Applications of hidden symmetries to black hole physics

This work is a brief review of applications of hidden symmetries to black hole physics. Symmetry is one of the most important concepts of the science. In physics and mathematics the symmetry allows one to simplify a problem, and often to make it solvable. According to the Noether theorem symmetries are responsible for conservation laws. Besides evident (explicit) spacetime symmetries, responsible for conservation of energy, momentum, and angular momentum of a system, there also exist what is called hidden symmetries, which are connected with higher order in momentum integrals of motion. A remarkable fact is that black holes in four and higher dimensions always possess a set (`tower') of explicit and hidden symmetries which make the equations of motion of particles and light completely integrable. The paper gives a general review of the recently obtained results. The main focus is on understanding why at all black holes have something (symmetry) to hide.Comment: This is an extended version of the talks at NEB-14 conference (June,Ioannina,Greece) and JGRG20 meeting (September, Kyoto, Japan

Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants

A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions

We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar properties to those of Sasakian geometry. As an example of them, we present an explicit expression of local metrics and see how Sasakian structure is deformed by the presence of torsion. We also demonstrate that our example of the metrics admits the existence of hidden symmetries described by non-trivial odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using these metrics as an {\it ansatz}, we construct exact solutions in five dimensional minimal (un-)gauged supergravity and eleven dimensional supergravity. Finally, we discuss the global structures of the solutions and obtain regular metrics on compact manifolds in five dimensions, which give natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and $L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra

Hidden and Generalized Conformal Symmetry of Kerr-Sen Spacetimes

It is recently conjectured that generic non-extremal Kerr black hole could be holographically dual to a hidden conformal field theory in two dimensions. Moreover, it is known that there are two CFT duals (pictures) to describe the charged rotating black holes which correspond to angular momentum $J$ and electric charge $Q$ of the black hole. Furthermore these two pictures can be incorporated by the CFT duals (general picture) that are generated by $SL(2,\mathbb{Z})$ modular group. The general conformal structure can be revealed by looking at charged scalar wave equation in some appropriate values of frequency and charge. In this regard, we consider the wave equation of a charged massless scalar field in background of Kerr-Sen black hole and show in the "near region", the wave equation can be reproduced by the Casimir operator of a local $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetry. We can find the exact agreement between macroscopic and microscopic physical quantities like entropy and absorption cross section of scalars for Kerr-Sen black hole. We then find an extension of vector fields that in turn yields an extended local family of $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetries, parameterized by one parameter. For some special values of the parameter, we find a copy of $SL(2,\mathbb{R})$ hidden conformal algebra for the charged Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the strong deflection limit.Comment: 16 pages, new material and results added, extensive improvements in interpretation of results, references adde

Separability of Black Holes in String Theory

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)^2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.Comment: 27 page

No more CKY two-forms in the NHEK

We show that in the near-horizon limit of a Kerr-NUT-AdS black hole, the space of conformal Killing-Yano two-forms does not enhance and remains of dimension two. The same holds for an analogous polar limit in the case of extremal NUT charge. We also derive the conformal Killing-Yano $p$-form equation for any background in arbitrary dimension in the form of parallel transport.Comment: 36 pages, 12 pdf figures, v2: minor change

The Fluctuating Phenotype of the Lymphohematopoietic Stem Cell with Cell Cycle Transit

The most primitive engrafting hematopoietic stem cell has been assumed to have a fixed phenotype, with changes in engraftment and renewal potential occurring in a stepwise irreversible fashion linked with differentiation. Recent work shows that in vitro cytokine stimulation of murine marrow cells induces cell cycle transit of primitive stem cells, taking 40 h for progression from G0 to mitosis and 12 h for subsequent doublings. At 48 h of culture, progenitors are expanded, but stem cell engraftment is markedly diminished. We have investigated whether this effect on engraftment was an irreversible step or a reversible plastic feature correlated with cell cycle progression. Long-term engraftment (2 and 6 mo) of male BALB/c marrow cells exposed in vitro to interleukin (IL)-3, IL-6, IL-11, and steel factor was assessed at 2–4-h intervals of culture over 24–48 h using irradiated female hosts; the engraftment phenotype showed marked fluctuations over 2–4-h intervals, with engraftment nadirs occurring in late S and early G2. These data show that early stem cell regulation is cell cycle based, and have critical implications for strategies for stem cell expansion and engraftment or gene therapy, since position in cell cycle will determine whether effective engraftment occurs in either setting

