arXiv subjects

Kjell Rosquist

Publications and source records attributed to Kjell Rosquist.

At least 19 recordsLinked to original sources

arXiv2025

Cosmologies with a magnetic field, dust, and Lambda

We investigate exact solutions of the Einstein-Maxwell equations with the cosmological constant where the source of the gravitational field consists of a magnetic field and dust. In particular, we restrict our study to the case of Bianchi type III models. All these solutions either start with a singularity and then expand, or they are initially collapsing and end at a singularity. We discuss the physical meaning of the parameters appearing in the metrics and examine the possible subcases and the relative importance of the dust and the magnetic field as we approach the singularity.

gr-qc↗

arXiv2024

Interacting Kerr-Newman Electromagnetic Fields

In this paper, we study some of the properties of the $G \to 0$ limit of the Kerr-Newman solution of Einstein-Maxwell equations. Noting Carter's observation of the near equality between the $g = 2$ gyromagnetic ratio in the Kerr-Newman solution and that of the electron, we discuss additional such coincidences relating to the Kerr-Newman multipoles and properties of the electron. In contrast to the Coulomb field, this spinning Maxwell field has a finite Lagrangian. Moreover, by evaluating the Lagrangian for the superposition of two such Kerr-Newman electromagnetic fields on a flat background, we are able to find their interaction potential. This yields a correction to the Coulomb interaction due to the spin of the field.

gr-qc↗

arXiv2021

Helicity, Spin, and Infra-zilch of Light: a Lorentz Covariant Formulation

In this paper, a novel conserved Lorentz covariant tensor, termed the helicity tensor, is introduced in Maxwell theory. The conservation of the helicity tensor expresses the conservation laws contained in the helicity array, introduced by Cameron et al., including helicity, spin, and the spin-flux or infra-zilch. The Lorentz covariance of the helicity tensor is in contrast to previous formulations of the helicity hierarchy of conservation laws, which required the non-Lorentz covariant transverse gauge. The helicity tensor is shown to arise as a Noether current for a variational symmetry of a duality-symmetric Lagrangian for Maxwell theory. This symmetry transformation generalizes the duality symmetry and includes the symmetry underlying the conservation of the spin part of the angular momentum.

physics.optics↗

arXiv2021

The Zilch Electromagnetic Conservation Law Revisited

It is shown that the zilch conservation law arises as the Noether current corresponding to a variational symmetry of a duality-symmetric Maxwell Lagrangian. The action of the corresponding symmetry generator on the duality-symmetric Lagrangian, while non-vanishing, is a total divergence as required by the Noether theory. The variational nature of the zilch conservation law was previously known only for some of the components of the zilch tensor, notably the optical chirality. By contrast, our analysis is fully covariant and is therefore valid for all components of the zilch tensor. The analysis is presented here for both real and complex versions of duality-symmetric Maxwell Lagrangians.

math-ph↗

arXiv2021

Spinning Particles in Twisted Gravitational Wave Spacetimes

Twisted gravitational waves (TGWs) are nonplanar waves with twisted rays that move along a fixed direction in space. We study further the physical characteristics of a recent class of Ricci-flat solutions of general relativity representing TGWs with wave fronts that have negative Gaussian curvature. In particular, we investigate the influence of TGWs on the polarization of test electromagnetic waves and on the motion of classical spinning test particles in such radiation fields. To distinguish the polarization effects of twisted waves from plane waves, we examine the theoretical possibility of existence of spin-twist coupling and show that this interaction is generally consistent with our results.

gr-qc↗

arXiv2021

Observational backreaction in discrete black holes lattice cosmological models

Applying the Sachs formalism, the optical properties encoded in the distance modulus are studied along curves exhibiting local rotational symmetry for some closed inhomogeneous cosmological models whose mass content is discretized by Schwarzschild-like sources. These models may challenge the concordance model in its use of the distance modulus data of type Ia supernovae, because they do not violate any energy condition. This result relies only on the symmetry properties considered, and not on the way in which the mass is discretized. The models with different number of sources are then compared among themselves and with a Friedmann-Lemaitre-Robertson-Walker model with the same total mass content by introducing a compactness parameter. The analysis shows that observational backreaction occurs because increasing the number of sources the features of a universe with a continuous matter distribution are not recovered. Our models are shown to exhibit a non-trivial relationship between kinematical, dynamical and observational backreactions, the kinematical one being asymptotically decreasing while the latter two are present. Furthermore, the electric part of the Weyl tensor contributes to the luminosity distance by affecting the evolution of the scale factor, while the magnetic part has an indirect role by affecting only the evolution of the former

