2. In other words, the approach to extremality is not continuous, as the non-extremal Reissner-Nordström solution splits into two spacetimes at extremality: an extremal black hole and a disconnected AdS space. We suggest that the unusual nature of this limit may help in understanding the entropy of extremal black holes.
https://arxiv.org/abs/0901.0931
Extremal black holes, gravitational entropy and nonstationary metric fields
Ariel Edery, Benjamin Constantineau
We show that extremal black holes have zero entropy by pointing out a simple fact: they are time-independent throughout the spacetime and correspond to a single classical microstate. We show that non-extremal black holes, including the Schwarzschild black hole, contain a region hidden behind the event horizon where all their Killing vectors are spacelike. This region is nonstationary and the time t labels a continuous set of classical microstates, the phase space [hab(t),Pab(t)], where hab is a three-metric induced on a spacelike hypersurface Σt and Pab is its momentum conjugate. We determine explicitly the phase space in the interior region of the Schwarzschild black hole. We identify its entropy as a measure of an outside observer's ignorance of the classical microstates in the interior since the parameter t which labels the states lies anywhere between 0 and 2M. We provide numerical evidence from recent simulations of gravitational collapse in isotropic coordinates that the entropy of the Schwarzschild black hole stems from the region inside and near the event horizon where the metric fields are nonstationary; the rest of the spacetime, which is static, makes no contribution. Extremal black holes have an event horizon but in contrast to non-extremal black holes, their extended spacetimes do not possess a bifurcate Killing horizon. This is consistent with the fact that extremal black holes are time-independent and therefore have no distinct time-reverse.
https://arxiv.org/abs/1010.5844
Geometric aspects of Extremal Kerr black hole entropy
E M Howard
Extreme Black holes are an important theoretical laboratory for exploring the nature of entropy. We suggest that this unusual nature of the extremal limit could explain the entropy of extremal Kerr black holes. The time-independence of the extremal black hole, the zero surface gravity, the zero entropy and the absence of a bifurcate Killing horizon are all related properties that define and reduce to one single unique feature of the extremal Kerr spacetime. We suggest the presence of a true geometric discontinuity as the underlying cause of a vanishing entropy.
Comments: 10 pages, published in Journal of Modern Physics, 2013, 4, 357-363. arXiv admin note: text overlap with arXiv:hep-th/9608162, arXiv:1201.4017 by other authors
" We show that extremal black holes have zero entropy"
"The time-independence of the extremal black hole, the zero surface gravity, the zero entropy"
vs
Microscopic Origin of the Bekenstein-Hawking Entropy
A. Strominger, C. Vafa
The Bekenstein-Hawking area-entropy relation SBH=A/4 is derived for a class of five-dimensional extremal black holes in string theory by counting the degeneracy of BPS soliton bound states.
Comments: 12 pages. Relatively minor corrections and additions to discussion
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Report number: HUTP-96/A002, RU-96-01
Cite as: arXiv:hep-th/9601029
what do you think about extremal black holes ?
I have no opinion about external black holes.
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