Approximate twistors and positive mass

In this paper the problem of comparing initial data to a reference solution for the vacuum Einstein field equations is considered. This is not done in a coordinate sense, but through quantification of the deviation from a specific symmetry. In a recent paper [T. B\"ackdahl, J.A. Valiente Kroon, Phys. Rev. Lett. 104, 231102 (2010)] this problem was studied with the Kerr solution as a reference solution. This analysis was based on valence 2 Killing spinors. In order to better understand this construction, in the present article we analyse the analogous construction for valence 1 spinors solving the twistor equation. This yields an invariant that measures how much the initial data deviates from Minkowski data. Furthermore, we prove that this invariant vanishes if and only of the mass vanishes. Hence, we get a proof of the positivity of mass.Comment: 18 pages, corrected typos, updated reference

The human polyomavirus KI: A study on cell permissivity, sub-cellular localization of VP1 and presence in cerebrospinal fluid and urine

KI polyomavirus (KIPyV) is a relatively newly discovered human polyomavirus originally identified in respiratory tract samples. Little is known about the route of infection or transmission, and the pathogenic properties of this virus are virtually unknown. The life cycle of KIPyV has not been studied as a permissive cell system has not been identified so far. The bona fide sites of viral replication in the human body remain unknown, but indications of a respiratory or oral route of infection led us to investigate whether the A549 lung cell line was permissive to KIPyV. In this thesis we have investigated if the A549 cell line allows KIPyV propagation and if viral protein is detectable by antibodies directed against KIPyV VP1. This was performed by transfecting with KIPyV genome and analyzing the cells for mRNA expression of LT-ag and antibody detection of VP1 by western blotting. LT-ag mRNA was successfully detected by PCR but detection of KIPyV VP1 by the use of our antibody was unsuccessful. The sub-cellular localization of KIPyV VP1 protein has been investigated by confocal microscopy using EGFP-KI VP1 fusion protein. Both A549 and Vero cell line were studied and the EGFP signal localized differently in the two cell lines. In A549 cells the localization was mainly in the nucleus while in Vero cells cytoplasm localization was mostly observed. We have also examined cerebrospinal fluid from patients with suspicion of neurological diseases and urine specimens from immunocompromised patients with systemic lupus erythematosus for KIPyV DNA by nested PCR. We have indicated the presence of KIPyV VP1 DNA by nested PCR and sequencing of the PCR products

On certain quasi-local spin-angular momentum expressions for small spheres

The Ludvigsen-Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius $r$ about a point $o$. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common leading term is of order $r^4$, and it is the product of the contraction of the energy-momentum tensor and an average of the approximate boost-rotation Killing vector that vanishes at $o$ and of the 3-volume of the ball of radius $r$. In vacuum spacetimes the leading term is of order $r^6$, and the factor of proportionality is the contraction of the Bel-Robinson tensor and an other average of the same approximate boost-rotation Killing vector.Comment: 16 pages, Plain Te

Positive Mass Theorem for Black Holes in Einstein-Maxwell Axion-dilaton Gravity

We presented the proof of the positive mass theorem for black holes in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. We show that the total mass of a spacetime containing a black hole is greater or equal to the square root of the sum of squares of the adequate dilaton-electric and dilaton-axion charges.Comment: latex file, to appear in Classical Quantum Gravit

Two dimensional Sen connections and quasi-local energy-momentum

The recently constructed two dimensional Sen connection is applied in the problem of quasi-local energy-momentum in general relativity. First it is shown that, because of one of the two 2 dimensional Sen--Witten identities, Penrose's quasi-local charge integral can be expressed as a Nester--Witten integral.Then, to find the appropriate spinor propagation laws to the Nester--Witten integral, all the possible first order linear differential operators that can be constructed only from the irreducible chiral parts of the Sen operator alone are determined and examined. It is only the holomorphy or anti-holomorphy operator that can define acceptable propagation laws. The 2 dimensional Sen connection thus naturally defines a quasi-local energy-momentum, which is precisely that of Dougan and Mason. Then provided the dominant energy condition holds and the 2-sphere S is convex we show that the next statements are equivalent: i. the quasi-local mass (energy-momentum) associated with S is zero; ii.the Cauchy development $D(\Sigma)$ is a pp-wave geometry with pure radiation ($D(\Sigma)$ is flat), where $\Sigma$ is a spacelike hypersurface whose boundary is S; iii. there exist a Sen--constant spinor field (two spinor fields) on S. Thus the pp-wave Cauchy developments can be characterized by the geometry of a two rather than a three dimensional submanifold.Comment: 20 pages, Plain Tex, I

