scholarly journals Slowly rotating neutron stars in scalar torsion theory

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Hamza Boumaza
Keyword(s):  
Equations Of State ◽  
Equations Of Motion ◽  
Specific Model ◽  
Torsion Theory ◽  
Moment Of Inertia ◽  
Radial Coordinate ◽  
Universal Relation ◽  
Slow Rotation ◽  
Axially Symmetric ◽  
Symmetric Spacetime

AbstractIn this present paper, a slowly rotating stat is investigated in shift symmetric scalar torsion theory framework using a nondiagonal tetrad that gives an axially symmetric spacetime. We present the general equations for a general Lagrangian in a spherical symmetric space time and then in an axially symmetric spacetime. The obtained equations will allow us to study the behaviour of a specific model at the center of the star and at large distance. We find that this particular model affects the behaviour at the center but it is not case for large value of the radial coordinate r. The integration of the equations of motion, for different realistic equations of state (EoS), confirms that the mass, the radius as well as the moment of inertia are effected by varying the parameters of the model. Finally, we examine the universal relation of normalized moment of inertia and the stellar compactness of neutron star in slow rotation approximation. We showed that for all values of parameters present in the model leads to a deviation from GR for all EoS with a relative deviation below $$10\%$$ 10 % .

CHARGED PARTICLE DYNAMICS IN THE FIELD OF A SLOWLY ROTATING COMPACT STAR

2005 ◽  
Vol 14 (03n04) ◽  
pp. 609-620 ◽  
Author(s):  
BABUR M. MIRZA
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Compact Star ◽  
Equations Of Motion ◽  
Geodesic Equation ◽  
Slow Rotation ◽  
Axially Symmetric ◽  
Kerr Spacetime ◽  
Frame Dragging ◽  
Set Up

We study the dynamics of a charged particle in the field of a slowly rotating compact star in the gravitoelectromagnetic approximation to the geodesic equation. The star is assumed to be surrounded by an ideal, highly conducting plasma (taken as a magneto-hydrodynamic fluid) with a stationary, axially symmetric electromagnetic field. The general relativistic Maxwell equations are solved to obtain the effects of the background spacetime on the electromagnetic field in the linearized Kerr spacetime. The equations of motion are then set up and solved numerically to incorporate the gravitational as well as the electromagnetic effects. The analysis shows that in the slow rotation approximation, the frame dragging effects on the electromagnetic field are absent. However the particle is directly effected by the rotating gravitational source such that close to the star the gravitational and electromagnetic field produce contrary effects on the particle trajectories.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

Non-Newtonian effects in axially symmetric oscillatory flows of some elastico-viscous liquids

1970 ◽  
Vol 68 (3) ◽  
pp. 731-750 ◽  
Author(s):  
J. R. Jones
Keyword(s):  
Elastic Properties ◽  
Equations Of State ◽  
Time Lag ◽  
Physical Constant ◽  
Oscillatory Motion ◽  
Axially Symmetric ◽  
Metric Tensor ◽  
Oscillatory Flows ◽  
Viscous Liquids ◽  
Deformation Stress

In (general) elastico-viscous liquids the response to stress at any instant will depend on previous rheological history, the equations of state needed to describe the rheological properties of a typical material element at any instant t being expressible in the form of a (properly invariant†) set of integro-differential equations relating its deformation, stress and temperature histories (as defined by a metric tensor (of a convected frame of reference), a stress tensor and the temperature measured in the element as functions of previous time t'( < t)) together with the time lag (t – t') and physical constant tensors associated with the element (1). Thus in any type of oscillatory motion a rheological history will necessarily be a function of the frequency of the forcing agent, the rheological history of a number of different types of elastico-viscous liquids in some simple shearing oscillatory flows being a rather simple oscillatory history (see, for example, (2–4)). It is, therefore, to be expected that a liquid with elastic properties will behave somewhat differently from any inelastic viscous liquid when subjected to any kind of oscillatory motion, and it is for this reason that oscillatory motions have been used extensively to detect and measure the elastic properties of liquids (see, for example, (2–5)).

