arXiv subjects

Bahram Mashhoon

Publications and source records attributed to Bahram Mashhoon.

At least 55 records · Page 3Linked to original sources

arXiv2019

Quasinormal Modes of a Black Hole with Quadrupole Moment

We analytically determine the quasinormal mode (QNM) frequencies of a black hole with quadrupole moment in the eikonal limit using the light-ring method. The generalized black holes that are discussed in this work possess arbitrary quadrupole and higher mass moments in addition to mass and angular momentum. Static collapsed configurations with mass and quadrupole moment are treated in detail and the QNM frequencies associated with two such configurations are evaluated to linear order in the quadrupole moment. Furthermore, we touch upon the treatment of rotating systems. In particular, the generalized black hole that we consider for our extensive QNM calculations is a completely collapsed configuration whose exterior gravitational field can be described by the Hartle-Thorne spacetime [Astrophys. J. 153, 807-834 (1968)]. This collapsed system as well as its QNMs is characterized by mass $M$, quadrupole moment $Q$ and angular momentum $J$, where the latter two parameters are treated to first and second orders of approximation, respectively. When the quadrupole moment is set equal to the relativistic quadrupole moment of the corresponding Kerr black hole, $J^2/(Mc^2)$, the Hartle-Thorne QNMs reduce to those of the Kerr black hole to second order in angular momentum $J$. Using ringdown frequencies, one cannot observationally distinguish a generalized Hartle-Thorne black hole with arbitrary quadrupole moment from a Kerr black hole provided the dimensionless parameter given by $|QMc^2-J^2|c^2/(G^2M^4)$ is sufficiently small compared to unity.

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arXiv2018

Twisted Gravitational Waves of Petrov Type D

Twisted gravitational waves (TGWs) are nonplanar unidirectional Ricci-flat solutions of general relativity. Thus far only TGWs of Petrov type \emph{II} are implicitly known that depend on a solution of a partial differential equation and have wave fronts with negative Gaussian curvature. A special Petrov type \emph{D} class of such solutions that depends on an arbitrary function is explicitly studied in this paper and its Killing vectors are worked out. Moreover, we concentrate on two solutions of this class, namely, the Harrison solution and a simpler solution we call the $w$-metric and determine their Penrose plane-wave limits. The corresponding transition from a nonplanar TGW to a plane gravitational wave is elucidated.

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arXiv2018

Twisted Gravitational Waves

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts. It turns out, however, that GR also admits exact solutions representing gravitational waves propagating along a fixed direction that are nonplanar. The wave front is then nonuniform and the bundle of rays is twisted. We find a class of solutions representing nonplanar unidirectional gravitational waves and study some of the properties of these twisted waves.

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arXiv2017

Anisotropic Gravitational Collapse and Cosmic Jets

Consider a dynamic general relativistic spacetime in which the proper infinitesimal interval along one spatial coordinate direction decreases monotonically with time, while the corresponding intervals increase along other spatial directions. In a system undergoing such complete anisotropic collapse/expansion, we look for the formation of a cosmic double-jet configuration: free test particles in the ambient medium, relative to the collapsing system, gain energy from the gravitational field and asymptotically line up parallel and antiparallel to the direction of collapse such that their Lorentz factors approach infinity. A strong burst of electromagnetic radiation is expected to accompany this event if some of the free test particles carry electric charge. Previous work in this direction involved mainly Ricci-flat spacetimes; hence, we concentrate here on inhomogeneous perfect fluid spacetimes. We briefly explore the possible connection between these theoretical cosmic jets and astrophysical jets. We also discuss other general relativistic scenarios for the formation of cosmic jets.

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arXiv2016

Relativistic Gravity Gradiometry: The Mashhoon--Theiss Effect

In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an observer. The observer's 4-velocity vector defines its local temporal axis and its local spatial frame is defined by a set of three orthonormal nonrotating gyro directions. The general tidal matrix for the timelike geodesics of Kerr spacetime has been calculated by Marck\cite{Marck}. We are interested in the measured components of the curvature tensor along the inclined "circular" geodesic orbit of a test mass about a slowly rotating astronomical object of mass $M$ and angular momentum $J$. Therefore, we specialize Marck's results to such a "circular" orbit that is tilted with respect to the equatorial plane of the Kerr source. To linear order in $J$, we recover the Mashhoon--Theiss effect, which is due to a small denominator ("resonance") phenomenon involving the frequency of geodetic precession. The Mashhoon--Theiss effect shows up as a special long-period gravitomagnetic part of the relativistic tidal matrix. The physical interpretation of this effect is briefly discussed.

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arXiv2016

Nonlocal gravity: Conformally flat spacetimes

The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity in two-dimensional spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein's field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of nonlocal gravity.

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arXiv2015

Weitzenböck's Torsion, Fermi Coordinates and Adapted Frames

We study Weitzenböck's torsion and discuss its properties. Specifically, we calculate the measured components of Weitzenböck's torsion tensor for a frame field adapted to static observers in a Fermi normal coordinate system that we establish along the world line of an arbitrary accelerated observer in general relativity. A similar calculation is carried out in the standard Schwarzschild-like coordinates for static observers in the exterior Kerr spacetime; we then compare our results with the corresponding curvature components. Our work supports the contention that in the extended general relativistic framework involving both the Levi-Civita and Weitzenböck connections, curvature and torsion provide complementary representations of the gravitational field.

