Background Spacetime Research Articles

Topological defects on relativistic quantum oscillator in wormhole space–time background

In this research work, the relativistic quantum dynamics of oscillator field in wormhole background with a topological defect produced by a cosmic string is investigated. We consider an example of Morris–Thorne-type wormhole including a osmic string and derived the wave equation of the relativistic quantum oscillator. Through the Heun equation, we solve analytically the radial equation and obtain the ground state energy level [Formula: see text] and the radial wave function [Formula: see text] as particular cases. In fact, it is shown that the eigenvalue solution of the oscillator field is influenced by the topological defect of cosmic string and shifted the result. Furthermore, the wormhole throat radius also modifies the energy levels and the wave function of the relativistic quantum oscillator.

Hermitian realizations of the Yang model

The Yang model is an example of noncommutative geometry on a background spacetime of constant curvature. We discuss the Hermitian realizations of its associated algebra on phase space in a perturbative expansion up to sixth order. We also discuss its realizations on extended phase spaces, that include additional tensorial and/or vectorial degrees or freedom.

Impact of spacetime curvature on the physical behaviour of Vaidya and Tikekar (VT) type anisotropic compact objects

The Vaidya and Tikekar (1982) ansatz has so far provided numerous stellar solutions which are useful for the description of compact stars like neutron stars and quark stars. We re-examine the impacts of the spacetime curvature parameter of the Vaidya–Tikekar ansatz on the physical properties of the relativistic anisotropic star. For a spherically symmetric, static and anisotropic stellar configuration, in the Vaidya–Tikekar background spacetime, we develop new exact solutions by assuming a polytropic type equation of state pr=kρ1+1n−β. Recent data from observed pulsars are taken as input parameters to validate the developed model. We examine the impact of the spheroidal curvature parameter of the VT spacetime on the stellar behaviour and mass–radius (M–R) relationship. It is observed that with the increase in the departure from spherical geometry, values of physical quantities, such as density and pressure, increase.

The Relativistic Rotation Transformation and the Observer Manifold

We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore, not a parameterised motion on a background space or spacetime, but is determined by a particular sequence of tetrads related by specific special Lorentz transformations or boosts. Because such Lorentz boosts do not form a group, these tetrads represent distinct observers that cannot put together their local descriptions into a manifold in the usual sense. The choice of observer manifold depends on the dynamical situation under consideration, and is not solely determined by the kinematics. Three examples are given: Franklin’s rotation transformation for uniform plane rotation, the Thomas precession of a vector attached to an electron, and the motion of a charged particle in an electromagnetic field. In each case, at each point of its trajectory, there is a distinguished tetrad and a special Lorentz transformation that maps Minkowski space to the spacetime of the local observer on the curve.

Quantum (in)stability of maximally symmetric space-times

Classical gravity coupled to a CFT4 (matter) is considered. The effect of the quantum dynamics of matter on gravity is studied around maximally symmetric spaces (flat, de Sitter and Anti de Sitter). The structure of the graviton propagator is modified and non-trivial poles appear due to matter quantum effects. The position and residues of such poles are mapped as a function of the relevant parameters, the central charge of the CFT4, the two R2 couplings of gravity as well as the curvature of the background space-time. The instabilities induced are determined. Such instabilities can be important in cosmology as they trigger the departure from de Sitter space and in some regions of parameters are more important than the well-known scalar instabilities. It is also determined when the presence of such instabilities is unreliable if the associated scales are larger than the “species” cutoff of the gravitational theory.

Schrödinger oscillators in a deformed point-like global monopole spacetime and a Wu–Yang magnetic monopole: Position-dependent mass correspondence and isospectrality

We show that a specific transformation/deformation in a point-like global monopole (PGM) spacetime background would yield an effective position-dependent mass (PDM) Schrödinger equation (i.e., a von Roos PDM Schrödinger equation). We discuss PDM Schrödinger oscillators in a PGM spacetime in the presence of a Wu–Yang magnetic monopole. Within our transformed/deformed global monopole spacetime, we show that all PDM Schrödinger oscillators admit isospectrality and invariance with the constant mass Schrödinger oscillators in the regular global monopole spacetime in the presence of a Wu–Yang magnetic monopole. The exclusive dependence of the thermodynamical partition function on the energy eigenvalues manifestly suggests that the Schrödinger oscillators and the PDM Schrödinger oscillators share the same thermodynamical properties as mandated by their isospectrality. Moreover, we discuss the hard-wall effect on the energy levels of the PDM Schrödinger oscillators in a PGM spacetime without and with a Wu–Yang magnetic monopole. Drastic energy levels’ shift-ups are observed as a consequence of such hard-wall effect.

