Relativistic Systems Research Articles

A novel gravitational lensing feature by wormholes

Horizonless compact objects with light rings (or photon spheres) are becoming increasingly popular in recent years for several reasons. In this paper, we show that a horizonless object such as a wormhole of Morris–Thorne type can have two photon spheres. In particular, we show that, in addition to the one present outside a wormhole throat, the throat can itself act as an effective photon sphere. Such wormholes exhibit two sets of relativistic Einstein ring systems formed due to strong gravitational lensing. We consider a previously obtained wormhole solution as a specific example. If such type of wormhole casts a shadow at all, then the inner set of the relativistic Einstein rings will form the outer bright edge of the shadow. Such a novel lensing feature might serve as a distinguishing feature between wormholes and other celestial objects as far as gravitational lensing is concerned.

Relativistic motion of an Airy wave packet in a lattice potential

We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its velocity, and so the acceleration cannot continue indefinitely. Instead, we show that the wavepacket's motion is described by relativistic equations of motion, which surprisingly, arise naturally from evolution under the standard non-relativistic Schr\"odinger equation. The presence of the lattice potential allows the wavepacket's motion to be controlled by means of Floquet engineering. In particular, in the deep relativistic limit when the wavepacket's motion is photon-like, this form of control allows it to mimic both standard and negative refraction. Airy wavepackets held in lattice potentials can thus be used as powerful and flexible simulators of relativistic quantum systems.

Relativistic nonlinear whistler waves in cold magnetized plasmas

Starting from the Vlasov-Maxwell equations describing the dynamics of various species in a quasi-neutral plasma immersed in an external solenoidal magnetic field and utilizing a technique known as the hydrodynamic substitution, a relativistic hydrodynamic system of equations governing the dynamics of various species has been obtained. Based on the method of multiple scales, a system comprising three nonlinear Schrodinger equation for the transverse envelopes of the three basic whistler modes, has been derived. Using the method of formal series of Dubois-Violette, a traveling wave solution of the derived set of coupled nonlinear Schrodinger equations in both the relativistic and the non relativistic case has been obtained. An intriguing feature of our description is that whistler waves do not perturb the initial uniform density of plasma electrons. The plasma response to the induced whistler waves consists in transverse velocity redistribution, which follows exactly the behaviour of the electromagnetic whistlers. This property may have an important application for transverse focusing of charged particle beams in future laser plasma accelerators. Yet another interesting peculiarity are the selection rules governing the nonlinear mode coupling. According to these rules self coupling between modes in the non relativistic regime is absent, which is a direct consequence of the vector character of the interaction governed by the Lorentz force.

Anisotropic nonlinear optical response of phosphorene

The pseudorelativistic behaviour of carriers is found in the energy bands of certain class of two dimensional (2D) semi-conducting materials such as phosphorene. In this article, the nonlinear optical response of pseudorelativistic electrons in phosphorene under intense applied electromagnetic field is investigated. Using Floquet theory, we demonstrate the anisotropic behaviour of anomalous Rabi oscillations in phosphorene, which occurs far from the conventional resonance. The role of anisotropy on anomalous Rabi oscillations in phosphorene is also justified numerically. The Bloch-Siegert shift is observed under strong driving field that strongly depends on the anisotropy of the energy bands of phosphorene. A theoretical description of the pump-probe experiment is given to detect the anomalous Rabi oscillations in phosphorene. The differential transmission coefficient shows a sinusoidal behaviour as a function of pump pulse duration whose amplitude exhibits a power law decay, which is quite different from graphene (relativistic fermionic system). So the Floquet theory can be used to characterize the different fermionic systems.

Superintegrable relativistic systems in scalar background fields

We consider a relativistic charged particle in a background scalar field depending on both space and time. Poincaré, dilation and special conformal symmetries of the field generate conserved quantities in the charge motion, and we exploit this to generate examples of superintegrable relativistic systems. We also show that the corresponding single-particle wavefunctions needed for the quantum scattering problem can be found exactly, by solving the Klein–Gordon equation.

