scholarly journals The post - Newtonian rotation of Earth: a first approach

1988 ◽  
Vol 128 ◽  
pp. 341-347
Author(s):  
J. Schastok ◽  
M. Soffel ◽  
H. Ruder ◽  
M. Schneider
Keyword(s):  
Angular Momentum ◽  
Rotational Motion ◽  
Symmetric Model ◽  
Free Precession ◽  
Axially Symmetric ◽  
Relativistic Description ◽  
Theories Of Gravity ◽  
Momentum Complex ◽  
Tensor Of Inertia ◽  
Corotating Frame

The problems of dynamics of extended bodies in metric theories of gravity are reviewed. In a first approach towards the relativistic description of the Earth's rotational motion the post - Newtonian treatment of the free precession of a pseudo - rigid and axially symmetric model Earth is presented. Definitions of angular momentum, pseudo - rigidity, the corotating frame, tensor of inertia and axial symmetry of the rotating body are based upon the choice of the standard post - Newtonian (PN) coordinates and the full PN energy momentum complex. In this framework, the relation between angular momentum and angular (coordinate) velocity is obtained. Since the PN Euler equations for the angular velocity here formally take their usual Newtonian form it is concluded that apart from PN modifications (renormalizations) of the inertia tensor, the rotational motion of our pseudo - rigid and axially symmetric model Earth essentially is “Newtonian”.

scholarly journals Effects of magnetic field on the runaway instability of relativistic accretion tori near a rotating black hole

2013 ◽  
Vol 9 (S303) ◽  
pp. 424-426
Author(s):  
V. Karas ◽  
J. Hamerský
Keyword(s):  
Magnetic Field ◽  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Radial Profile ◽  
Symmetric Model ◽  
Axially Symmetric ◽  
Central Black Hole ◽  
Self Gravity

AbstractRunaway instability operates in accretion tori around black holes, where it affects systems close to the critical (cusp overflowing) configuration. The runaway effect depends on the radial profile l(R) of the angular momentum distribution of the fluid, on the dimension-less spin a of the central black hole (|a| ≤ 1), and other factors, such as self-gravity. Here we discuss the role of runaway instability within a framework of an axially symmetric model of perfect fluid endowed with a purely toroidal magnetic field.

scholarly journals CHARGED AXIALLY SYMMETRIC SOLUTION, ENERGY AND ANGULAR MOMENTUM IN TETRAD THEORY OF GRAVITATION

2006 ◽  
Vol 21 (15) ◽  
pp. 3181-3197 ◽  
Author(s):  
GAMAL G. L. NASHED
Keyword(s):  
Angular Momentum ◽  
Symmetric Solution ◽  
Vector Fields ◽  
Momentum Density ◽  
Relativity Theory ◽  
Axially Symmetric ◽  
Theory Of Gravitation ◽  
Charge Parameter ◽  
Momentum Complex ◽  
Tetrad Theory

Charged axially symmetric solution of the coupled gravitational and electromagnetic fields in the tetrad theory of gravitation is derived. The metric associated with this solution is an axially symmetric metric which is characterized by three parameters "the gravitational mass M, the charge parameter Q and the rotation parameter a." The parallel vector fields and the electromagnetic vector potential are axially symmetric. We calculate the total exterior energy. The energy–momentum complex given by Møller in the framework of the Weitzenböck geometry "characterized by vanishing the curvature tensor constructed from the connection of this geometry" has been used. This energy–momentum complex is considered as a better definition for calculation of energy and momentum than those of general relativity theory. The energy contained in a sphere is found to be consistent with pervious results which is shared by its interior and exterior. Switching off the charge parameter, one finds that no energy is shared by the exterior of the charged axially symmetric solution. The components of the momentum density are also calculated and used to evaluate the angular momentum distribution. We found no angular momentum contributes to the exterior of the charged axially symmetric solution if zero charge parameter is used.

Correlation Between LDA and Ultrasound Heart Catheter Measurements in a Stenosed Arterial Model

1995 ◽  
Vol 117 (1) ◽  
pp. 103-106 ◽  
Author(s):  
D. Liepsch ◽  
A. Poll ◽  
R. Blasini
Keyword(s):  
Cross Section ◽  
Laser Doppler Anemometry ◽  
Water Solution ◽  
Maximum Velocity ◽  
Symmetric Model ◽  
Axially Symmetric ◽  
Flow Conditions ◽  
Future Studies ◽  
Glycerine Water ◽  
Arterial Model

Ultrasound heart catheters are used to measure the velocity in coronary arteries. However, the act of introducing a catheter into the vessel disturbs the very flow being measured. We used laser Doppler anemometry to measure the velocity distribution in an axially symmetric model, both with and without a catheter inserted. The catheter reduced the center-line velocity by as much as 60 percent at a distance of 2 mm downstream from the catheter, and by as much as 25 percent at a distance of 10 mm. This means the velocity measured with an ultrasound catheter does not show the maximum velocity of the undisturbed flow in the tube center. In the constriction, however, the measured velocities with the LDA and ultrasound catheter are almost the same. Thus, catheter measurements in the stenosis achieve accurate results. The velocity profile in the stenosed areas is flattened over nearly the whole cross section. The velocity is extremely reduced only close to the wall. The measurements outside of the stenosis lead to large differences which need to be studied carefully in the future. The disturbed flow finally disappeared 15 mm downstream of the catheter. The measurements were done at steady flow using a glycerine water solution with a dynamic viscosity of 4.35m Pas. In future studies, these experiments will be repeated for pulsatile flow conditions using non-Newtonian blood-like fluids.

