scholarly journals Carter constant and angular momentum

2017 ◽  
Vol 27 (01) ◽  
pp. 1750180 ◽  
Author(s):  
Sajal Mukherjee ◽  
K. Rajesh Nayak
Keyword(s):  
Angular Momentum ◽  
Kerr Solution ◽  
Newtonian Mechanics ◽  
Axially Symmetric ◽  
Missing Link ◽  
Symmetric Spacetimes ◽  
Dipolar Potential ◽  
Carry Over ◽  
Definition Of ◽  
Special Case

We investigate the Carter-like constant in the case of a particle moving in a nonrelativistic dipolar potential. This special case is a missing link between the Carter constant in stationary and axially symmetric spacetimes (SASS) such as Kerr solution and its possible Newtonian counterpart. We use this system to carry over the definition of angular momentum from the Newtonian mechanics to the relativistic SASS.

scholarly journals TELEPARALLEL ENERGY–MOMENTUM DISTRIBUTION OF STATIC AXIALLY SYMMETRIC SPACETIMES

2008 ◽  
Vol 23 (37) ◽  
pp. 3167-3177 ◽  
Author(s):  
M. SHARIF ◽  
M. JAMIL AMIR
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Momentum Distribution ◽  
Coupling Constant ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Teleparallel Theory ◽  
Theory Of Gravity ◽  
Comparison Of The Results ◽  
Special Case

This paper is devoted to discuss the energy–momentum for static axially symmetric spacetimes in the framework of teleparallel theory of gravity. For this purpose, we use the teleparallel versions of Einstein, Landau–Lifshitz, Bergmann and Möller prescriptions. A comparison of the results shows that the energy density is different but the momentum turns out to be constant in each prescription. This is exactly similar to the results available in literature using the framework of general relativity. It is mentioned here that Möller energy–momentum distribution is independent of the coupling constant λ. Finally, we calculate energy–momentum distribution for the Curzon metric, a special case of the above-mentioned spacetime.

CENTER OF MASS AND SPIN FOR AXIALLY SYMMETRIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 717-728 ◽  
Author(s):  
CARLOS KOZAMEH ◽  
RAUL ORTEGA ◽  
TERESITA ROJAS
Keyword(s):  
Angular Momentum ◽  
Gravitational Radiation ◽  
Total Angular Momentum ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Axially Symmetric ◽  
Symmetric Spacetimes ◽  
Intrinsic Angular Momentum

We give equations of motion for the center of mass and intrinsic angular momentum of axially symmetric sources that emit gravitational radiation. This symmetry is used to uniquely define the notion of total angular momentum. The center of mass then singles out the intrinsic angular momentum of the system.

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

Introductory Rotational Dynamics

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Angular Momentum ◽  
Angular Displacement ◽  
Rigid Bodies ◽  
Rotational Dynamics ◽  
Circular Motion ◽  
Uniform Rotation ◽  
Chemical Systems ◽  
Inertial Frames ◽  
Rotating Frames ◽  
Special Case

This chapter discusses the importance of circular motion and rotations, whose applications to chemical systems are plentiful. Circular motion is the book’s first example of a special case of motion using the laws developed in previous chapters. The chapter begins with the basic definitions of circular motion; as uniform rotation around a principle axis is much easier to consider, it is the focus of this chapter and is used to develop some key ideas. The chapter discusses angular displacement, angular velocity, angular momentum, torque, rigid bodies, orbital and spin momenta, inertia tensors and non-inertial frames and explores fictitious forces as well as transformations in rotating frames.

scholarly journals On the Bean critical-state model in superconductivity

1996 ◽  
Vol 7 (3) ◽  
pp. 237-247 ◽  
Author(s):  
L. Prigozhin
Keyword(s):  
Variational Inequalities ◽  
Critical State ◽  
Existence And Uniqueness ◽  
Critical State Model ◽  
Type Ii ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Uniqueness Of The Solution ◽  
Type Ii Superconductivity ◽  
Special Case

