arXiv subjects

C. Chicone

Publications and source records attributed to C. Chicone.

At least 19 recordsLinked to original sources

arXiv2017

Cosmological Implications of Nonlocal Gravity

We present extensions of the treatment contained in our recent paper on nonlocal Newtonian cosmology [C. Chicone and B. Mashhoon, J. Math. Phys. 57, 072501 (2016)]. That is, the implications of the recent nonlocal generalization of Einstein's theory of gravitation are further investigated within the regime of Newtonian cosmology. In particular, we treat the nonlocal problem of structure formation for a spherically symmetric expanding dust model and show numerically that as the central density contrast grows, it tends to decrease slowly with radial distance as the universe expands. The nonlocal violation of Newton's shell theorem provides a physical interpretation of our numerical results.

gr-qc↗

arXiv2016

Nonlocal Newtonian Cosmology

We explore some of the cosmological implications of the recent classical nonlocal generalization of Einstein's theory of gravitation in which nonlocality is due to the gravitational memory of past events. In the Newtonian regime of this theory, the nonlocal character of gravity simulates dark matter in spiral galaxies and clusters of galaxies. However, dark matter is considered indispensable as well for structure formation in standard models of cosmology. Can nonlocal gravity solve the problem of structure formation without recourse to dark matter? Here we make a beginning in this direction by extending nonlocal gravity in the Newtonian regime to the cosmological domain. The nonlocal analog of the Zel'dovich solution is formulated and the consequences of the resulting nonlocal Zel'dovich model are investigated in detail.

gr-qc↗

arXiv2016

Nonlocal Gravity in the Solar System

The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity appears to simulate dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a_0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a_0 is determined.

gr-qc↗

arXiv2013

Linearized Gravitational Waves in Nonlocal General Relativity

We investigate gravitational radiation in the linear approximation within the framework of the recent nonlocal generalization of Einstein's theory of gravitation. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data regarding the rotation curves of spiral galaxies, nonlocality is associated with a characteristic length scale of order λ_0 = 10 kpc. It follows that in nonlocal gravity, the treatment of extremely low-frequency (~ 10^{-12} Hz) gravitational waves with wavelengths of order λ_0 would be quite different than in general relativity. However, for radiation of frequency > 10^{-8} Hz, which is the frequency range that is the focus of current observational searches, the corresponding wavelengths are very small compared to λ_0. We find that in this frequency regime the nonlocal deviations from general relativity essentially average out and can be safely neglected in practice.

gr-qc↗

arXiv2012

Spacetime Splitting, Admissible Coordinates and Causality

To confront relativity theory with observation, it is necessary to split spacetime into its temporal and spatial components. The (1+3) timelike threading approach involves restrictions on the gravitational potentials $(g_{μν})$, while the (3+1) spacelike slicing approach involves restrictions on $(g^{μν})$. These latter coordinate conditions protect chronology within any such coordinate patch. While the threading coordinate conditions can be naturally integrated into the structure of Lorentzian geometry and constitute the standard coordinate conditions in general relativity, this circumstance does not extend to the slicing coordinate conditions. We explore the influence of chronology violation on wave motion. In particular, we consider the propagation of radiation parallel to the rotation axis of stationary Gödel-type universes characterized by parameters $η> 0$ and $λ> 0$ such that for $η< 1$ ($η>1$) chronology is protected (violated). We show that in the WKB approximation such waves can freely propagate only when chronology is protected.

gr-qc↗

arXiv2012

Nonlocal Gravity: Modified Poisson's Equation

The recent nonlocal generalization of Einstein's theory of gravitation reduces in the Newtonian regime to a nonlocal and nonlinear modification of Poisson's equation of Newtonian gravity. The nonlocally modified Poisson equation implies that nonlocality can simulate dark matter. Observational data regarding dark matter provide limited information about the functional form of the reciprocal kernel, from which the original nonlocal kernel of the theory must be determined. We study this inverse problem of nonlocal gravity in the linear domain, where the applicability of the Fourier transform method is critically examined and the conditions for the existence of the nonlocal kernel are discussed. This approach is illustrated via simple explicit examples for which the kernels are numerically evaluated. We then turn to a general discussion of the modified Poisson equation and present a formal solution of this equation via a successive approximation scheme. The treatment is specialized to the gravitational potential of a point mass, where in the linear regime we recover the Tohline-Kuhn approach to modified gravity.

gr-qc↗

arXiv2011

Double-Kasner Spacetime: Peculiar Velocities and Cosmic Jets

In dynamic spacetimes in which asymmetric gravitational collapse/expansion is taking place, the timelike geodesic equation appears to exhibit an interesting property: Relative to the collapsing configuration, free test particles undergo gravitational "acceleration" and form a double-jet configuration parallel to the axis of collapse. We illustrate this aspect of peculiar motion in simple spatially homogeneous cosmological models such as the Kasner spacetime. To estimate the effect of spatial inhomogeneities on cosmic jets, timelike geodesics in the Ricci-flat double-Kasner spacetime are studied in detail. While spatial inhomogeneities can significantly modify the structure of cosmic jets, we find that under favorable conditions the double-jet pattern can initially persist over a finite period of time for sufficiently small inhomogeneities.

gr-qc↗

arXiv2011

Gravitomagnetic Jets

We present a family of dynamic rotating cylindrically symmetric Ricci-flat gravitational fields whose geodesic motions have the structure of gravitomagnetic jets. These correspond to helical motions of free test particles up and down parallel to the axis of cylindrical symmetry and are reminiscent of the motion of test charges in a magnetic field. The speed of a test particle in a gravitomagnetic jet asymptotically approaches the speed of light. Moreover, numerical evidence suggests that jets are attractors. The possible implications of our results for the role of gravitomagnetism in the formation of astrophysical jets are briefly discussed.