A Project in the Determination of the Moment of Inertia

2005 ◽  
Vol 33 (4) ◽  
pp. 319-338
Author(s):  
Ron P. Podhorodeski ◽  
Paul Sobejko
Keyword(s):  
Dynamic Properties ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Moment Of Inertia ◽  
Educational Goal ◽  
Centre Of Mass ◽  
Comparison Of Results ◽  
Physical Testing ◽  
The Moment

Analysis of the forces involved in mechanical systems requires an understanding of the dynamic properties of the system's components. In this work, a project on the determination of both the location of the centre of mass and inertial properties is described. The project involves physical testing, the proposal of approximate models, and the comparison of results. The educational goal of the project is to give students and appreciation of second mass moments and the validity of assumptions that are often applied in component modelling. This work reviews relevant equations of motion and discusses techniques to determine or estimate the centre of mass and second moment of inertia. An example project problem and solutions are presented. The value of such project problems within a first course on the theory of mechanisms is discussed.

scholarly journals Exact Axially Symmetric Solution inf(T)Gravity Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Vacuum Solution ◽  
Gravity Theory ◽  
Kerr Metric ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Kerr Spacetime ◽  
Euler’S Angles

A general tetrad field with sixteen unknown functions is applied to the field equations off(T)gravity theory. An analytic vacuum solution is derived with two constants of integration and an angleΦthat depends on the angle coordinateϕand radial coordinater. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.

Pitching Dynamic Response of Variable Sweep Wing Aircraft

2012 ◽  
Vol 197 ◽  
pp. 159-163 ◽  
Author(s):  
Lai Bin Xu ◽  
Shu Xing Yang ◽  
Bo Mo
Keyword(s):  
Dynamic Response ◽  
Flight Control ◽  
Equations Of Motion ◽  
Center Of Gravity ◽  
Moment Of Inertia ◽  
Morphing Wing ◽  
Wing Morphing

The dynamic response of Variable Sweep Wing Aircraft (VSWA) with the wing sweeping is presented. The center of gravity (cg) of the aircraft, location of each wing partition , and moment of inertia alter significantly due to the wing morphing, resulting in considerably change of the dynamics of the aircraft. The extended equations of motion (EOMs) suitable for morphing wing aircraft are derived. Compared with the traditional EOMs, there are 4 additional forces and moments exhibiting in the extended EOMs due to the wing morphing. The results show that the additional forces and moments can affect the flight control considerably.

Longitudinal Wave Propagation in a Circular Bar Loaded Suddenly by a Radially Distributed End Stress

1969 ◽  
Vol 36 (3) ◽  
pp. 470-478 ◽  
Author(s):  
L. W. Kennedy ◽  
O. E. Jones
Keyword(s):  
Wave Propagation ◽  
Longitudinal Wave ◽  
Numerical Technique ◽  
Axial Stress ◽  
Equations Of Motion ◽  
Propagation Distance ◽  
Radial Dependence ◽  
Radial Coordinate ◽  
Longitudinal Wave Propagation ◽  
Loading Parameter

Transient longitudinal wave propagation in a semi-infinite, circular, elastic bar loaded by a radially distributed pressure-step end stress is investigated on the basis of the exact equations of motion. The stress applied to the end of the bar has a radial dependence which can be continuously varied, by means of a loading parameter, from a uniform distribution to a load concentrated at the bar axis. Both analytical and numerical techniques are employed to obtain a complete description of the pulse head strain (ezz + eθθ), as a function of the nonuniformity of the loading, the radial coordinate, the distance from the bar end, and time. The analytic solution, which is valid asymptotically at large distances from the bar end, describes the first mode and shows only very small effects from even a high degree of radial nonuniformity in the applied stress. Near the bar end, solutions for (ezz + eθθ) and the axial stress τzz are obtained by direct numerical integration of the equations of motion. Good agreement between the numerical and analytic results at a propagation distance of 20 dia demonstrates the accuracy of the numerical technique. At distances less than 20 dia from the bar end, the effect of increasing the nonuniformity of the end loading is to greatly enhance the contributions of the higher modes, especially at the bar axis. With regard to a dynamic Saint Venant’s principle, differences in average dynamic stresses and strains resulting from statically equivalent but different radial end stress distributions are negligible at distances greater than 5 bar dia from the end. Differences in peak values are insignificant only at distances greater than 20 bar dia from the end.