Temperatures of renormalizable quantum field theories in curved spacetime

In this paper we compute the temperature registered by an Unruh–DeWitt detector coupled to a Hadamard renormalizable quantum field in an arbitrary state, moving along an accelerated trajectory in a curved spacetime. For a massless and conformally invariant field, the generalized expression for the temperature is given by the quadratic sum of the 4-acceleration, Raychaudhuri scalar, and renormalized field polarization. We can further find a novel constraint on the renormalized quantum field polarization in relativistic systems that are in global thermal equilibrium.

Testing velocity-dependent CPT -violating gravitational forces with radio pulsars

In the spirit of effective field theory, the Standard-Model Extension (SME) provides a comprehensive framework to systematically probe the possibility of Lorentz/CPT violation. In the pure gravity sector, operators with mass dimension larger than 4, while in general being advantageous to short-range experiments, are hard to investigate with systems of astronomical size. However, there is exception if the leading-order effects are CPT-violating and velocity-dependent. Here we study the lowest-order operators in the pure gravity sector that violate the CPT symmetry with carefully chosen relativistic binary pulsar systems. Applying the existing analytical results to the dynamics of a binary orbit, we put constraints on various coefficients for Lorentz/CPT violation with mass dimension 5. These constraints, being derived from the post-Newtonian dynamics for the first time, are complementary to those obtained from the kinematics in the propagation of gravitational waves.

Generalized Electromagnetic Fields Associated with the Hydrogen-Like Atom Problem

Abstract It is known that the principle of minimal coupling in quantum mechanics determines a unique interaction form for a charged particle. By properly redefining the canonical commutation relation between (canonical) conjugate components of position and momentum of the particle, e.g. an electron, we restate the Dirac equation for the hydrogen-like atom problem incorporating a generalized minimal electromagnetic coupling. The corresponding interaction keeps the 1 / | q | $1/\left|\mathbf{q}\right|$ dependence in both the scalar potential V ( | q | ) $V\left({\left|\mathbf{q}\right|}\right)$ and the vector potential A ( q ) $\mathbf{A}\left(\mathbf{q}\right)$ ( | A ( q ) | ∼ 1 / | q | $\left|{\mathbf{A}\left(\mathbf{q}\right)}\right|\sim 1/\left|\mathbf{q}\right|$ ). This problem turns out to be exactly solvable; moreover, the eigenstates and eigenvalues can be obtained in an elementary fashion. Some feasible models within this approach are discussed. Then we make a few remarks about the breaking of supersymmetry. Finally, we briefly comment on the possible Lie algebra (dynamical symmetry algebra) of these relativistic quantum systems.

Classical Incompressible Fluid Dynamics as a Limit of Relativistic Compressible Fluid Dynamics

Properly scaled, the relativistic Euler system for an arbitrary isentropic, causally compressible fluid is shown to formally converge, as c → ∞, to the non-relativistic Euler system for the homogeneously incompressible fluid. The limit is particularly interesting in the case of the relativistic stiff fluid, for which all modes are linearly degenerate in the sense of the theory of hyperbolic systems of conservation laws. This case connects the continuation problem for regular solutions to the incompressible version of the classical Euler equations with the old conjecture that for hyperbolic systems linear degeneracy of all modes prevent gradient blowup. One could say that questions in two different areas of the theory of partial differential equations are linked to each other through Einstein’s theory of relativity.

Structure scalars of spherically symmetric dissipative fluids with f ( G , T ) $f(G,T)$ gravity

The aim of this study is to analyze the role of modification of gravity on some dynamical properties of spherically symmetric relativistic systems. In this settings, the mathematical modeling of scalar variables associated with the shearing viscous dissipative anisotropic spherical stars is explored. We assume that the non-static diagonally symmetric spherical structure is coupled with a relativistic matter content in the presence of $f(G,T)=\alpha G^{n}+\beta \ln [G]+\lambda T$ gravity. After using Misner–Sharp mass function, we have made correspondence between metric scale factors, tidal forces and structure parameters. We have adopted Herrera’s technique for the orthogonally breaking down of the Riemann tensor, in order to formulate modified forms of structure scalars. The role of these invariants is then explored in the evolutionary properties of radiating spheres. The parameters responsible for the outbreak of inhomogeneities are being examined in the presence and absence of constant $f(G,T)$ terms. It is inferred that the evolutionary phases of the spherical interiors can be well studied via extended versions of scalar variables.