gr-qc↗

arXiv2018

Twisted Gravitational Waves of Petrov Type D

Twisted gravitational waves (TGWs) are nonplanar unidirectional Ricci-flat solutions of general relativity. Thus far only TGWs of Petrov type \emph{II} are implicitly known that depend on a solution of a partial differential equation and have wave fronts with negative Gaussian curvature. A special Petrov type \emph{D} class of such solutions that depends on an arbitrary function is explicitly studied in this paper and its Killing vectors are worked out. Moreover, we concentrate on two solutions of this class, namely, the Harrison solution and a simpler solution we call the $w$-metric and determine their Penrose plane-wave limits. The corresponding transition from a nonplanar TGW to a plane gravitational wave is elucidated.

gr-qc↗

arXiv2018

Analytic Analysis of Irregular Discrete Universes

In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight identical cells, each having a single edge which is shared by all cells. The shared edge is enforced to be locally rotationally symmetric (LRS), thereby allowing for solving the dynamics to high accuracy along this edge. Each cell will then carry an identical (up to parity) configuration which can however have an arbitrarily random distribution. The dynamics of such models is compared to that of previous works on regularly distributed black holes as well as with the standard isotropic dust models of the FLRW type. The irregular models are shown to have richer dynamics than that of the regular models. The randomization of the distribution of the black holes is done both without bias and also with a certain clustering bias. The geometry of the initial configuration of our models is shown to be qualitatively different from the regular case in the way it approaches the isotropic model

gr-qc↗

arXiv2018

Black-Hole Lattices as Cosmological Models

The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a specific subclass of discrete cosmologies, Black-Hole Lattice models. In particular, we illustrate the techniques used for the construction of these spacetimes, and examine their resulting physical properties. This includes their large-scale dynamics, the dressing of mass due to the interaction between individual black holes, along with features of direct observational interest such as the distance-to-redshift relation. This collection of results provides a novel perspective on the physical effects of averaging in General Relativity, as well as on the emergence of gravitational structures from solutions with isolated objects.

gr-qc↗

arXiv2017

The Magnetic Part of the Weyl Tensor, and the Expansion of Discrete Universes

We examine the effect that the magnetic part of the Weyl tensor has on the large-scale expansion of space. This is done within the context of a class of cosmological models that contain regularly arranged discrete masses, rather than a continuous perfect fluid. The natural set of geodesic curves that one should use to consider the cosmological expansion of these models requires the existence of a non-zero magnetic part of the Weyl tensor. We include this object in the evolution equations of these models by performing a Taylor series expansion about a hypersurface where it initially vanishes. At the same cosmological time, measured as a fraction of the age of the universe, we find that the influence of the magnetic part of the Weyl tensor increases as the number of masses in the universe is increased. We also find that the influence of the magnetic part of the Weyl tensor increases with time, relative to the leading-order electric part, so that its contribution to the scale of the universe can reach values of ~1%, before the Taylor series approximation starts to break down.

gr-qc↗

arXiv2014

Piecewise Silence in Discrete Cosmological Models

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to consider the evolution of a number of geometrically distinguished surfaces that exist within each of them. We find that the evolution equations for the reflection symmetric surfaces can be written as a simple set of Friedmann-like equations, with source terms that behave like a set of interacting effective fluids. We then show that gravitational waves are effectively trapped within small chambers for all time, and are not free to propagate throughout the space-time. Each chamber therefore evolves as if it were in isolation from the rest of the universe. We call this phenomenon "piecewise silence".

gr-qc↗

arXiv2013

Exact Evolution of Discrete Relativistic Cosmological Models

We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions.

gr-qc↗

arXiv2013

An exact quantification of backreaction in relativistic cosmology

An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (<10) then the amount of backreaction in dust models can be large, with O(1) deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (>100), however, then our measures of backreaction become small (<1%). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of backreaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about backreaction that could be applied in more complicated and realistic settings.