Efficacy and safety of metabolic interventions for the treatment of severe COVID-19: in vitro, observational, and non-randomized open-label interventional study

Background: Viral infection is associated with a significant rewire of the host metabolic pathways, presenting attractive metabolic targets for intervention. Methods: We chart the metabolic response of lung epithelial cells to SARS-CoV-2 infection in primary cultures and COVID-19 patient samples and perform in vitro metabolism-focused drug screen on primary lung epithelial cells infected with different strains of the virus. We perform observational analysis of Israeli patients hospitalized due to COVID-19 and comparative epidemiological analysis from cohorts in Italy and the Veteran's Health Administration in the United States. In addition, we perform a prospective non-randomized interventional open-label study in which 15 patients hospitalized with severe COVID-19 were given 145 mg/day of nanocrystallized fenofibrate added to the standard of care. Results: SARS-CoV-2 infection produced transcriptional changes associated with increased glycolysis and lipid accumulation. Metabolism-focused drug screen showed that fenofibrate reversed lipid accumulation and blocked SARS-CoV-2 replication through a PPARα-dependent mechanism in both alpha and delta variants. Analysis of 3233 Israeli patients hospitalized due to COVID-19 supported in vitro findings. Patients taking fibrates showed significantly lower markers of immunoinflammation and faster recovery. Additional corroboration was received by comparative epidemiological analysis from cohorts in Europe and the United States. A subsequent prospective non-randomized interventional open-label study was carried out on 15 patients hospitalized with severe COVID-19. The patients were treated with 145 mg/day of nanocrystallized fenofibrate in addition to standard-of-care. Patients receiving fenofibrate demonstrated a rapid reduction in inflammation and a significantly faster recovery compared to patients admitted during the same period. Conclusions: Taken together, our data suggest that pharmacological modulation of PPARα should be strongly considered as a potential therapeutic approach for SARS-CoV-2 infection and emphasizes the need to complete the study of fenofibrate in large randomized controlled clinical trials. Funding: Funding was provided by European Research Council Consolidator Grants OCLD (project no. 681870) and generous gifts from the Nikoh Foundation and the Sam and Rina Frankel Foundation (YN). The interventional study was supported by Abbott (project FENOC0003). Clinical trial number: NCT04661930

Direct Recognition of Fusobacterium nucleatum by the NK Cell Natural Cytotoxicity Receptor NKp46 Aggravates Periodontal Disease

Periodontitis is a common human chronic inflammatory disease that results in the destruction of the tooth attachment apparatus and tooth loss. Although infections with periopathogenic bacteria such as Porphyromonas gingivalis (P. gingivalis) and Fusobacterium nucleatum (F. nucleatum) are essential for inducing periodontitis, the nature and magnitude of the disease is determined by the host's immune response. Here, we investigate the role played by the NK killer receptor NKp46 (NCR1 in mice), in the pathogenesis of periodontitis. Using an oral infection periodontitis model we demonstrate that following F. nucleatum infection no alveolar bone loss is observed in mice deficient for NCR1 expression, whereas around 20% bone loss is observed in wild type mice and in mice infected with P. gingivalis. By using subcutaneous chambers inoculated with F. nucleatum we demonstrate that immune cells, including NK cells, rapidly accumulate in the chambers and that this leads to a fast and transient, NCR1-dependant TNF-α secretion. We further show that both the mouse NCR1 and the human NKp46 bind directly to F. nucleatum and we demonstrate that this binding is sensitive to heat, to proteinase K and to pronase treatments. Finally, we show in vitro that the interaction of NK cells with F. nucleatum leads to an NCR1-dependent secretion of TNF-α. Thus, the present study provides the first evidence that NCR1 and NKp46 directly recognize a periodontal pathogen and that this interaction influences the outcome of F. nucleatum-mediated periodontitis

Hidden Symmetries for Ellipsoid-Solitonic Deformations of Kerr-Sen Black Holes and Quantum Anomalies

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and studied hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.Comment: latex2e, 11pt, 34 pages, the variant accepted by EPJC, with additional explanations, modifications and new references requested by refere