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arXiv2014

Peculiar velocities in dynamic spacetimes

We investigate the asymptotic behavior of peculiar velocities in certain physically significant time-dependent gravitational fields. Previous studies of the motion of free test particles have focused on the \emph{collapse scenario}, according to which a double-jet pattern with Lorentz factor $γ\to \infty$ develops asymptotically along the direction of complete gravitational collapse. In the present work, we identify a second \emph{wave scenario}, in which a single-jet pattern with Lorentz factor $γ\to \infty$ develops asymptotically along the direction of wave propagation. The possibility of a connection between the two scenarios for the formation of cosmic jets is critically examined.

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arXiv2013

Spin Precession in Inertial and Gravitational Fields

We discuss the motion of spin in inertial and gravitational fields. The coupling of spin with rotation and the gravitomagnetic field has already been extensively studied; therefore, we focus here on the inertial and gravitational spin-orbit couplings. In particular, we investigate the classical and quantum aspects of spin precession and spin-orbit coupling in an arbitrary translationally accelerated frame of reference as well as the exterior Schwarzschild spacetime. Moreover, in connection with Einstein's principle of equivalence, we clarify the relation between the inertial and gravitational spin-orbit couplings.

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arXiv2012

Nonlocal Special Relativity: Amplitude Shift in Spin-Rotation Coupling

The standard theory of relativity is based on the hypothesis of locality. The locality principle assumes that an object is affected only by its immediate surroundings and not by variables in the past. It follows that in standard relativity theory even wave properties are measured instantaneously. This contradicts the Bohr-Rosenfeld principle, according to which fields cannot be determined instantaneously. Nonlocal special relativity resolves the problem by taking past history into account. The current status of nonlocal electrodynamics is discussed and a new consequence of nonlocality, namely, a certain additional amplitude shift due to nonlocality in the spin-rotation coupling is presented.

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arXiv2012

Nonlocal Gravity

The analysis of measurements of accelerated observers in Minkowski spacetime has led to the development of nonlocal special relativity theory. Inertia and gravitation are intimately connected in accordance with the principle of equivalence. We therefore seek a nonlocal generalization of the theory of gravitation such that in the new theory the field equations are integro-differential equations for the local gravitational field. We show that it is possible to develop a nonlocal generalization of Einstein's theory of gravitation via the introduction of a scalar "constitutive" kernel in the teleparallel equivalent of general relativity. The resulting nonlocal theory is essentially equivalent to Einstein's theory plus "dark matter". That is, nonlocality simulates dark matter by introducing a new source term into general relativity. In the linear approximation for the nonlocal modification of Newtonian gravity, we recover the theoretical basis for the phenomenological Tohline-Kuhn modified gravity approach to the explanation of the astrophysical evidence for dark matter.

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arXiv2010

Necessity of Acceleration-Induced Nonlocality

The purpose of this paper is to explain clearly why nonlocality must be an essential part of the theory of relativity. In the standard local version of this theory, Lorentz invariance is extended to accelerated observers by assuming that they are pointwise inertial. This locality postulate is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic fields, as field properties in general cannot be measured instantaneously. The problem is corrected in nonlocal relativity by supplementing the locality postulate with a certain average over the past world line of the observer.

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arXiv2010

Tidal Dynamics in Cosmological Spacetimes

We study the relative motion of nearby free test particles in cosmological spacetimes, such as the FLRW and LTB models. In particular, the influence of spatial inhomogeneities on local tidal accelerations is investigated. The implications of our results for the dynamics of the solar system are briefly discussed. That is, on the basis of the models studied in this paper, we estimate the tidal influence of the cosmic gravitational field on the orbit of the Earth around the Sun and show that the corresponding temporal rate of variation of the astronomical unit is negligibly small.

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arXiv2010

Nonlocal Modification of Newtonian Gravity

The Newtonian regime of a recent nonlocal extension of general relativity (GR) is investigated. Nonlocality is introduced via a scalar "constitutive" kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of GR. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson's equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.

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arXiv2009

Nonlocal Transformations for Accelerated Observers

According to the locality postulate of special relativity, the measurements of physical fields by accelerated observers at a given event in Minkowski spacetime are related to each other by the representations of the Lorentz group. Nonlocal extensions of these representations are necessary, however, once acceleration-induced nonlocality is taken into account. The particular case of Dirac spinors is treated in detail and the corresponding nonlocal transformation group is studied.

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arXiv2009

Optics of Rotating Systems

Electrodynamics of rotating systems is expected to exhibit novel nonlocal features that come about when acceleration-induced nonlocality is introduced into the special relativity theory in conformity with the Bohr-Rosenfeld principle. The implications of nonlocality for the amplitude and frequency of electromagnetic radiation received by uniformly rotating observers are investigated.

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arXiv2009

A formal framework for a nonlocal generalization of Einstein's theory of gravitation

The analogy between electrodynamics and the translational gauge theory of gravity is employed in this paper to develop an ansatz for a nonlocal generalization of Einstein's theory of gravitation. Working in the linear approximation, we show that the resulting nonlocal theory is equivalent to general relativity with "dark matter". The nature of the predicted "dark matter", which is the manifestation of the nonlocal character of gravity in our model, is briefly discussed. It is demonstrated that this approach can provide a basis for the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.

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arXiv2009

Nonlocal Gravity Simulates Dark Matter

A nonlocal generalization of Einstein's theory of gravitation is constructed within the framework of the translational gauge theory of gravity. In the linear approximation, the nonlocal theory can be interpreted as linearized general relativity but in the presence of "dark matter" that can be simply expressed as an integral transform of matter. It is shown that this approach can accommodate the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.

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