arXiv subjects

B. Mashhoon

Publications and source records attributed to B. Mashhoon.

At least 19 recordsLinked to original sources

arXiv2025

G\"odel's Universe and the Local Limit of Nonlocal Gravity

We consider the G\"odel universe within the context of the local limit of nonlocal gravity. This theory differs from Einstein's general relativity (GR) through the existence of a scalar susceptibility function $S(x)$ that is a characteristic feature of the gravitational field and vanishes in the GR limit. We show that G\"odel's spacetime is a solution of the modified gravitational field equations provided $S$ is a constant, in conformity with the spatial homogeneity of the G\"odel universe.

gr-qc↗

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.

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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.

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arXiv2016

Virial Theorem in Nonlocal Newtonian Gravity

Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.

astro-ph.GA↗

arXiv2016

Mach's Principle and the Origin of Inertia

The current status of Mach's principle is discussed within the context of general relativity. The inertial properties of a particle are determined by its mass and spin, since these characterize the irreducible unitary representations of the inhomogeneous Lorentz group. The origin of the inertia of mass and intrinsic spin are discussed and the inertia of intrinsic spin is studied via the coupling of intrinsic spin with rotation. The implications of spin-rotation coupling and the possibility of history dependence and nonlocality in relativistic physics are briefly mentioned.

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.

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arXiv2014

Nonlocal General Relativity

A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenböck's torsion, and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. 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 dark matter, nonlocality is associated with a characteristic length scale of order 1 kpc. The confrontation of nonlocal gravity with observation is briefly discussed.

gr-qc↗

arXiv2014

Nonlocal Gravity: The General Linear Approximation

The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field equations is derived. The linear approximation of nonlocal gravity (NLG) is thoroughly examined and the solutions of the corresponding field equations are discussed. It is shown that nonlocality, with a characteristic length scale of order 1 kpc, simulates dark matter in the linear regime while preserving causality. Light deflection in linearized nonlocal gravity is studied in connection with gravitational lensing; in particular, the propagation of light in the weak gravitational field of a uniformly moving source is investigated. The astrophysical implications of the results are briefly mentioned.

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arXiv2014

Observational Tests of Nonlocal Gravity: Galaxy Rotation Curves and Clusters of Galaxies

A classical nonlocal generalization of Einstein's theory of gravitation has recently been developed via the introduction of a scalar causal "constitutive" kernel that must ultimately be determined from observational data. It turns out that the nonlocal aspect of gravity in this theory can simulate dark matter; indeed, in the Newtonian regime of nonlocal gravity, we recover the phenomenological Tohline-Kuhn approach to modified gravity. A simple generalization of the Kuhn kernel in the context of nonlocal general relativity leads to a two-parameter modified Newtonian force law that involves an additional repulsive Yukawa-type interaction. We determine the parameters of our nonlocal kernel by comparing the predictions of the theory with observational data regarding the rotation curves of spiral galaxies. The best-fitting stellar mass-to-light ratio turns out to be in agreement with astrophysical models; moreover, our results are consistent with the Tully-Fisher relation for spiral galaxies. Light deflection in nonlocal gravity is consistent with general relativity at Solar System scales, while beyond galactic scales an enhanced deflection angle is predicted that is compatible with lensing by the effective "dark matter". Furthermore, we extend our results to the internal dynamics of rich clusters of galaxies and show that the dynamical mass of the cluster obtained from nonlocal gravity is consistent with the measured baryonic mass.

astro-ph.GA↗

arXiv2013

Nonlocal Gravity: Damping of Linearized Gravitational Waves

In nonlocal general relativity, linearized gravitational waves are damped as they propagate from the source to the receiver in the Minkowski vacuum. Nonlocal gravity is a generalization of Einstein's theory of gravitation in which nonlocality is due to the gravitational memory of past events. That nonlocal gravity is dissipative is demonstrated in this paper within certain approximation schemes. The gravitational memory drag leads to the decay of the amplitude of gravitational waves given by the exponential damping factor exp (-t/τ), where $τ$ depends on the kernel of nonlocal gravity. The damping time $τ$ is estimated for gravitational waves of current observational interest and is found to be of the order of, or longer than, the age of the universe.

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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↗

arXiv2013

Observers in Spacetime and Nonlocality

Characteristics of observers in relativity theory are critically examined. For field measurements in Minkowski spacetime, the Bohr-Rosenfeld principle implies that the connection between actual (i.e., noninertial) and inertial observers must be nonlocal. Nonlocal electrodynamics of non-uniformly rotating observers is discussed and the consequences of this theory for the phenomenon of spin-rotation coupling are briefly explored.

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.

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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.

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arXiv2012

Mach, the Universe, and Foundations of Mechanics

Barbour's response to our recent paper on "Mach's principle and higher-dimensional dynamics" describes an approach to Mach's principle in which the universe as a whole is involved in the definition of inertial frames of reference. Moreover, Barbour's theoretical procedure is in agreement with general relativity for a finite universe that is spatially closed. However, we prefer an operational approach that relies ultimately on observational data.

gr-qc↗

arXiv2011

Mach's Principle and Higher-Dimensional Dynamics

We briefly discuss the current status of Mach's principle in general relativity and point out that its last vestige, namely, the gravitomagnetic field associated with rotation, has recently been measured for the earth in the GP-B experiment. Furthermore, in his analysis of the foundations of Newtonian mechanics, Mach provided an operational definition for inertial mass and pointed out that time and space are conceptually distinct from their operational definitions by means of masses. Mach recognized that this circumstance is due to the lack of any a priori connection between the inertial mass of a body and its Newtonian state in space and time. One possible way to improve upon this situation in classical physics is to associate mass with an extra dimension. Indeed, Einstein's theory of gravitation can be locally embedded in a Ricci-flat 5D manifold such that the 4D energy-momentum tensor appears to originate from the existence of the extra dimension. An outline of such a 5D Machian extension of Einstein's general relativity is presented.

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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.

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