Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e⁺e^-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω_H where m is an integer and Ω_H is the hole's angular velocity.

Gauge Invariant Spectral Cauchy Characteristic Extraction of Gravitational Waves in Computational General Relativity

We present a complete system for Spectral Cauchy characteristic extraction (Spectral CCE). Implemented in C++ within the Spectral Einstein Code (SpEC), the method employs numerous innovative algorithms to efficiently calculate the Bondi strain, news, and flux.

Spectral CCE was envisioned to ensure physically accurate gravitational wave-forms computed for the Laser Interferometer Gravitational wave Observatory (LIGO) and similar experiments, while working toward a template bank with more than a thousand waveforms to span the binary black hole (BBH) problem’s seven-dimensional parameter space.

The Bondi strain, news, and flux are physical quantities central to efforts to understand and detect astrophysical gravitational wave sources within the Simulations of eXtreme Spacetime (SXS) collaboration, with the ultimate aim of providing the first strong field probe of the Einstein field equation.

In a series of included papers, we demonstrate stability, convergence, and gauge invariance. We also demonstrate agreement between Spectral CCE and the legacy Pitt null code, while achieving a factor of 200 improvement in computational efficiency.

Spectral CCE represents a significant computational advance. It is the foundation upon which further capability will be built, specifically enabling the complete calculation of junk-free, gauge-free, and physically valid waveform data on the fly within SpEC.

Pain relativity in motor control.

Motivational theories of pain highlight its role in people's choices of actions that avoid bodily damage. By contrast, little is known regarding how pain influences action implementation. To explore this less-understood area, we conducted a study in which participants had to rapidly point to a target area to win money while avoiding an overlapping penalty area that would cause pain in their contralateral hand. We found that pain intensity and target-penalty proximity repelled participants' movement away from pain and that motor execution was influenced not by absolute pain magnitudes but by relative pain differences. Our results indicate that the magnitude and probability of pain have a precise role in guiding motor control and that representations of pain that guide action are, at least in part, relative rather than absolute. Additionally, our study shows that the implicit monetary valuation of pain, like many explicit valuations (e.g., patients' use of rating scales in medical contexts), is unstable, a finding that has implications for pain treatment in clinical contexts.

Axial symmetry and transverse trace-free tensors in numerical relativity

Transverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.

Why does relativity allow quantum tunnelling to 'take no time'?

In quantum tunnelling, what appears to be an infinitely fast barrier traversal can be explained in terms of an Aharonov-like weak measurement of the tunnelling time, in which the role of the pointer is played by the particle's own coordinate. A relativistic wave packet is shown to be reshaped through a series of subluminal shifts which together produce an anomalous 'superluminal' result.

Relativity and screening effects in heavy-ion collisions

Diatomic correlation diagrams are the main basis for the description of heavy-ion collisions. We have constructed the first realistic relativistic many-electron correlation diagrams based on nonrelativistic self-consistent-field, Hartree-Fock calculations of diatomic molecules plus relativistic corrections. We discuss the relativistic influences as well as the many-electron screening effects in the I-Au system with a combined charge of Z = 132 as an example.

Linguistic relativity in foreign language teaching : a didactic proposal. 'Relatividad linguística en la enseñanza de lenguas extranjeras'.

Resumen de la revista

The Bruton tenancy: a matter of relativity

Argues that the controversial "Bruton tenancies" created by the House of Lords decision in Bruton v London & Quadrant Housing Trust should be seen as a form of proprietary tenancy. Discusses the view that those without an estate in land are prevented by the nemo dat principle from granting a lease, the scope for tenancies derived from equitable interests, and the challenges to Bruton tenancies posed by the Court of Appeal ruling in Milmo v Carreras. Explains how Bruton tenancies create a circumscribed proprietary interest in land, best understood through the concept of relativity of title.

Thinking for speaking and linguistic relativity among bilinguals: towards a new research agenda

This article evaluates how the different papers in this special issue fill a gap in our understanding of cognitive processes that are being activated when second language learners or bilinguals prepare to speak. All papers are framed in Slobin’s (1987) Thinking for Speaking theory, and aim to test whether the conceptualisation patterns that were learned in early childhood can be relearned or restructured in L2 acquisition. In many papers the focus is on identifying constraints on this restructuring process. Among these constraints, the role of typological differences between languages is investigated in great depth. The studies involve different types of learners, language combinations and tasks. As all informants were given verbal rather than non-verbal tasks, the focus is here on the effects of conceptual transfer from one language on another, and not on the effects of language on non-linguistic cognition. The paper also sketches different avenues for further research in this field and proposes that researchers working in this field might want to take up the challenge of investigating whether speakers of different languages perceive motion outside explicitly verbal contexts differently, as this will enable us to gain an understanding of linguistic relativity effects in this domain. Studying which teaching methods can help learners to restructure their conceptualisation patterns may also shed new light on the aspects of discourse organization and motion event construal that are most difficult for learners.

Linguistic relativity in SLA: towards a new research programme

The purpose of the current article is to support the investigation of linguistic relativity in second language acquisition and sketch methodological and theoretical prerequisites toward developing the domain into a full research program. We identify and discuss three theoretical-methodological components that we believe are needed to succeed in this enterprise. First, we highlight the importance of using nonverbal methods to study linguistic relativity effects in second language (L2) speakers. The use of nonverbal tasks is necessary in order to avoid the circularity that arises when inferences about nonverbal behavior are made on the basis of verbal evidence alone. Second, we identify and delineate the likely cognitive mechanisms underpinning cognitive restructuring in L2 speakers by introducing the theoretical framework of associative learning. By doing so, we demonstrate that the extent and nature of cognitive restructuring in L2 speakers is essentially a function of variation in individual learners’ trajectories. Third, we offer an in-depth discussion of the factors (e.g., L2 proficiency and L2 use) that characterize those trajectories, anchoring them to the framework of associative learning, and reinterpreting their relative strength in predicting L2 speaker cognition

de Sitter special relativity

A special relativity based on the de Sitter group is introduced, which is a theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary special relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincare group, this theory turns out to be a specific kind of deformed (or doubly) special relativity. Some experimental consequences, as well as the causal structure of spacetime-modified by the presence of the de Sitter horizon-are briefly discussed.

Gravitational deflection of massive particles in classical and semiclassical general relativity

We calculate the gravitational deflection of massive particles moving with relativistic velocity in the solar system to second post-Newtonian order. For a particle passing close to the Sun with impact parameter b, the deflection in classical general relativity is Phi(C)[GRAPHICS]where v(0) is the particle speed at infinity and M is the Sun's mass. We compute afterwards the gravitational deflection of a spinless neutral particle of mass m in the same static gravitational field as above, treated now as an external field. For a scalar boson with energy E, the deflection in semiclassical general relativity (SGR) is Phisc[GRAPHICS]This result shows that the propagation of the =2E spinless massive boson produces inexorably dispersive effects. It also shows that the semiclassical prediction is always greater than the geometrical one, no matter what the boson mass is. In addition, it is found that SGR predicts a deflection angle of similar to2.6 arcsec for a nonrelativistic spinless massive boson passing at the Sun's limb.

De Sitter Special Relativity: Effects on cosmology

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)