The universal one-loop effective action with gravity

We complete the so-called Universal One-Loop Effective Action (UOLEA) with effects of gravity and provide a systematic approach to incorporate higher dimensional operators in curved spacetime. The functional determinant stemming from the path integral is computed using the Covariant Derivative Expansion (CDE), in a momentum representation that does not rely on a specific choice of coordinate to be defined, as it often is. This efficient approach manifests an interesting novelty as it allows to integrate out chiral fermions in curved spacetime in a direct manner leading to new operators involving the curvature, and provides a new alternative to the use of Feynman diagrams in that regard. The method presented would very well fit in a code that performs CDE, offering the possibility to integrate out at one-loop fields on a curved spacetime background, including spin-2 fields, like the graviton. Eventually these results should provide an interesting way to study low energy effects of UV completions of gravity.

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

MASSIVE PARTICLE TUNNELING RATE OF KERR-NEWMAN-ANTI-DE SITTER BLACK HOLE BY HAMILTON-JACOBI METHOD

Using Parikh and Wilczek’s opinion tunneling rate of Hawking radiations of Kerr-Newman-anti-de Sitter (KNAdS) black hole has been investigated by Hamilton-Jacobi method. Involving the self-gravitation effect of the emitted particles, energy and angular momentum has been taken as conserved and considered the space time background as dynamical. The explored results shown that the massive particle tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum.

Massless KG-oscillators in Som-Raychaudhuri cosmic string spacetime in a fine tuned rainbow gravity

A fine tuned rainbow gravity describes both relativistic quantum particles and anti-particles alike. That is, the ratio y=E/EP in the rainbow functions g0(y) and g1(y) should be fine tuned into 0≤y=E/EP≤1⇒y=|E|/EP, otherwise rainbow gravity will only secure Planck's energy scale Ep as the maximal energy for relativistic particles and the anti-particles are left unfortunate (in the sense that their energies will be indefinitely unbounded). Using this fine tuning we discuss the rainbow gravity effect on Klein-Gordon (KG) oscillators in Som-Raychaudhuri cosmic string rainbow gravity spacetime background. We use the rainbow functions: (i) g0(y)=1, g1(y)=1−ϵyn,n=1,2, loop quantum gravity motivated pairs, (ii) g0(y)=g1(y)=(1−ϵy)−1, a horizon problem motivated pair, and (iii) g0(y)=(eϵy−1)/ϵy, g1(y)=1, a gamma-ray bursts motivated pair. We show that the energies obtained using the first two rainbow functions in (i) completely comply with the rainbow gravity model and secure Planck's energy Ep as the maximal energy for both particles and anti-particles. The rainbow function pair in (ii) has no effect on massless KG-oscillators. Whereas, the one in (iii) does not show any eminent tendency towards the Planck's energy as the maximal energy.

Three-dimensional wormhole with cosmic string effects on eigenvalue solution of non-relativistic quantum particles

In this paper, we explore the quantum system of non-relativistic particles in a unique scenario: a circularly symmetric and static three-dimensional wormhole space-time accompanied by cosmic strings. We focus on a specific case where the redshift function varPhi (r) to be zero and defining the shape function as A(r)=frac{b}{r^2}. After establishing this background space-time, we investigate the behavior of a harmonic oscillator within the same wormhole context. By doing so, we observe the effects of the cosmic string and wormhole throat radius on the eigenvalue solution of the oscillator’s eigenvalue problem. The primary finding is that these cosmic features lead to modifications in the energy spectrum and wave functions of the system, breaking the degeneracy of energy levels that would typically be present in a more conventional setting. As a particular case, we present the specific energy level E_{1,ell } and the corresponding wave function psi _{1,ell }, which are associated with the ground state of the quantum system. These results highlight the fascinating and unique properties of the harmonic oscillator in the background of a circularly symmetric, static wormhole space-time with cosmic strings.