gr-qc↗

arXiv2013

Variable jet properties in GRB110721A: Time resolved observations of the jet photosphere

{\it Fermi Gamma-ray Space Telescope} observations of GRB110721A have revealed two emission components from the relativistic jet: emission from the photosphere, peaking at $\sim 100$ keV and a non-thermal component, which peaks at $\sim 1000$ keV. We use the photospheric component to calculate the properties of the relativistic outflow. We find a strong evolution in the flow properties: the Lorentz factor decreases with time during the bursts from $Γ\sim 1000$ to $\sim 150$ (assuming a redshift $z=2$; the values are only weakly dependent on unknown efficiency parameters). Such a decrease is contrary to the expectations from the internal shocks and the isolated magnetar birth models. Moreover, the position of the flow nozzle measured from the central engine, $r_0$, increases by more than two orders of magnitude. Assuming a moderately magnetised outflow we estimate that $r_0$ varies from $10^6$ cm to $\sim 10^9$ cm during the burst. We suggest that the maximal value reflects the size of the progenitor core. Finally, we show that these jet properties naturally explain the observed broken power-law decay of the temperature which has been reported as a characteristic for GRB pulses.

astro-ph.HE↗

arXiv2009

Carter's constant revealed

A new formulation of Carter's constant for geodesic motion in Kerr black holes is given. It is shown that Carter's constant corresponds to the total angular momentum plus a precisely defined part which is quadratic in the linear momenta. The characterization is exact in the weak field limit obtained by letting the gravitational constant go to zero. It is suggested that the new form can be useful in current studies of the dynamics of extreme mass ratio inspiral (EMRI) systems emitting gravitational radiation.

gr-qc↗

arXiv2008

Configurational invariants of Hamiltonian systems

In this paper we explore the general conditions in order that a 2-dimensional natural Hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore Liouville integrable. We examine the possibility that the invariant is preserved by the Hamiltonian flow on a given energy hypersurface only (weak integrability) and derive the additional requirement necessary to have conservation at arbitrary energy (strong integrability). Using null complex coordinates, we show that the leading order coefficient of the polynomial is an arbitrary holomorphic function in the case of weak integrability and a polynomial in the coordinates in the strongly integrable one. We review the results obtained so far with strong invariants up to degree four and provide some new examples of weakly integrable systems with linear and quadratic invariants.

nlin.SI↗

arXiv2008

Invariants at fixed and arbitrary energy. A unified geometric approach

Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using Killing tensors we obtain an integrability condition for quadratic invariants which involves an arbitrary analytic function $S(z)$. For invariants at arbitrary energy the function $S(z)$ is a second degree polynomial with real second derivative. The integrability condition then reduces to Darboux's condition for quadratic invariants at arbitrary energy. The four types of classical quadratic invariants for positive definite 2-dimensional Hamiltonians are shown to correspond to certain conformal transformations. We derive the explicit relation between invariants in the physical and Jacobi time gauges. In this way knowledge about the invariant in the physical time gauge enables one to directly write down the components of the corresponding Killing tensor for the Jacobi metric. We also discuss the possibility of searching for linear and quadratic invariants at fixed energy and its connection to the problem of the third integral in galactic dynamics. In our approach linear and quadratic invariants at fixed energy can be found by solving a linear ordinary differential equation of the first or second degree respectively.

nlin.SI↗

arXiv2008

Some Consequences of Gravitationally Induced Electromagnetic Effects in Microphysics

We discuss the relation between the gravitational and electromagnetic fields as governed by the Einstein-Maxwell field equations. It is emphasized that the tendency of the gravitational field to induce electromagnetic effects increases as the size of the system goes down. In particular, the gravitational field, according to general relativity, tends to become dominated by the spin at distances of the order of the Compton wavelength. The relevant quantity which governs this behavior is the ratio S/M^2 where S is the (spin) angular momentum. For an electron, S/M^2 ~ 10^44. Therefore, gravitomagnetic effects will play a significant role in the subatomic domain. To analyze this situation we use the asymptotic structure in the form of the multipole fields. Some important consequences for the electromagnetic fields of charged particles with spin are pointed out. In particular, the gravitational field may induce corrections to the Coulomb field which can be tested experimentally.

gr-qc↗