Black hole solutions to the F4F_4-model and their orbits (I)

In this paper we continue the program of the classification of nilpotent orbits using the approach developed in arXiv:1107.5986, within the study of black hole solutions in D=4 supergravities. Our goal in this work is to classify static, single center black hole solutions to a specific N=2 four dimensional "magic" model, with special K\"ahler scalar manifold ${\rm Sp}(6,\mathbb{R})/{\rm U}(3)$, as orbits of geodesics on the pseudo-quaternionic manifold ${\rm F}_{4(4)}/[{\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})]$ with respect to the action of the isometry group ${\rm F}_{4(4)}$. Our analysis amounts to the classification of the orbits of the geodesic "velocity" vector with respect to the isotropy group $H^*={\rm SL}(2,\mathbb{R})\times {\rm Sp}(6,\mathbb{R})$, which include a thorough classification of the \emph{nilpotent orbits} associated with extremal solutions and reveals a richer structure than the one predicted by the $\beta-\gamma$ labels alone, based on the Kostant Sekiguchi approach. We provide a general proof of the conjecture made in arXiv:0908.1742 which states that regular single center solutions belong to orbits with coinciding $\beta-\gamma$ labels. We also prove that the reverse is not true by finding distinct orbits with the same $\beta-\gamma$ labels, which are distinguished by suitably devised tensor classifiers. Only one of these is generated by regular solutions. Since regular static solutions only occur with nilpotent degree not exceeding 3, we only discuss representatives of these orbits in terms of black hole solutions. We prove that these representatives can be found in the form of a purely dilatonic four-charge solution (the generating solution in D=3) and this allows us to identify the orbit corresponding to the regular four-dimensional metrics.Comment: 81 pages, 24 tables, new section 4.4 about the fake superpotential added, typos corrected, references added, accepted in Nuclear Physics B.

Selfduality of non-linear electrodynamics with derivative corrections

In this paper we investigate how electromagnetic duality survives derivative corrections to classical non-linear electrodynamics. In particular, we establish that electromagnetic selfduality is satisfied to all orders in $\alpha'$ for the four-point function sector of the four dimensional open string effective action.Comment: 8 page

alpha'-Corrections to Heterotic Superstring Effective Action Revisited

In this letter we establish that the supersymmetric R^2 effective action for the heterotic string, obtained from the supersymmetrisation of the Lorentz Chern-Simons term, is to order $\alpha'$ equivalent modulo field redefinitions to heterotic string effective actions computed by different methods.Comment: 7 page

Fake supersymmetry versus Hamilton-Jacobi

We explain when the first-order Hamilton-Jacobi equations for black holes (and domain walls) in (gauged) supergravity, reduce to the usual first-order equations derived from a fake superpotential. This turns out to be equivalent to the vanishing of a newly found constant of motion and we illustrate this with various examples. We show that fake supersymmetry is a necessary condition for having physically sensible extremal black hole solutions. We furthermore observe that small black holes become scaling solutions near the horizon. When combined with fake supersymmetry, this leads to a precise extension of the attractor mechanism to small black holes: The attractor solution is such that the scalars move on specific curves, determined by the black hole charges, that are purely geodesic, although there is a non-zero potential.Comment: 20 pages, v2: Typos corrected, references adde

Black holes in supergravity and integrability

Stationary black holes of massless supergravity theories are described by certain geodesic curves on the target space that is obtained after dimensional reduction over time. When the target space is a symmetric coset space we make use of the group-theoretical structure to prove that the second order geodesic equations are integrable in the sense of Liouville, by explicitly constructing the correct amount of Hamiltonians in involution. This implies that the Hamilton-Jacobi formalism can be applied, which proves that all such black hole solutions, including non-extremal solutions, possess a description in terms of a (fake) superpotential. Furthermore, we improve the existing integration method by the construction of a Lax integration algorithm that integrates the second order equations in one step instead of the usual two step procedure. We illustrate this technology with a specific example.Comment: 44 pages, small typos correcte

Beirut explosion: TNT equivalence from the fireball evolution in the first 170 milliseconds

