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

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

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

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

Safety and Security Battles: Unpacking the Players and Arenas of the Safe Standing movement in English Football (1989-2022)

This article advances recent debates on social movement (relational) fields, outcomes, and successes by suggesting that the analysis of such fields as a whole must be temporal. The relational interpersonal and intersubjective choices made by interdependent actors in social life take place in fields of interaction, but these interactions and their networks of social relations have a history. Hence, the social movement field is characterised by multiple temporal periods through which the actions of activists both shape and are shaped by the long-term socio-political environments in which they are embedded. To develop this analysis, we identify a football supporter-movement in England, ‘Safe Standing’, revealing the complex interplay of cultural and technological patterns of interaction across the compelling timeframes and orientations of a 30-year movement field. Adopting a theoretical framework which synthesises research on the strategic interactions of movement ‘players’ and ‘arenas’, and sport-focused security fields, we identify a series of compound and sub-players across the political, symbolic, mediatised, technological, and legislative arenas which constitute the security field of contention, in what is an under-researched lifeworld in sociology

Measurements of linewidth variations within external-cavitymodes of a gratingcavity laser

Abstract Linewidth variations within an external-cavity mode of a grating-cavity laser were measured with high accuracy using the self-homodyne technique with a short delay line. To our knowledge, this is the first time that these variations have been accurately measured. In our laser, we observed the linewidth to change by a factor of five from 30 kHz to more than 150 kHz when the laser was tuned over a single external-cavity mode. A simple model based on a linear relationship between the chirp reduction factor and the frequency tuning of the laser is used to describe the results.