We consider two-dimensional and axially symmetric critical-state problems in type-II superconductivity, and show that these problems are equivalent to evolutionary quasi-variational inequalities. In a special case, where the inequalities become variational, the existence and uniqueness of the solution are proved.

scholarly journals The Structure of n Harmonic Points and Generalization of Desargues’ Theorems

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1018
Author(s):  
Xhevdet Thaqi ◽  
Ekrem Aljimi
Keyword(s):  
Fourth Harmonic ◽  
New Findings ◽  
Rank 2 ◽  
Definition Of ◽  
Special Case

: In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n = 4) of the sets of H-points of rank 2, which is indicated by P42.

scholarly journals Launch Velocities in Successful Golf Putting: An Analytical Analysis

2017 ◽  
Vol 5 (2) ◽  
pp. 24
Author(s):  
John F. Mahoney ◽  
Daniel P. Connaughton
Keyword(s):  
Critical Value ◽  
Theoretical Studies ◽  
Newtonian Mechanics ◽  
Ambient Conditions ◽  
Analytical Analysis ◽  
Bouncing Ball ◽  
Golf Putting ◽  
A Value ◽  
Special Case

Background: This study is concerned with the special case of a putted ball intersecting a standard golf hole at its diameter. The velocity of the ball at the initial rim of the hole is termed the launch velocity and depending upon its value the ball may either be captured or it may escape capture by jumping over the hole. The critical value of the launch velocity (V) is such that lesser values result in capture while greater values produce escape. Purpose: Since the value of the V entered prominently in some theoretical studies of putting, the aim of the current study is to provide an original re-evaluation of V and to contrast our results with existing results. Method: This analytical analysis relies on trigonometry in conjunction with Newtonian mechanics and the mathematics of projectiles. The results of a recent study into the mathematics of a bouncing ball which included the notions of restitution and friction were also employed in the analysis. Results: If bouncing and slipping do not occur when the ball hits the far rim of the hole our analysis produces a value of V of 1.356 m/s. When bouncing and slipping are present we find that V is at least 1.609 m/s but increases beyond this value as slipping and friction become greater. Useful relations which relate the dynamics and geometry of the ball to V are provided. Conclusion: Since ambient conditions may influence the extent of bounce and slippage we conjecture that the value of V is not unique.

An Overview of the Proof

2019 ◽  
pp. 3-22
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Motivic Cohomology ◽  
Norm Residue ◽  
Cohomology Operations ◽  
Definition Of ◽  
Special Case

This chapter provides the main steps in the proof of Theorems A and B regarding the norm residue homomorphism. It also proves several equivalent (but more technical) assertions in order to prove the theorems in question. This chapter also supplements its approach by defining the Beilinson–Lichtenbaum condition. It thus begins with the first reductions, the first of which is a special case of the transfer argument. From there, the chapter presents the proof that the norm residue is an isomorphism. The definition of norm varieties and Rost varieties are also given some attention. The chapter also constructs a simplicial scheme and introduces some features of its cohomology. To conclude, the chapter discusses another fundamental tool—motivic cohomology operations—as well as some historical notes.

Computer Simulations

2019 ◽  
pp. 9-20
Author(s):  
Paul Humphreys
Keyword(s):  
Computer Simulation ◽  
Numerical Methods ◽  
Computer Simulations ◽  
Scientific Progress ◽  
Computational Science ◽  
Working Definition ◽  
Mathematical Techniques ◽  
Definition Of ◽  
Special Case ◽  
Numerical Treatments

The need to solve analytically intractable models has led to the rise of a new kind of science, computational science, of which computer simulations are a special case. It is noted that the development of novel mathematical techniques often drives scientific progress and that even relatively simple models require numerical treatments. A working definition of a computer simulation is given and the relation of simulations to numerical methods is explored. Examples where computational methods are unavoidable are provided. Some epistemological consequences for philosophy of science are suggested and the need to take into account what is possible in practice is emphasized.

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