General formalism of the quantum equivalence principle

A consistent theory of quantum gravity will require a fully quantum formulation of the classical equivalence principle. Such a formulation has been recently proposed in terms of the equality of the rest, inertial and gravitational mass operators, and for non-relativistic particles in a weak gravitational field. In this work, we propose a generalization to a fully relativistic formalism of the quantum equivalence principle, valid for all background space-times, as well as for massive bosons and fermions. The principle is trivially satisfied for massless particles. We show that if the equivalence principle is broken at the quantum level, it implies the modification of the standard Lorentz transformations in flat space-time and a corresponding modification of the metric in curved space-time by the different mass ratios. In other words, the observed geometry would effectively depend on the properties of the test particle. Testable predictions of potential violations of the quantum equivalence principle are proposed.

A description of classical and quantum cosmology for a single scalar field torsion gravity

In the background of homogeneous and isotropic flat FLRW spacetime, both classical and quantum cosmologies have been studied for teleparallel dark energy (DE) model. Using Noether symmetry analysis, not only the symmetry vector but also the coupling function in the Lagrangian and the potential of the scalar field have been determined. Also symmetry analysis identifies a cyclic variable in the Lagrangian along the symmetry vector and as a result the Lagrangian simplifies to a great extent so that classical solution is obtained. Subsequently, in quantum cosmology Wheeler–DeWitt (WD) equation has been constructed and the quantum version of the conserved momenta corresponding to Noether symmetry identifies the periodic part of the wave function of the universe and as a result the WD equation becomes solvable. Finally, quantum description shows finite nonzero probability at the classical big bang singularity.

Global Stability for Charged Scalar Fields in an Asymptotically Flat Metric in Harmonic Gauge

We prove global stability for the charged scalar field system on a background spacetime, which is close to 1+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+3$$\\end{document}-dimensional Minkowski space and whose outward light cones converge to those for the Schwarzs-child metric at null infinity. The key technique to this proof is the use of a modified null frame, depending only on the mass M of the metric, which captures the asymptotic behavior of the metric at future null infinity. Our results are analogous to results obtained in Minkowski space by Lindblad and Sterbenz in (IMRP Int Math Res Pap 2006:52976, 2006) up to a change in coordinates, and will in the sequel be used to prove the full structure of the Einstein–charge scalar field system in these modified harmonic coordinates.

Feshbach–Villars oscillator in Kaluza-Klein theory

This research focuses on exploring the relativistic quantum dynamics of spin-0 scalar massive charged particles within the framework of the relativistic Feshbach-Villars oscillator (FVO) in the context of the Kaluza-Klein Theory (KKT). Specifically, we investigate the behavior of these particles in the presence of a cosmic string space-time within the framework of the Kaluza-Klein theory. To begin, we solve the Feshbach-Villars equation in the background of a cosmic string space-time by considering the principles of the Kaluza-Klein theory. We obtain the eigenvalue solution, which provides valuable insights into the behavior of the system. Next, we re-examine this system by considering the Feshbach-Villars quantum oscillator, a specific mathematical representation of the Feshbach-Villars equation. By employing this oscillator, we are able to analytically determine the eigenvalues of the system. This analytical solution allows for a deeper understanding of the system's characteristics. In the subsequent stage, we investigate the interaction between the Feshbach-Villars equation and oscillator in the presence of a cosmic dislocation within the framework of the Kaluza-Klein Theory. We analytically solve the wave equation associated with this system, shedding light on the behavior of the wave function. Furthermore, we analyze the influence of the topological defect (cosmic dislocation) on the quantification of energy and the wave function of the Feshbach-Villars oscillator. We also explore the impact of external fields on the system. These analyses provide valuable insights into how these factors affect the behavior and properties of the Feshbach-Villars oscillator.

