A class of exact interior solutions of the Einstein-Maxwell equations

1977 ◽  
Vol 353 (1675) ◽  
pp. 523-531 ◽  
Keyword(s):  
Angular Velocity ◽  
Laplace Equation ◽  
Maxwell Equations ◽  
Flat Space ◽  
Stationary Solutions ◽  
Constant Angular Velocity ◽  
Arbitrary Solution ◽  
Charged Matter ◽  
Axis Of Symmetry ◽  
Interior Solutions

A class of exact interior stationary solutions of the Einstein-Maxwell equations is found in terms of an arbitrary solution of the flat-space Laplace equation. These solutions represent pressure-free charged matter rotating with constant angular velocity about an axis of symmetry. Some properties of the solution are discussed.

scholarly journals ON MAGNETIC FIELDS IN ROTATING NUCLEAR MATTER CORES OF STELLAR DIMENSIONS

2012 ◽  
Vol 12 ◽  
pp. 58-67 ◽  
Author(s):  
KUANTAY BOSHKAYEV ◽  
MICHAEL ROTONDO ◽  
REMO RUFFINI
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Charge Distribution ◽  
Constant Angular Velocity ◽  
Classical Electrodynamics ◽  
Neutral System ◽  
Nuclear Density ◽  
Axis Of Symmetry ◽  
A Charge ◽  
The Magnetic Field

We consider a degenerate globally neutral system of stellar dimensions consisting of Nn neutrons, Np protons and Ne electrons in beta equilibrium. Such a system at nuclear density having mass numbers A ≈ 1057 can exhibit a charge distribution different from zero. We present the analysis in the framework of classical electrodynamics to investigate the magnetic field induced by this charge distribution when the system is allowed to rotate as a whole rigid body with constant angular velocity around the axis of symmetry.

Mathematical modeling of Couette flow in anomalous thermoviscous liquid

2011 ◽  
Vol 8 (1) ◽  
pp. 143-152
Author(s):  
S.F. Khizbullina
Keyword(s):  
Mathematical Modeling ◽  
Angular Velocity ◽  
Numerical Experiment ◽  
Temperature Dependence ◽  
Steady Flow ◽  
Couette Flow ◽  
Outer Cylinder ◽  
Flow Regimes ◽  
Constant Angular Velocity ◽  
Coaxial Cylinders

The steady flow of anomalous thermoviscous liquid between the coaxial cylinders is considered. The inner cylinder rotates at a constant angular velocity while the outer cylinder is at rest. On the basis of numerical experiment various flow regimes depending on the parameter of viscosity temperature dependence are found.

The Swimming of Nymphon Gracile (Pyconogonida)

1971 ◽  
Vol 55 (1) ◽  
pp. 273-287
Author(s):  
ELFED MORGAN
Keyword(s):  
Angular Velocity ◽  
Hydrodynamic Force ◽  
Beat Frequency ◽  
High Elevation ◽  
Dorsal Side ◽  
Constant Angular Velocity ◽  
Power Stroke ◽  
Lateral Thrust ◽  
Constant Depth ◽  
Recovery Stroke

1. The organization of the swimming legs of N. gracile has been described. The legs beat ventrally so the animal swims with the dorsal side foremost. The joints between the major segments of the leg are extended for most of the power stroke, but the distal segments articulate sequentially later in the beat, commencing with the flexion of the femoro-tibial joint at the end of the power stroke. Continued flexion reduces the leg radius considerably during the recovery stroke. 2. Animals swimming at constant depth were found to have a leg-beat frequency of about 1 beat/s. Above this the rate of ascent increased rapidly with increasing frequency of beat. Abduction or adduction of the leg usually occurred prior to the start of the power stroke with the femur in the elevated position. 3. Assuming a fixed limb profile at constant angular velocity, maximum lift was calculated to have occurred with the femur inclined at an angle of about 50° to the dorso-ventral body axis. The outward component of the lateral thrust decreased to zero at this point, and with further declination of the femur the lateral forces became inwardly directed. Of the different segments of the leg, tibia 2 and the tarsus and propodium contribute most of the hydrodynamic force. 4. The angular velocity of the leg varied during the power stroke, and the actual forces generated during two beats having the same amplitude and angular velocity but of high and low elevation were calculated. Greater lift occurred during the high-elevation beat when the leg continued to provide lift throughout the power stroke, whereas the low-elevation beat acquired negative lift values towards the end of the power stroke. The lateral thrust was now directed entirely inwards.

