The Effects of Stress Tensor Fluctuations upon Focusing

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources. We give explicit results for the case of a scalar field on a flat background in a thermal state.Comment: 26 pages, 1 figure, new material added in Sect. III and in Appendices B and

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

VAR (video-assistant-referee) as Neo-Colonialism? Reading the FIFA 2018 Mens World Cup YouTube Video Comments

The 2018 FIFA Mens World Cup saw the introduction of video-assistant-referee (VAR) as one of its main talking points. For the first time officials had the assistance of replays and VARs to support decisions. Nevertheless, the introduction of VAR was not without controversies. To understand how fans experienced VAR we employed a digital sociological approach (Marres, 2017) by focusing on one loosely defined community (FIFA’s Official YouTube channel), and used digital tools (Rieder, 2015) to scrap users’ comments. We scrapped over 300,000 comments from 31 videos that were analysed through CDA (Chouliaraki & Fairclough, 1999). Three main categories emerged: Global North vs Global South; Non-Neutrality of Technology; VAR is Killing the Beautiful Game. In this paper our analysis focus on the first category - using the remaining two as support - to argue that VAR was comprehended as a tool for neo-colonialism. Fans recognised VAR as: favouring loosely defined Global North sides; improving Global North sides’ chances; controlling Global South players’ actions. We argue that VAR operated as a panopticon (Foucault, 1985) that rationalised/standardised the ways of playing (Mignolo, 1999; Santos, 2014) following an Eurocentric interpretation of the rules. Our findings highlight the paradoxes of technology, where VAR operated as a tool for systemic control and YouTube acted as a site for anti-systemic movements (Bragança & Wallerstein, 1982) that allowed for transnational networks of hope (Castells, 2012). We conclude by showing the reflexive nature of borders (Beck, 2004) where boundaries, barriers and belongings become more transient and fluid

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

Trapped surfaces and the Penrose inequality in spherically symmetric geometries

We demonstrate that the Penrose inequality is valid for spherically symmetric geometries even when the horizon is immersed in matter. The matter field need not be at rest. The only restriction is that the source satisfies the weak energy condition outside the horizon. No restrictions are placed on the matter inside the horizon. The proof of the Penrose inequality gives a new necessary condition for the formation of trapped surfaces. This formulation can also be adapted to give a sufficient condition. We show that a modification of the Penrose inequality proposed by Gibbons for charged black holes can be broken in early stages of gravitational collapse. This investigation is based exclusively on the initial data formulation of General Relativity.Comment: plain te

Between global events and local reverberations: Globalization, local media framing and the 2014 FIFA World Cup

This article advances sociological work on globalization processes. It concerns itself with conceptualizations of how the local and global ‘clash’, utilizing Ulrich Beck's work on globalization, cosmopolitanism and power. By employing Brazil's 2014 Fédération Internationale de Football Association (FIFA) men's World Cup as a case, this article seeks to build on Beck's theorizations, into the field of football; using the General Law of the World Cup as a symbolic representation for the global/local, interest‐driven interactions between Brazil and FIFA. In particular, this article is concerned with how FIFA's requirements, standards and norms, as imposed on the host nation, were framed within local media and journalistic discourses. The article extends Beck's insights by problematizing how global demands meet local socio‐spatial, legal and cultural contexts and how these demands, seeking to regulate and secure consumption, are resisted by various domestic and localized actors situated within a power game

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 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

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

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