We are studying the dynamics of a one-dimensional field in a non-commutative Euclidean space. The non-commutative space we consider is the one that emerges in the context of three dimensional Euclidean quantum gravity: it is a deformation of the classical Euclidean space and the Planck length plays the role of the deformation parameter. The field is interpreted as a particle which evolves in a quantum background. When the dynamics of the particle is linear, the resulting motion is similar to the standard motion in the classical space. However, non-linear dynamics on the non-commutative space are different from the corresponding non-linear dynamics on the classical space. These discrepencies are interpreted as "quantum gravity" effects. Finally, we propose a background independent description of the propagation of the particle in the quantum geometry.
Test particle geodesic motion is analysed in detail for the background spacetimes of the degenerate Ferrari-Ibanez colliding gravitational wave solutions. Killing vectors have been used to reduce the equations of motion to a first order system of differential equations which have been integrated numerically. The associated constants of the motion have also been used to match the geodesics as they cross over the boundary between the single plane wave and interaction zones.
We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the variations of the kinetic energy of the particle during passage of the waves. We also explicitly compute the change in the orbit due to a wave with constant curvature.
The influence of spin on a photon's motion in a Schwarzschild and FRW spacetimes is studied. The first order correction to the geodesic motion is found. It is shown that unlike the world-lines of spinless particles, the photons world-lines do not lie in a plane.
The photon motion in a Michelson interferometer is re-analyzed in both geometrical optics and wave optics. The classical paths of the photons in the background of gravitational wave are derived from Fermat principle, which is the same as the null geodesics in general relativity. The deformed Maxwell equations and the wave equations of electric fields in the background of gravitational wave are presented in flat-space approximation. Both methods show that the response of an interferometer depends on the frequency of a gravitational wave, however it is almost independent of the frequency of the …
When Morris and Thorne first proposed the possible existence of traversable wormholes, they adopted the following strategy: maintain complete control over the geometry, thereby leaving open the determination of the stress-energy tensor. In this paper we determine this tensor by starting with a noncommutative-geometry background and assuming that the static and spherically symmetric spacetime admits conformal motions. This had been established in a previous collaboration with Rahaman et al. using a slightly different approach. Accordingly, the main purpose of this paper is to show that the worm…
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is investigated in the background of a space-time characterized by this class of solutions. We focus on the study of circular stable and unstable orbits obtained by taking account particular harmonic functions defining the gravitational potential. We show that is possible to have repulsive force generated by the charge distribution of the source. As the space-t…
The dynamics of closed cosmic strings in Peres background, using finite-difference method, has been considered. It is shown that motion of the strings is very complicated and its perform complex oscillations and deformed to form loops and cusps.
A technique for extracting from the appropriate field equations the relativistic motion of Schwarzschild, Reissner-Nordstrom and Kerr particles moving in external fields is motivated and illustrated. The key assumptions are that (a) the particles are isolated and (b) near the particles the wave fronts of the radiation generated by their motion are smoothly deformed spheres. No divergent integrals arise in this approach. The particles are not test particles. The formalism is used, however, to derive the Mathisson-Papapetrou equations of motion of spinning test particles, neglecting spin-spin te…
Quasi-classical picture of motion of spin 1/2 massive particle in a curved spacetime is built on base of simple Lagrangian model. The one is constructed due to analogy with Lagrangian of massive vector particle. Equations of motion and spin propagation coincide with Papapetrou equations describing dynamic of classical spinning particle in a curved spacetime.
We show that the Dirac equation on de Sitter background can be analytically solved in a special static frame where the energy eigenspinors can be expressed in terms of usual angular spinors known from special relativity, and a pair of radial wave functions.
We discuss the leading order correction to the equation of motion of a particle with spin on an arbitrary spacetime. A particle traveling in a curved spacetime is known to trace a geodesic of the background spacetime if the mass of the particle is negligibly small. For a spinning particle, it is known that there appears a term due to the coupling of the spin and the Riemann tensor of the background spacetime. Recently we have found the equation of motion of a non-spinning particle which includes the effect of gravitational radiation reaction. This paper is devoted to discussion of a consistent…
The motion of spinless particles in Riemann-Cartan (RC) $U_{4}$ and teleparallel spacetimes is revisited on the light of gravitational waves hitting on the spinless test particles. It is shown that in the case Cartan contortion is totally skew-symmetric the spinless particles follow geodesics but if this symmetry is dropped they are able to follow nongeodesic worldlines in torsionic background. The case of totally skew contortion and spinning particles may appear either in $T_{4}$ or $U_{4}$ spacetimes. We consider $T_{4}$ nongeodesic motion of spinless test particles in the field of gravitati…
Quasi-classical picture of motion of spin 1/2 massless particle in a curved spacetime is built on base of simple Lagrangian model. The one is constructed due to analogy with Lagrangian of massive spin 1/2 particle. Equations of motion and spin propagation coincide with Papapetrou equations describing dynamic of photon in a curved spacetime.
