Energy of Isolated Systems at Retarded Times as the Null Limit of Quasilocal Energy

We define the energy of a perfectly isolated system at a given retarded time as the suitable null limit of the quasilocal energy $E$. The result coincides with the Bondi-Sachs mass. Our $E$ is the lapse-unity shift-zero boundary value of the gravitational Hamiltonian appropriate for the partial system $\Sigma$ contained within a finite topologically spherical boundary $B = \partial \Sigma$. Moreover, we show that with an arbitrary lapse and zero shift the same null limit of the Hamiltonian defines a physically meaningful element in the space dual to supertranslations. This result is specialized to yield an expression for the full Bondi-Sachs four-momentum in terms of Hamiltonian values.Comment: REVTEX, 16 pages, 1 figur

Chronology Protection and Non-Naked Singularity

We test the chronology protection conjecture in classical general relativity by investigating finitely vicious space-times. First we present singularity theorems in finitely vicious space-times by imposing some restrictions on the chronology violating sets. In the theorems we can refer to the location of an occurring singularity and do not assume any asymptotic conditions such as the existence of null infinities. Further introducing the concept of a non-naked singularity, we show that a restricted class of chronology violations cannot arise if all occurring singularities are the non-naked singularities. Our results suggest that the causal feature of the occurring singularities is the key to prevent the appearance of causality violation.Comment: 17 pages including 3 eps figures. Accepted for publication in Classical and 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

Angular momentum and an invariant quasilocal energy in general relativity

Owing to its transformation property under local boosts, the Brown-York quasilocal energy surface density is the analogue of E in the special relativity formula: E^2-p^2=m^2. In this paper I will motivate the general relativistic version of this formula, and thereby arrive at a geometrically natural definition of an `invariant quasilocal energy', or IQE. In analogy with the invariant mass m, the IQE is invariant under local boosts of the set of observers on a given two-surface S in spacetime. A reference energy subtraction procedure is required, but in contrast to the Brown-York procedure, S is isometrically embedded into a four-dimensional reference spacetime. This virtually eliminates the embeddability problem inherent in the use of a three-dimensional reference space, but introduces a new one: such embeddings are not unique, leading to an ambiguity in the reference IQE. However, in this codimension-two setting there are two curvatures associated with S: the curvatures of its tangent and normal bundles. Taking advantage of this fact, I will suggest a possible way to resolve the embedding ambiguity, which at the same time will be seen to incorporate angular momentum into the energy at the quasilocal level. I will analyze the IQE in the following cases: both the spatial and future null infinity limits of a large sphere in asymptotically flat spacetimes; a small sphere shrinking toward a point along either spatial or null directions; and finally, in asymptotically anti-de Sitter spacetimes. The last case reveals a striking similarity between the reference IQE and a certain counterterm energy recently proposed in the context of the conjectured AdS/CFT correspondence.Comment: 54 pages LaTeX, no figures, includes brief summary of results, submitted to Physical Review

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

Antigen-specific B-cell receptor sensitizes B cells to infection by influenza virus

Influenza A virus-specific B lymphocytes and the antibodies they produce protect against infection. However, the outcome of interactions between an influenza haemagglutinin-specific B cell via its receptor (BCR) and virus is unclear. Through somatic cell nuclear transfer we generated mice that harbour B cells with a BCR specific for the haemagglutinin of influenza A/WSN/33 virus (FluBI mice). Their B cells secrete an immunoglobulin gamma 2b that neutralizes infectious virus. Whereas B cells from FluBI and control mice bind equivalent amounts of virus through interaction of haemagglutinin with surface-disposed sialic acids, the A/WSN/33 virus infects only the haemagglutinin-specific B cells. Mere binding of virus is not sufficient for infection of B cells: this requires interactions of the BCR with haemagglutinin, causing both disruption of antibody secretion and FluBI B-cell death within 18 h. In mice infected with A/WSN/33, lung-resident FluBI B cells are infected by the virus, thus delaying the onset of protective antibody release into the lungs, whereas FluBI cells in the draining lymph node are not infected and proliferate. We propose that influenza targets and kills influenza-specific B cells in the lung, thus allowing the virus to gain purchase before the initiation of an effective adaptive response.National Institutes of Health (U.S.