Anomalous Behavior of the Terrestrial Electric Field Intensity at Multiple Frequencies of Relativistic Binary Star Systems

The vertical component of the terrestrial electric field intensity has been proven to be spectrally localized at multiple frequencies of forty-three relativistic binary star systems. The used four time series contain multiannual observations of the terrestrial electric field intensity in the infralow frequency range. The used method is eigenoscopy developed by the present authors. The matrix of second sample moments is computed at finite time spans. The eigenvectors of the moment matrix and their amplitude spectra are computed and analyzed. A database of the discovered anomalous behavior has been built.

Relativistic Measurement Backaction in the Quantum Dirac Oscillator.

An elegant method to circumvent quantum measurement backaction is the use of quantum mechanics free subsystems (QMFS), with one approach involving the use of two oscillators with effective masses of opposite signs. Since negative energies, and hence masses, are a characteristic of relativistic systems a natural question is to what extent QMFS can be realized in this context. Using the example of a one-dimensional Dirac oscillator we investigate conditions under which this can be achieved, and identify Zitterbewegung or virtual pair creation as the physical mechanism that fundamentally limits the feasibility of the scheme. We propose a tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction.

How a relativistic electron beam-ion channel system can act as a polarizer.

The polarization evolution of electromagnetic radiation propagating through an electron beam-ion channel system is studied in the presence of the coupling instability. Employing the system's dielectric tensor and the full four-component Stokes vector description, the obtained differential Mueller matrix is used to determine the polarization state of the initially polarized radiated wave at any arbitrary point in the system. It is shown that an unpolarized EM wave propagating through the electron beam-ion channel system will achieve a linearly polarization state aligned to the perpendicular self-magnetic field vector and propagation direction.

Looking for a new test of general relativity in the solar system

This paper discusses three matter-of-principle methods for measuring the general relativity correction to the Newtonian values of the position of collinear Lagrangian points L1 and L2 of the Sun–Earth-satellite system. All approaches are based on time measurements. The first approach exploits a pulsar emitting signals and two receiving antennas located at L1 and L2, respectively. The second method is based on a relativistic positioning system based on the Lagrangian points themselves. These first two methods depend crucially on the synchronization of clocks at L1 and L2. The third method combines a pulsar and an artificial emitter at the stable points L4 or L5 forming a basis for the positioning of the collinear points L1 and L2. Further possibilities are mentioned and the feasibility of the measurements is considered.

Conserved schemes with high pressure ratio, high particle density ratio and self-similar method

The paper proposes a numerical investigation for three conserved schemes when applied to the nonlinear ultra-relativistic Euler equations with an initial high pressure ratio and with an initial high particle density ratio. The results show that two of these schemes work efficiently and the third one may present inaccurate results even applied over a very delicate mesh. Several problems of the relativistic Euler system have self-similar solutions which can be solved by more efficient techniques. We also introduce a representation for self-similar ultra-relativistic Euler equations, which can be solved by the proposed schemes in this article and does not need to reconstruct schemes. Numerical tests are given for the one-dimensional shock tube problems to deal with the problem under consideration. These tests display that increasing the order of accuracy does not help much in upgrading the results. It is also indicated that one-dimensional results solved by self-similar ultra-relativistic Euler equations are almost identical to the exact solutions.

Rapid evolution of the relativistic jet system SS 433

Abstract. We analyzed a 40-year set of multicolor photometry and a 15-year set of synoptic monitoring of SS 433 along with fragmentary spectral and radio data. This system contains a neutron star and an A3–A7 I giant. The system is found to be either close, in contact, or it has a common envelope from time to time. The A-type giant is now in transition to the dynamical mass transfer.

Star clusters, self-interacting dark matter halos, and black hole cusps: The fluid conduction model and its extension to general relativity.