Kinetic field theory: generic effects of alternative gravity theories on non-linear cosmic density-fluctuations

Non-linear cosmic structures contain valuable information on the expansion history of the background space-time, the nature of dark matter, and the gravitational interaction. The recently developed kinetic field theory of cosmic structure formation (KFT) allows to accurately calculate the non-linear power spectrum of cosmic density fluctuations up to wave numbers of k ≲ 10 h Mpc-1 at redshift zero. Cosmology and gravity enter this calculation via two functions, viz. the background expansion function and possibly a time-dependent modification of the gravitational coupling strength.The success of the cosmological standard model based on general relativity suggests that cosmological models in generalized theories of gravity should have observable effects differing only weakly from those in standard cosmology. Based on this assumption, we derive the functional, first-order Taylor expansion of the non-linear power spectrum of cosmic density fluctuations obtained from the mean-field approximation in KFT in terms of the expansion function and the gravitational coupling strength. This allows us to study non-linear power spectra expected in large classes of generalized gravity theories. To give one example, we apply our formalism to generalized Proca theories.

Curved spacetime as a dispersive multiferroic medium for an electromagnetic wave: Polarization and magnetization vectors in the Schwarzschild spacetime

We study one of the interesting properties of the electromagnetic wave propagation in the Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum general relativistic Maxwell’s equations. It is shown that the solutions for the electromagnetic field can be expanded in the spherical harmonic functions and all components of the electromagnetic fields can be expressed in terms of two radial profile functions. These radial profile functions can be expressed in terms of the confluent Heun function. The calculated behavior of the electric and magnetic susceptibilities near the event horizon appears to be similar to the susceptibilities of multiferroic materials near phase transition. The Curie temperature of this phase transition appears to coincide with the Hawking temperature.

The Dirac equation with /non--symmetric potentials in curved spacetime backgrounds

In this paper, we have presented the Dirac equation in the frame of position-dependent mass on two dimensional gravitational static background in the presence of /non--symmetric potential interactions. The exponential metric component have formed the reduced Dirac operator into the general supersymmetric model within mass changing with coordinates. We have obtained the eigenvalues of the Dirac operator for the complex Morse and trigonometric complex Scarf-II potentials SL(2, C) using Lie algebras and the supersymmetric quantum mechanical approaches. Moreover, after obtaining a general Sturm-Liouville type equation using a convenient mapping, the system have become available to be investigated within η- pseudo-Hermiticity. With this context, η operator is found for the examples of complex trigonometric Rosen-Morse potential and complex Morse potentials with real and complex parameters of the initial system and finally the solutions are obtained for each model with the graphics of energy values and probability densities.

Late-time asymptotics for geometric wave equations with inverse-square potentials

We introduce a new, physical-space-based method for deriving the precise leading-order late-time behaviour of solutions to geometric wave equations on asymptotically flat spacetime backgrounds and apply it to the setting of wave equations with asymptotically inverse-square potentials on Schwarzschild black holes. This provides a useful toy model setting for introducing methods that are applicable to more general linear and nonlinear geometric wave equations, such as wave equations for electromagnetically charged scalar fields, wave equations on extremal Kerr black holes and geometric wave equations in even space dimensions, where existing proofs for deriving precise late-time asymptotics might not apply. The method we introduce relies on exploiting the spatial decay properties of time integrals of solutions to derive the existence and precise genericity properties of asymptotic late-time tails and obtain sharp, uniform decay estimates in time.

Polar gravitational waves in f(R, T ϕ ) framework

This work analyzes the propagation of polar gravitational waves for flat FRW cosmic background and in view of f(R, T ϕ ) theory. In what follows, we opt for the Regge-Wheeler polar perturbation scheme in flat geometry of background spacetime and corresponding scalar, field source is also perturbed. The two sets of field equations for flat and perturbed geometry are constructed and furthermore used to evaluate perturbation parameters. The obtained expressions suggest that polar fluctuations affect both geometry and scalar field. The radial and temporal parts of perturbation parameters χ and σ are plotted explicitly while the behavior of ψ is observed via a numerical solution plotted as a 3D graph. The change in these fluctuations for different values of model parameter λ is noticed through these plots.