gr-qc↗

arXiv2011

Cosmic Jets

We discuss time-dependent gravitational fields that "accelerate" free test particles to the speed of light resulting in cosmic double-jet configurations. It turns out that complete gravitational collapse along a spatial axis together with corresponding expansion along the other two axes leads to the accelerated motion of free test particles up and down parallel to the collapse axis such that a double-jet pattern is asymptotically formed with respect to the collapsed configuration.

gr-qc↗

arXiv2010

Gravitomagnetic Accelerators

We study a simple class of time-dependent rotating Ricci-flat cylindrically symmetric spacetime manifolds whose geodesics admit gravitomagnetic jets. The helical paths of free test particles in these jets up and down parallel to the rotation axis are analogous to those of charged particles in a magnetic field. The jets are attractors. The jet speed asymptotically approaches the speed of light. In effect, such source-free spacetime regions act as "gravitomagnetic accelerators".

gr-qc↗

arXiv2008

Time-Varying Lense-Thirring System

We consider bound geodesic orbits of test masses in the exterior gravitational field of a rotating astronomical source whose proper angular momentum varies linearly with time. The linear perturbation approach of Lense and Thirring is herein extended to the nonstationary case. In particular, we investigate the instability of Lense-Thirring precessing orbits due to the slow temporal variation of the gravitomagnetic field of the source.

gr-qc↗

arXiv2007

Nonlocal Lagrangians for Accelerated Systems

Acceleration-induced nonlocality and the corresponding Lorentz-invariant nonlocal field equations of accelerated systems in Minkowski spacetime are discussed. Under physically reasonable conditions, the nonlocal equation of motion of the field can be derived from a variational principle of stationary action involving a nonlocal Lagrangian that is simply obtained by composing the local inertial Lagrangian with the nonlocal transformation of the field to the accelerated system. The implications of this approach for the electromagnetic and Dirac fields are briefly discussed.

hep-th↗

arXiv2006

Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes

Fermi coordinates are directly constructed in de Sitter and Goedel spacetimes and the corresponding exact coordinate transformations are given explicitly. The quasi-inertial Fermi coordinates are then employed to discuss the dynamics of a free test particle in these spacetimes and the results are compared to the corresponding generalized Jacobi equations that contain only the lowest-order tidal terms. The domain of validity of the generalized Jacobi equation is thus examined in these cases. Furthermore, the difficulty of constructing explicit Fermi coordinates in black-hole spacetimes is demonstrated.

gr-qc↗

arXiv2006

Tidal Dynamics in Kerr Spacetime

The motion of free nearby test particles relative to a stable equatorial circular geodesic orbit about a Kerr source is investigated. It is shown that the nonlinear generalized Jacobi equation can be transformed in this case to an autonomous form. Tidal dynamics beyond the critical speed c/sqrt(2) is studied. We show, in particular, that a free test particle vertically launched from the circular orbit parallel or antiparallel to the Kerr rotation axis is tidally accelerated if its initial relative speed exceeds c/sqrt(2). Possible applications of our results to high-energy astrophysics are briefly mentioned.

gr-qc↗

arXiv2005

Tidal Acceleration of Ultrarelativistic Particles

We investigate the motion of free relativistic particles relative to the ambient medium around a gravitationally collapsed system. If the relative speed exceeds a critical value given by c/sqrt(2), the gravitational tidal effects exhibit novel features that are contrary to Newtonian expectations. In particular, ultrarelativistic jet clumps moving freely outward along the rotation axis strongly decelerate with respect to the ambient medium, while ultrarelativistic particles strongly accelerate in directions normal to the jet axis. The implications of these direct consequences of general relativity for jets in microquasars and the origin of the high-energy cosmic rays are briefly mentioned.

astro-ph↗

arXiv2005

Relativistic Motion of Spinning Particles in a Gravitational Field

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.

gr-qc↗

arXiv2005

A Gravitational Mechanism for the Acceleration of Ultrarelativistic Particles

Imagine a swarm of free particles near a point P outside a gravitating mass M and a free reference particle at P that is on a radial escape trajectory away from M. Relative to this reference particle and in a Fermi normal coordinate system constructed along its worldline, the particles in the swarm that move along the radial direction and are ultrarelativistic (that is, they have speeds above c/sqrt(2)) decelerate toward this terminal speed. On the other hand, the swarm particles that are ultrarelativistic and move in directions normal to the radial (jet) directions accelerate to almost the speed of light by the gravitational tidal force of the mass M. The implications of these effects as well as the influence of the higher-order terms on the tidal acceleration mechanism are investigated. The observational evidence in support of these general relativistic effects is briefly discussed.

astro-ph↗

arXiv2004

Tidal Dynamics of Relativistic Flows Near Black Holes

We point out novel consequences of general relativity involving tidal dynamics of ultrarelativistic relative motion. Specifically, we use the generalized Jacobi equation and its extension to study the force-free dynamics of relativistic flows near a massive rotating source. We show that along the rotation axis of the gravitational source, relativistic tidal effects strongly decelerate an initially ultrarelativistic flow with respect to the ambient medium, contrary to Newtonian expectations. Moreover, an initially ultrarelativistic flow perpendicular to the axis of rotation is strongly accelerated by the relativistic tidal forces. The astrophysical implications of these results for jets and ultrahigh energy cosmic rays are briefly mentioned.

astro-ph↗