We adopt the fluid conduction approximation to study the evolution of spherical star clusters and self-interacting dark matter (SIDM) halos. We also explore the formation and dynamical impact of density cusps that arise in both systems due to the presence of a massive, central black hole. The large N-body, self-gravitating systems we treat are "weakly collisional": the mean free time between star or SIDM particle collisions is much longer than their characteristic crossing (dynamical) time scale, but shorter than the system lifetime. The fluid conduction model reliably tracks the "gravothermal catastrophe" in star clusters and SIDM halos without black holes. For a star cluster with a massive, central black hole, this approximation reproduces the familiar Bahcall-Wolf quasistatic density cusp for the stars bound to the black hole and shows how the cusp halts the "gravothermal catastrophe" and causes the cluster to re-expand. An SIDM halo with an initial black hole central density spike that matches onto to an exterior NFW profile relaxes to a core-halo structure with a central density cusp determined by the velocity dependence of the SIDM interaction cross section. The success and relative simplicity of the fluid conduction approach in evolving such "weakly collisional," quasiequilibrium Newtonian systems motivates its extension to relativistic systems. We present a general relativistic extension here.

Exploring Hyperon Structure with Electromagnetic Transverse Densities

We explore the structure of the spin-1/2 flavor-octet baryons (hyperons) through their electromagnetic transverse densities. The transverse densities describe the distribution of charge and magnetization at fixed light-front time and enable a spatial representation of the baryons as relativistic systems. At peripheral distances $$b \sim 1/M_\pi $$ the transverse densities are computed using a new method that combines chiral effective field theory ( $$\chi $$ EFT) and dispersion analysis. The peripheral isovector densities arise from two-pion exchange, which includes the $$\rho $$ resonance through elastic unitarity. The isoscalar densities are estimated from vector meson exchange ( $$\omega , \phi )$$ . We find that the “pion cloud” in the charged $$\varSigma $$ hyperons is comparable to the nucleon, while in the $$\varXi $$ it is suppressed. The $$\varLambda $$ – $$\varSigma ^0$$ transition density is pure isovector and represents a clear manifestation of peripheral two-pion dynamics.

Postmodernist Relativism: A Return to Polytheism?

Despite distancing themselves from traditional religions, (Western) post-secular societies are still heavily concerned with ‘spirituality’ and other forms of self-realisation. Within our working postmodernist framework, where ‘truth’, ‘knowledge’ and ‘God’ are found to be relative, this concern often translates into a combination of religiously inspired practices – such as (Hinduist) yoga or (Buddhist) meditation – and a scientific, modern approach to the knowledge of the world. Can this coexistence of practices be a new kind of polytheism? This paper shows that postmodernist, relativistic belief systems share the poly-, or multiplicity of approaches to life and reality, but not the -theist, or conceptualisation of their beliefs as ‘divine’.

Canonical tensor model through data analysis: Dimensions, topologies, and geometries

The canonical tensor model (CTM) is a tensor model in Hamilton formalism and is studied as a model for gravity in both classical and quantum frameworks. Its dynamical variables are a canonical conjugate pair of real symmetric three-index tensors, and a question in this model was how to extract spacetime pictures from the tensors. We give such an extraction procedure by using two techniques widely known in data analysis. One is the tensor-rank (or CP, etc.) decomposition, which is a certain generalization of the singular value decomposition of a matrix and decomposes a tensor into a number of vectors. By regarding the vectors as points forming a space, topological properties can be extracted by using the other data analysis technique called persistent homology, and geometries by virtual diffusion processes over points. Thus, time evolutions of the tensors in the CTM can be interpreted as topological and geometric evolutions of spaces. We have performed some initial investigations of the classical equation of motion of the CTM in terms of these techniques for a homogeneous fuzzy circle and homogeneous two- and three-dimensional fuzzy spheres as spaces, and have obtained agreement with the general relativistic system obtained previously in a formal continuum limit of the CTM. It is also demonstrated by some concrete examples that the procedure is general for any dimensions and topologies, showing the generality of the CTM.