We derive the equations of motion of an electrically neutral test particle for modified gravity theories in which the covariant divergence of the ordinary matter energy-momentum tensor dose not vanish (i.e. $\nabla_μT^{μν}\neq0$). In fact, we generalize the Mathisson-Papapetrou equations by deriving a general form for the equations of motion of a test particle. Furthermore, using the generalized Mathisson-Papapetrou equations, we investigate the equations of motion of a pole-dipole (spinning) particle in the context of Modified Gravity (MOG).
It was recently suggested that the gravitational action could contain a scale-dependent cosmological term, depending on the length or momentum scale characteristic of the processes under consideration. In this work we explore a simple possible consequence of this assumption. We compute the field generated in empty space by a static spherical source (the Schwarzschild metric), using the modified action. The resulting static potential turns out to contain a tiny non-Newtonian component which depends on the size of the test particles. The possible relevance of this small correction for the analys…
We examine motion of test particles with various masses, electric charges and dilatonic charges in a background metric and fields of a charged dilatonic black hole.
Motion of massive and massless test particle in equilibrium and non-equilibrium case is discussed in a dyadosphere geometry through Hamilton-Jacobi method. Geodesics of particles are discussed through Lagrangian method too. Scalar wave equation for massless particle is analyzed to show the absence of superradiance.
We have investigated the motion of timelike particles along geodesic in the background of accelerating and rotating black hole spacetime. We confirmed that the chaos exists in the geodesic motion of the particles by Poincaré sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram. Moreover, we probe the effects of the acceleration and rotation parameters on the chaotic behavior of a timelike geodesic particle in the black hole spacetime. Our results show that the acceleration brings richer physics for the geodesic motion of particles.
Based on the coupling between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagnetic field, which is also the origin of Lense-Thirring effects. In post-Newtonian approximations, this equation gives out the same results as those of Papapetrou equation. Effect of the deviation of geode…
From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations of motion are valid for massless particles as well, since mass does not enter the equations explicitely.
Gravitational perturbations due to a point particle moving on a static black hole background are naturally described in Regge-Wheeler gauge. The first-order field equations reduce to a single master wave equation for each radiative mode. The master function satisfying this wave equation is a linear combination of the metric perturbation amplitudes with a source term arising from the stress-energy tensor of the point particle. The original master functions were found by Regge and Wheeler (odd parity) and Zerilli (even parity). Subsequent work by Moncrief and then Cunningham, Price and Moncrief …
In the Schwarzchild black hole spacetime, we show that chaotic motion can be triggered by the spin of a particle. Taking the spin of the particle as a perturbation and using the Melnikov method, we find that the perturbed stable and unstable orbits are entangled with each other and that illustrates the onset of chaotic behavior in the motion of the particle.
In this article we study the geodesic motion of charged particles in the spacetime of an extremal rotating dyonic black hole in Kaluza-Klein theory. We derive the equations of motion and present their analytical solutions in terns of elliptic and hyperelliptic functions. Furthermore, we analyze the geodesic motions with the help of parametric diagrams and effective potentials.
Based in the framework of article (arXiv:1609.02110), where we have presented the general problems one encounters in the construction of balanced equations of motions for particles in relativistic theories of gravity, we present in this work the explicit balanced equations of motion for a compact object in general relativity in the harmonic gauge.
Brane model of universe is considered for a particle. Conservation laws inside the brane are obtained. Equation of motion is derived for a particle using variation principle from these conservation laws. This equation includes terms accounting the variation of brane topology. Its solution is obtained at some approximations and dispersion relation for a particle is derived.
We investigate Brownian motions of a particle coupled to vacuum fluctuations of a quantum field. The Unruh effect predicts that an observer in an accelerated motion sees the Minkowski vacuum as thermally excited. This addresses the problem of whether a thermal property appears in a perturbative random motion of a particle in an accelerated motion due to the coupling or not. We revisit this problem by solving the equation of motion of a particle coupled to vacuum fluctuations including the radiation reaction force. We compute a Fourier integral for the variance of the random velocity in a rigor…
We present firstly the equation of motion for the test scalar particle coupling to the Chern-Simons invariant in Kerr black hole spacetime by the short-wave approximation. We have analyzed the dynamical behaviors of the test coupled particles by applying techniques including Poincaré sections, fast Lyapunov exponent indicator, bifurcation diagram and basins of attraction. It is shown that there exists chaotic phenomenon in the motion of scalar particle interacted with the Chern-Simons invariant in a Kerr black hole spacetime. With the increase of the coupling strength, the motion of the couple…
This paper focuses on the motion of a test particle moving around the Reissner-Nordstrom black hole. It deals with circular motion and radial motion of the neutral massive test particles, and shortly handles circular motion of the charged massive test particles. Both neutral and charged particles are affected by black hole's charge, but it is due to the fact that charge of the black hole bends the spacetime more strongly. This procedure has nothing to do with electromagnetic interactions, and these are only considered for charged test particles. However, it only treats mathematically easy, app…
The motion of spinning massless particles in gravitationally curved backgrounds is revisited by considering new types of constraints. Those constraints guarantee zero mass ($P_μP^μ=0$) and they allow for the possibility of trajectories which are not simply null geodesics. To exemplify this previously unknown possibility, the equations of motion are solved for radial motion in Schwarzschild background. It is found that the particle experiences a spin-induced energy shift, which is proportional to the Hawking temperature of the black hole background.