Critical political economy, free movement and Brexit: Beyond the progressive’s dilemma

The progressive’s dilemma suggests that a trade-off exists between, on the one hand, labour and welfare rights underpinned by solidarity and shared identity and, on the other hand, open immigration regimes. With reference to debates on free movement in the UK, it is argued: (1) that a progressive European critical political economy literature of the Left has a tendency to accept this dilemma and resolve it in favour of a the former; (2) that it does so because it erroneously conflates the free movement of people with the (increasingly neoliberal) free movement of goods, capital and services; and (3) that it could and should treat human mobility as qualitatively different and, consequently, need not accept the terms of the progressive’s dilemma. The argument has important implications for a progressive politics in general and for the Left’s (particularly the Labour Party’s) position in the UK on free movement (and, by extension, on Brexit)

Gravitational Energy in Spherical Symmetry

Various properties of the Misner-Sharp spherically symmetric gravitational energy E are established or reviewed. In the Newtonian limit of a perfect fluid, E yields the Newtonian mass to leading order and the Newtonian kinetic and potential energy to the next order. For test particles, the corresponding Hajicek energy is conserved and has the behaviour appropriate to energy in the Newtonian and special-relativistic limits. In the small-sphere limit, the leading term in E is the product of volume and the energy density of the matter. In vacuo, E reduces to the Schwarzschild energy. At null and spatial infinity, E reduces to the Bondi-Sachs and Arnowitt-Deser-Misner energies respectively. The conserved Kodama current has charge E. A sphere is trapped if E>r/2, marginal if E=r/2 and untrapped if E<r/2, where r is the areal radius. A central singularity is spatial and trapped if E>0, and temporal and untrapped if E<0. On an untrapped sphere, E is non-decreasing in any outgoing spatial or null direction, assuming the dominant energy condition. It follows that E>=0 on an untrapped spatial hypersurface with regular centre, and E>=r_0/2 on an untrapped spatial hypersurface bounded at the inward end by a marginal sphere of radius r_0. All these inequalities extend to the asymptotic energies, recovering the Bondi-Sachs energy loss and the positivity of the asymptotic energies, as well as proving the conjectured Penrose inequality for black or white holes. Implications for the cosmic censorship hypothesis and for general definitions of gravitational energy are discussed.Comment: 23 pages. Belatedly replaced with substantially extended published versio

Meson-exchange Model for πN\pi N scattering and γN−>πN\gamma N -> \pi N reaction

An effective Hamiltonian consisting of bare $\Delta \leftrightarrow\pi N$, $\gamma N$ vertex interactions and energy-independent meson-exchange $\pi N \leftrightarrow \pi N, \gamma N$ transition operators is derived by applying a unitary transformation to a model Lagrangian with $N,\Delta,\pi$, $\rho$, $\omega$, and $\gamma$ fields. With appropraite phenomenological form factors and coupling constants for $\rho$ and $\Delta$, the model can give a good description of $\pi N$ scattering phase shifts up to the $\Delta$ excitation energy region. It is shown that the best reproduction of the recent LEGS data of the photon-asymmetry ratios in $\gamma p \rightarrow \pi ^0 p$ reactions provides rather restricted constraints on the coupling strengths $G_E$ of the electric $E2$ and $G_M$ of the magnetic $M1$ transitions of the bare $\Delta \leftrightarrow \gamma N$ vertex and the less well-determined coupling constant $g_{\omega NN}$ of $\omega$ meson. Within the ranges that $G_M = 1.9 \pm 0.05$, $G_E = 0.0 \pm 0.025$, and $7 \leq g_{\omega NN}\leq 10.5$, the predicted differential cross sections and photon-asymmetry ratios are in an overall good agreement with the data of $\gamma p \rightarrow \pi ^0 p$, $\gamma p \rightarrow \pi ^+ n$, and $\gamma n\rightarrow \pi ^- p$ reactions from 180 MeV to the $\Delta$ excitation region. The predicted $M_{1^+}$ and $E_{1^+}$ multipole amplitudes are also in good agreement with the empirical values determined by the amplitude analyses. The constructed effective Hamiltonian is free of the nucleon renormlization problem and hence is suitable for nuclear many-body calculations. We have also shown that the assumptions made in the $K$-matrix method, commonly used in extracting empirically the $\gamma N \rightarrow \Delta$ transition amplitudes from the data, are consistent withComment: 49 pages + 23 Figures, Revte