Quasi-Local Gravitational Energy

A dynamically preferred quasi-local definition of gravitational energy is given in terms of the Hamiltonian of a `2+2' formulation of general relativity. The energy is well-defined for any compact orientable spatial 2-surface, and depends on the fundamental forms only. The energy is zero for any surface in flat spacetime, and reduces to the Hawking mass in the absence of shear and twist. For asymptotically flat spacetimes, the energy tends to the Bondi mass at null infinity and the \ADM mass at spatial infinity, taking the limit along a foliation parametrised by area radius. The energy is calculated for the Schwarzschild, Reissner-Nordstr\"om and Robertson-Walker solutions, and for plane waves and colliding plane waves. Energy inequalities are discussed, and for static black holes the irreducible mass is obtained on the horizon. Criteria for an adequate definition of quasi-local energy are discussed.Comment: 16 page

COVID-19 information disorder:six types of harmful information during the pandemic in Europe

{Sten Hansson and Kati Orru and Sten Torpan and Asta Bäck and Austeja Kazemekaityte and Sunniva Frislid Meyer and Johanna Ludvigsen and Lucia Savadori and Alessandro Galvagni and Ala Pigrée}, {COVID-19 information disorder: six types of harmful information during the pandemic in Europe}, {Journal of Risk Research}, {24}, {3-4}, {380-393}, {2021}, {Routledge}, {10.1080/13669877.2020.1871058}, { https://doi.org/10.1080/13669877.2020.1871058}The outbreak of a novel coronavirus disease COVID-19 propelled the creation, transmission, and consumption of false information – unverified claims, misleading statements, false rumours, conspiracy theories, and so on – all around the world. When various official or unofficial sources issue erroneous, misleading or contradicting information during a crisis, people who are exposed to this may behave in ways that cause harm to the health and well-being of themselves or others, e.g., by not taking appropriate risk reducing measures or blaming or harassing vulnerable groups. To work towards a typology of informational content that may increase people’s vulnerability in the context of the coronavirus pandemic, we explored 98 instances of potentially harmful information that spread in six European countries – France, Italy, Norway, Finland, Lithuania, and Estonia – between March and May 2020. We suggest that during the pandemic, exposure to harmful information may have made people more vulnerable in six ways: (1) by discouraging appropriate protective actions against catching/spreading the virus, (2) by promoting the use of false (or harmful) remedies against the virus, (3) by misrepresenting the transmission mechanisms of the virus, (4) by downplaying the risks related to the pandemic, (5) by tricking people into buying fake protection against the virus or into revealing their confidential information, and (6) by victimising the alleged spreaders of the virus by harassment/hate speech. The proposed typology can be used to guide the development of risk communication plans to address each of these information-related vulnerabilities.publishedVersio

Two dimensional Sen connections in general relativity

The two dimensional version of the Sen connection for spinors and tensors on spacelike 2-surfaces is constructed. A complex metric $\gamma_{AB}$ on the spin spaces is found which characterizes both the algebraic and extrinsic geometrical properties of the 2-surface $\$$. The curvature of the two dimensional Sen operator $\Delta_e$ is the pull back to $\$$ of the anti-self-dual part of the spacetime curvature while its `torsion' is a boost gauge invariant expression of the extrinsic curvatures of $\$$. The difference of the 2 dimensional Sen and the induced spin connections is the anti-self-dual part of the `torsion'. The irreducible parts of $\Delta_e$ are shown to be the familiar 2-surface twistor and the Weyl--Sen--Witten operators. Two Sen--Witten type identities are derived, the first is an identity between the 2 dimensional twistor and the Weyl--Sen--Witten operators and the integrand of Penrose's charge integral, while the second contains the `torsion' as well. For spinor fields satisfying the 2-surface twistor equation the first reduces to Tod's formula for the kinematical twistor.Comment: 14 pages, Plain Tex, no report numbe

On global properties of passivity-based control of an inverted pendulum,”

SUMMARY The paper adresses the problem of stabilization of a speci"c target position of underactuated Lagrangian or Hamiltonian systems. We propose to solve the problem in two steps: "rst to stabilize a set with the target position being a limit point for all trajectories originating in this set and then to switch to a locally stabilizing controller. We illustrate this approach by the well-known example of inverted pendulum on a cart. Particularly, we design a controller which makes the upright position of the pendulum and zero displacement of the cart a limit point for almost all trajectories. We derive a family of static feedbacks such that any solution of the closed loop system except for those originating on some two-dimensional manifold approaches an arbitrarily small neighbourhood of the target position. The proposed technique is based on the passivity properties of the inverted pendulum. A possible extension to a more general class of underactuated mechanical systems is discussed

Lagrangian and Hamiltonian for the Bondi-Sachs metrics

We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the Einstein vacuum equations in a closed form. Following the Dirac approach to constrained systems we investigate the related Hamiltonian formulation.Comment: 8 page