We solve analytically the Schrödinger equation for the N-dimensional inverse square potential in quantum mechanics with a minimal length in terms of Heun's functions. We apply our results to the problem of a dipole in a cosmic string background. We find that a bound state exists only if the angle between the dipole moment and the string is larger than π/4. We compare our results with recent conflicting conclusions in the literature. The minimal length may be interpreted as a radius of the cosmic string.
We investigate the motion of a test particle in higher dimensions due to the presence of extended sources like D$p$-branes by studying the motion in the transverse space of the brane. This is contrasted with the motion of a point particle in the Schwarzschild background in higher dimensions. Since D$p$-branes are specific to 10-dimensional space time and exact solutions of geodesic equations for this particular space time has not been possible so far for the Schwarzschild background, we focus here to find the leading order solution of the geodesic equation (for motion of light rays). This enab…
Krein approach is used to study the particle creation during quasi-de Sitter inflation in different background space-times. In the conventional method for calculating the created particles spectrum, the background space-time is automatically considered flat. Selecting a flat background poses two fundamental problems: First, the method of calculating is not covariant relative to the curved space-time. Second, the number of created particles becomes negative. Krein approach can be considered as a covariant method to calculate two-point functions in curved space-time. So we extend this method for…
We study the spatially homogeneous relativistic Boltzmann equation for massless particles in an FLRW background with scattering kernels in a certain range of soft and hard potentials. We obtain the future global existence of small solutions in a weighted $L^1\cap L^\infty$ space.
The theory of quantum fields in classical backgrounds is re-examined for the cases in which the Lagrangian is quadratic in quantum fields. Various methods that describe particle production are discussed. It is found that all methods suffer from certain ambiguities, related to the choice of coordinates, gauge, or counter-terms. They also seem to be inconsistent with the conservation of energy. This suggests that such classical backgrounds may not cause particle production.
In this paper we investigate the innermost stable circular orbit (ISCO) for a classical spinning test particle in the background of Kerr-Newman black hole. It is shown that the orbit of the spinning particle is related to the spin of the test particle. The motion of the spinning test particle will be superluminal if its spin is too large. We give an additional condition by considering the superluminal constraint for the ISCO in the black hole backgrounds. We obtain numerically the relations between the ISCO and the properties of the black holes and the test particle. It is found that the radiu…
A metric with a Lorentz violating parameter is associated with the bumblebee gravity model. We study the motion of a particle in this bumblebee background where the dynamical variables satisfy non-canonical Snyder algebra along with some critical survey on the classical observations in the bumblebee background to see how these would likely differ from Schwarzschild background. It has been found that the perihelion shift acquires a generalized expression with two independent parameters. One of these two is connected with the Lorentz violating factor and the other is involved in the Snyder algeb…
In double field theory, the equation of motion for a point particle in the background field is considered. We find that the motion is described by a geodesic flow in the doubled geometry. Inspired by the analysis on the particle motion, we consider a modified model of quantum string cosmology, which includes two scale factors.
Nonrelativistic string theory is a unitary, ultraviolet finite quantum gravity theory with a nonrelativistic string spectrum. The vertex operators of the worldsheet theory determine the spacetime geometry of nonrelativistic string theory, known as the string Newton-Cartan geometry. We compute the Weyl anomaly of the nonrelativistic string worldsheet sigma model describing strings propagating in a string Newton-Cartan geometry, Kalb-Ramond and dilaton background. We derive the equations of motion that dictate the backgrounds on which nonrelativistic string theory can be consistently defined qua…
We obtain a new form for the action of a nonrelativistic particle coupled to Newtonian gravity. The result is different from that existing in the literature which, as shown here, is riddled with problems and inconsistencies. The present derivation is based on the formalism of galilean gauge theory, introduced by us as an alternative method of analysing nonrelativistic symmetries in gravitational background.