Influence of Heat Insulation Material on Thermal Stress of Long Nozzle

2012 ◽  
Vol 535-537 ◽  
pp. 1609-1614 ◽  
Author(s):  
Hui Min Liu
Keyword(s):  
Thermal Stress ◽  
Layer Thickness ◽  
Outer Layer ◽  
Heat Insulation ◽  
Outer Wall ◽  
Symmetric Model ◽  
Insulation Material ◽  
Axially Symmetric ◽  
Coefficient Of Thermal Conductivity ◽  
Heat Insulation Material

To prevent a long nozzle (LN) of non-preheating from rupture caused by thermal shock, heat insulation material (HIM) with a lower coefficient of thermal conductivity (CTC) was compounded in the inner hole (inner layer) or around the outer wall (outer layer), and the thermal stress was investigated. The two-dimension axially symmetric model of LN was proposed by simplifying the structure and boundary conditions. The influences of the HIM to the thermal stress of LN were analyzed by finite element method. The results show that the thermal stress suffered by LN can be drastically reduced by the inner layer, making the slow variation, but when its thickness increases from 2 mm to 3 mm, it almost has no influence on the thermal stress. The maximum thermal stress at the neck of LN reduces with the depression of the CTC at the inner layer thickness of 2 mm. The maximum thermal stress of LN can’t be reduced by outer layer, but the lasting time of higher stress can be shortened, and the thermal stress at the later period of steel-irrigating can be lowed. When the outer layer thickness is more than 2 mm, the increase of it has little influence on the thermal stress of LN, and the change of its CTC has little influence on the thermal stress either. The LN with tri-layer has lower thermal stress during all the period of steel-irrigating.

MØLLER ENERGY–MOMENTUM COMPLEX FOR HIGHER-DIMENSIONAL SPHERICALLY SYMMETRIC SPACETIME IN GENERAL RELATIVITY

2012 ◽  
Vol 27 (40) ◽  
pp. 1250231 ◽  
Author(s):  
HÜSNÜ BAYSAL
Keyword(s):  
General Relativity ◽  
Momentum Density ◽  
Momentum Tensor ◽  
Symmetric Model ◽  
Spherically Symmetric ◽  
Higher Dimensional ◽  
Energy And Momentum ◽  
Momentum Complex ◽  
Spherically Symmetric Metric ◽  
Spherically Symmetric Model

We have calculated the total energy–momentum distribution associated with (n+2)-dimensional spherically symmetric model of the universe by using the Møller energy–momentum definition in general relativity (GR). We have found that components of Møller energy and momentum tensor for given spacetimes are different from zero. Also, we are able to get energy and momentum density of various well-known wormholes and black hole models by using the (n+2)-dimensional spherically symmetric metric. Also, our results have been discussed and compared with the results for four-dimensional spacetimes in literature.

Axially Symmetric Model Planetary Nebulae

1970 ◽  
Vol 162 ◽  
pp. 33 ◽  
Author(s):  
Ronald C. Kirkpatrick
Keyword(s):  
Planetary Nebulae ◽  
Symmetric Model ◽  
Axially Symmetric

scholarly journals Transonic accretion and winds around Pseudo-Kerr black holes andcomparison with general relativistic solutions

2022 ◽  
Author(s):  
Abhrajit Bhattacharjee ◽  
Sandip Kumar Chakrabarti ◽  
Dipak Debnath
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Time Scale ◽  
Momentum Equation ◽  
Accretion Flows ◽  
Timing Properties ◽  
Surrounding Space ◽  
General Relativistic ◽  
Corotating Frame

Abstract Spectral and timing properties of accretion flows on a black hole depend on their density and temperature distributions, which, in turn come from the underlying dynamics. Thus, an accurate description of the flow which includes hydrodynamics and radiative transfer is a must to interpret the observational results. In the case of non-rotating black holes, Pseudo- Newtonian description of surrounding space-time enables one to make a significant progress in predicting spectral and timing properties. This formalism is lacking for the spinning black holes. In this paper, we show that there exists an exact form of ‘natural’ potential derivable from the general relativistic (GR) radial momentum equation written in the local corotating frame. Use of this potential in an otherwise Newtonian set of equations, allows us to describe transonic flows very accurately as is evidenced by comparing with solutions obtained from the full GR framework. We study the properties of the sonic points and the centrifugal pressure supported shocks in the parameter space spanned by the specific energy and the angular momentum, and compare with the results of GR hydrodynamics. We show that this potential can safely be used for the entire range of Kerr parameter −1 < a < 1 for modeling of observational results around spinning black holes. We assume the flow to be inviscid. Thus, it is non-dissipative with constant energy and angular momentum. These assumptions are valid very close to the black hole horizon as the infall time scale is much shorter as compared to the viscous time scale.

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