The evolution of the fireball resulting from the August 2020 Beirut explosion is traced using amateur videos taken during the first 400 ms after the detonation. Thirty-nine frames separated by 16.66–33.33 ms are extracted from six different videos located precisely on the map. Time evolution of the shock wave radius is traced by the fireball at consecutive time moments until about t≈170t≈170 ms and a distance d≈128d≈128 m. Pixel scales for the videos are calibrated by de-projecting the existing grain silos building, for which accurate as-built drawings are available, using the length, the width, and the height and by defining the line-of-sight incident angles. In the distance range d≈d≈ 60–128 m from the explosion center, the evolution of the fireball follows the Sedov–Taylor model with spherical geometry and an almost instantaneous energy release. This model is used to derive the energy available to drive the shock front at early times. Additionally, a drag model is fitted to the fireball evolution until its stopping at a time t≈500t≈500 ms at a distance d≈145±5d≈145±5 m. Using the derived TNT equivalent yield, the scaled stopping distance reached by the fireball and the shock wave-fireball detachment epoch within which the fireball is used to measure the shock wave are in excellent agreement with other experimental data. A total TNT equivalence of 200±80t200±80t at a distance d≈130d≈130 m is found. Finally, the dimensions of the crater size taken from a hydrographic survey conducted 6 days after the explosion are scaled with the known correlation equations yielding a close range of results. A recent published article by Dewey (Shock Waves 31:95–99, 2021) shows that the Beirut explosion TNT equivalence is an increasing function of distance. The results of the current paper are quantitatively in excellent agreement with this finding. These results present an argument that the actual mass of ammonium nitrate that contributed to the detonation is much less than the quantity that was officially claimed available

Brane solutions and integrability: a status report

We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes.Comment: 4 pages, Proceedings of ERE 2010, Granada, 6-10 september 201

Brane solutions and integrability: a status report

We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes.Comment: 4 pages, Proceedings of ERE 2010, Granada, 6-10 september 201

Domain-wall/Cosmology correspondence in adS/dS supergravity

We realize the domain-wall/cosmology correspondence for (pseudo)supersymmetric domain walls (cosmologies) in the context of four-dimensional supergravity. The OSp(2|4)-invariant anti-de Sitter (adS) vacuum of a particular N=2 Maxwell-Einstein supergravity theory is shown to correspond to the OSp(2^*|2,2)-invariant de Sitter (dS) vacuum of a particular pseudo-supergravity model, with `twisted' reality conditions on spinors. More generally, supersymmetric domain walls of the former model correspond to pseudo-supersymmetric cosmologies of the latter model, with time-dependent pseudo-Killing spinors that we give explicitly.Comment: 21 pages;v2: rewritten to clarify the link with fake supergravity -- main results unchanged; v3: typos corrected, two refs added, JHEP versio

Extremal Multicenter Black Holes: Nilpotent Orbits and Tits Satake Universality Classes

Four dimensional supergravity theories whose scalar manifold is a symmetric coset manifold U[D=4]/Hc are arranged into a finite list of Tits Satake universality classes. Stationary solutions of these theories, spherically symmetric or not, are identified with those of an euclidian three-dimensional sigma-model, whose target manifold is a Lorentzian coset U[D=3]/H* and the extremal ones are associated with H* nilpotent orbits in the K* representation emerging from the orthogonal decomposition of the algebra U[D=3] with respect to H*. It is shown that the classification of such orbits can always be reduced to the Tits-Satake projection and it is a class property of the Tits Satake universality classes. The construction procedure of Bossard et al of extremal multicenter solutions by means of a triangular hierarchy of integrable equations is completed and converted into a closed algorithm by means of a general formula that provides the transition from the symmetric to the solvable gauge. The question of the relation between H* orbits and charge orbits W of the corresponding black holes is addressed and also reduced to the corresponding question within the Tits Satake projection. It is conjectured that on the vanishing locus of the Taub-NUT current the relation between H*-orbit and W-orbit is rigid and one-to-one. All black holes emerging from multicenter solutions associated with a given H* orbit have the same W-type. For the S^3 model we provide a complete survey of its multicenter solutions associated with all of the previously classified nilpotent orbits of sl(2) x sl(2) within g[2,2]. We find a new intrinsic classification of the W-orbits of this model that might provide a paradigm for the analogous classification in all the other Tits Satake universality classes.Comment: 83 pages, LaTeX; v2: few misprints corrected and references adde