A local current of particle density for scalar fields in curved background is constructed. The current depends on the choice of a two-point function. There is a choice that leads to local non-conservation of the current in a time-dependent gravitational background, which describes local particle production consistent with the usual global description based on the Bogoliubov transformation. Another choice, which might be the most natural one, leads to the local conservation of the current.
We discuss the scattering of two light particles in a D-brane background. It is known that, if one light particle strikes the D brane at small impact parameter, quantum recoil effects induce entanglement entropy in both the excited D brane and the scattered particle. In this paper we compute the asymptotic `out' state of a second light particle scattering off the D brane at large impact parameter, showing that it also becomes mixed as a consequence of quantum D-brane recoil effects. We interpret this as a non-factorizing contribution to the superscattering operator S-dollar for the two light p…
The scalar background field and its consequences are discussed for the Friedmann type cosmological solutions of the scalar-tensor theory of gravity with the Higgs field of the Standard Model as the scalar gravitational field.
We study the motion of massive particles with electric and magnetic charges in the background of a magnetically charged Garfinkle-Horowitz-Strominger stringy black hole. We solve analytically the equations of motion of the test particles and we describe the orbital motion in terms of the Weierstrass elliptic functions. We find that there are critical values of the magnetic charge of the black hole and the magnetic charge of the test particle which characterize the bound and unbound orbits and we study two observables, the perihelion shift and the Lense-Thirring effect. The trajectories depend …
The relative motion of a classical relativistic spinning test particle is studied with respect to a nearby free test particle in the gravitational field of a rotating source. The effects of the spin-curvature coupling force are elucidated and the implications of the results for the motion of rotating plasma clumps in astrophysical jets are discussed.
We study inflation arising from the motion of a BPS D3-brane in the background of a stack of k parallel D5-branes. There are two scalar fields in this set up-- (i) the radion field R, a real scalar field, and (ii) a complex tachyonic scalar field chi living on the world volume of the open string stretched between the D3 and D5 branes. We find that inflation is realized by the potential of the radion field, which satisfies observational constraints coming from the Cosmic Microwave Background. After the radion becomes of order the string length scale l_s, the dynamics is governed by the potentia…
We consider motion in spherically symmetric but time-dependent backgrounds. This problem is of interest, for example, in the context of ultralight dark matter, where galactic haloes produce a time-dependent and periodic gravitational potential. We study the properties of motion of stars in such spacetimes, for different field strengths and frequency, and including dissipative effects. We show that orbital resonances may occur and that spectroscopic emission lines from stars in these geometries exhibit characteristic, periodic modulation patterns. In addition, we work out a fully relativistic a…
We assume that the cosmological dark matter is composed of massive neutral scalar particles that decay into two massless particles. The decay produces a stochastic background of gravitational waves (GWs) via a 'memory effect' mechanism. We calculate the spectral amplitude and slope of the resulting background, which is frequency independent (flat). We discuss its potential observability and show that the resulting background might dominate the cosmological GW background at frequencies above about 10 GHz. Penrose has proposed a cosmological model in which dark matter particles have the Planck m…
Temperature and polarization variations across the microwave sky include the fingerprints of quantum fluctuations in the early universe. They may soon reveal physics at unprecedented energy scales.
Quantum fields in time-dependent backgrounds generally lead to particle production. Here we consider "unexciting" backgrounds for which the net particle production vanishes. We start by considering the simple harmonic oscillator and explicitly construct all unexciting time-dependent frequencies. This allows us to construct homogeneous backgrounds in field theory for which there is no particle production in any given mode, though we are able to show that there are no homogeneous backgrounds for which the particle production vanishes in every mode. We then construct general inhomogeneous unexcit…
Starting from the Dirac equation coupled to a classical radiation field a set of equations of motion for charged quasi-particles in the classical limit for slowly varying radiation and matter fields is derived. The radiation reaction term derived in the paper is the Abraham-Lorentz-Dirac term.
We estimate the solar system motion relative to the cosmic microwave background using type Ia supernovae (SNe) measurements. We take into account the correlations in the error bars of the SNe measurements arising from correlated peculiar velocities. Without accounting for correlations in the peculiar velocities, the SNe data we use appear to detect the peculiar velocity of the solar system at about the 3.5 sigma level. However, when the correlations are correctly accounted for, the SNe data only detects the solar system peculiar velocity at about the 2.5 sigma level. We forecast that the solar…
We investigate analytically and numerically the orbits of spinning particles around black holes in the post Newtonian limit and in the presence of cosmic expansion. We show that orbits that are circular in the absence of spin, get deformed when the orbiting particle has spin. We show that the origin of this deformation is twofold: a. the background expansion rate which induces an attractive (repulsive) interaction due to the cosmic background fluid when the expansion is decelerating (accelerating) and b. a spin-orbit interaction which can be attractive or repulsive depending on the relative or…