scholarly journals Dependence of acoustic surface gravity on geometric configuration of matter for axially symmetric background flows in the Schwarzschild metric

2015 ◽  
Vol 24 (14) ◽  
pp. 1550096 ◽  
Author(s):  
Pratik Tarafdar ◽  
Tapas K. Das
Keyword(s):  
Black Holes ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Equations Of State ◽  
Initial Boundary ◽  
Stationary Flow ◽  
Geometric Configuration ◽  
Surface Gravity ◽  
Axially Symmetric ◽  
Schwarzschild Metric

In black hole evaporation process, the mass of the hole anti-correlates with the Hawking temperature. This indicates that the smaller holes have higher surface gravity. For analogue Hawking effects, however, the acoustic surface gravity is determined by the local values of the dynamical velocity of the stationary background fluid flow and the speed of propagation of the characteristic perturbation embedded in the background fluid, as well as by their space derivatives evaluated along the direction normal to the acoustic horizon, respectively. The mass of the analogue system — whether classical or quantum — does not directly contribute to extremize the value of the associated acoustic surface gravity. For general relativistic axially symmetric background fluid flow in the Schwarzschild metric, we show that the initial boundary conditions describing such accretion influence the maximization scheme of the acoustic surface gravity and associated analogue temperature. Aforementioned background flow onto black holes can assume three distinct geometric configurations. Identical set of initial boundary conditions can lead to entirely different phase-space behavior of the stationary flow solutions, as well as the salient features of the associated relativistic acoustic geometry. This implies that it is imperative to investigate how the measure of the acoustic surface gravity corresponding to the accreting black holes gets influenced by the geometric configuration of the inflow described by various thermodynamic equations of state. Such investigation is useful to study the effect of Einstenian gravity on the nonconventional classical features as observed in Hawking like effect in a dispersive medium in the limit of a strong dispersion relation.

scholarly journals GRAVITATIONAL FIELD OF A ROTATING GRAVITATIONAL DYON

2002 ◽  
Vol 17 (15n17) ◽  
pp. 1091-1096 ◽  
Author(s):  
N. DADHICH ◽  
Z. YA. TURAKULOV
Keyword(s):  
Gravitational Field ◽  
Gordon Equation ◽  
Equations Of Motion ◽  
Polar Angle ◽  
Vacuum Equation ◽  
Axially Symmetric ◽  
Einstein Vacuum Equation ◽  
Einstein Vacuum ◽  
Klein Gordon ◽  
Hamilton Jacobi Equation

We have obtained the general solution of the Einstein vacuum equation for the axially symmetric stationary metric in which both the Hamilton-Jacobi equation for particle motion and the Klein - Gordon equation are separable. It can be interpreted to describe the gravitational field of a rotating dyon, a particle endowed with both gravoelectric (mass) and gravomagnetic (NUT parameter) charges. Further, there also exists a duality relation between the two charges and the radial and the polar angle coordinates which keeps the solution invariant. The solution can however be transformed into the known Kerr - NUT solution indicating its uniqueness under the separability of equations of motion.

Kerr–Newman solution in modified teleparallel theory of gravity

2014 ◽  
Vol 24 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Gamal G. L. Nashed
Keyword(s):  
Azimuthal Angle ◽  
Polar Angle ◽  
Radial Coordinate ◽  
Lorentz Transformations ◽  
Square Root ◽  
Axially Symmetric ◽  
Field Equations ◽  
Tetrad Field ◽  
Teleparallel Theory ◽  
Theory Of Gravity

A nondiagonal tetrad field having six unknown functions plus an angle Φ, which is a function of the radial coordinate r, azimuthal angle θ and the polar angle ϕ, is applied to the charged field equations of modified teleparallel theory of gravity. A special nonvacuum solution is derived with three constants of integration. The tetrad field of this solution is axially symmetric and its scalar torsion is constant. The associated metric of the derived solution gives Kerr–Newman spacetime. We have shown that the derived solution can be described by a local Lorentz transformations plus a diagonal tetrad field that is the square root of the Kerr–Newman metric. We show that any solution of general relativity (GR) can be a solution in f(T) under certain conditions.

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