The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body

2018 ◽  
Vol 277 ◽  
pp. 168-177
Author(s):  
Mykhailo Berdnyk
Keyword(s):  
Temperature Field ◽  
Dirichlet Problem ◽  
Heat Exchange ◽  
Angular Velocity ◽  
Integral Transformation ◽  
Mathematic Model ◽  
Constant Angular Velocity ◽  
Temperature Fields ◽  
Finite Velocity ◽  
Finite Space

It is the first generalized 3D mathematic model, which is created for calculating temperature fields in the empty isotropic rotary body, which is restricted by end surfaces and lateral surface of rotation and rotates with constant angular velocity around the axis OZ, with taking into account finite velocity of the heat conductivity in the form of the Dirichlet problem. In this work, an integral transformation was formulated for the 2D finite space, with the help of which a temperature field in the empty isotropic rotary body was determined in the form of convergence series by the Fourier functions.

Some Dynamical Characteristics of Propellers

1934 ◽  
Vol 38 (288) ◽  
pp. 987-997
Author(s):  
J. Morris
Keyword(s):  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Dynamical Characteristics ◽  
Perpendicular Distance ◽  
Rigid Rod

Referring to Fig. 1, let xOy be the plane of rotation of a rigid rod AOA' consisting of a series of pairs of masses symmetrically disposed about O. Thus at a distance r on either side of O are masses mr. Let AOA' rotate with uniform angular velocity Ω, about the axis Oz and let the plane xOy simultaneously rotate about the axis Ox, supposed fixed in space, with constant angular velocity w. Let ρ be the perpendicular distance mrMr of mr to the axis Ox.

scholarly journals Complex Maxwell and Einstein Fields

1974 ◽  
Vol 64 ◽  
pp. 105-105
Author(s):  
Ezra T. Newman
Keyword(s):  
Maxwell Equations ◽  
Vector Fields ◽  
World Line ◽  
Flat Space ◽  
Null Vector ◽  
Einstein Equations ◽  
Maxwell Field ◽  
Real Solution ◽  
Complex Solution ◽  
Maxwell Fields

We consider the class of regular (in a certain precise sense) null vector fields, lμ which have the following properties; they are (1) tangent to geodesics, (2) diverging, (3) shear free, (4) twist (or curl) free. It is well known that the vacuum Einstein fields whose principle null vector field (pnvf) satisfies (1)–(4) are the Robinson-Trautman (1962) (RT) metrics and those which satisfy (1)–(3) are the algebraically special twisting metrics, (Kerr, 1963). To understand these metrics better we ask for those Maxwell fields (in flat space) whose pnvf also satisfy conditions (1)–(4) and (1)–(3). It can be shown that (1)–(4) imply (and are implied by) that the Maxwell field is a Lienard-Wiechart (LW) field. (This establishes the analogy between the RT metrics and the LW fields.) Conditions (1)–(3) imply that the Maxwell field is a complex LW field. (We mean by this that if the Maxwell equations are complexified (Newman, 1973) (in complex Minkowski space) then the real solution in question is induced from the complex solution which is associated with a charged particle moving along an arbitrary complex world line.) Finally it can be shown that the Einstein equations can be complexified and that the algebraically special twisting metrics can be interpreted as if they had a point source moving in the complex manifold and are thus analogous to the complex LW fields.

Zum Übergang von der Wellenoptik zur geometrischen Optik in der allgemeinen Relativitätstheorie

1967 ◽  
Vol 22 (9) ◽  
pp. 1328-1332 ◽  
Author(s):  
Jürgen Ehlers
Keyword(s):  
General Relativity ◽  
Maxwell Equations ◽  
Expansion Method ◽  
Flat Space ◽  
Space Time ◽  
Moving Medium ◽  
Formal Similarity ◽  
Curved Space ◽  
Optical Metric ◽  
Series Expansion Method

The transition from the (covariantly generalized) MAXWELL equations to the geometrical optics limit is discussed in the context of general relativity, by adapting the classical series expansion method to the case of curved space time. An arbitrarily moving ideal medium is also taken into account, and a close formal similarity between wave propagation in a moving medium in flat space time and in an empty, gravitationally curved space-time is established by means of a normal hyperbolic optical metric.

Inertial oscillations in a rigid axisymmetric container

1977 ◽  
Vol 358 (1692) ◽  
pp. 17-30 ◽  
Keyword(s):  
Angular Velocity ◽  
Constant Angular Velocity ◽  
Axial Plane ◽  
Axial Distance ◽  
Free Oscillations ◽  
Inertial Oscillations ◽  
Characteristic Cone ◽  
Characteristic Cones

Free oscillations of a fluid rotating with constant angular velocity Ω in a rigid axisymmetric container are considered. Approximations are sought for modes that vary rapidly in each axial plane, on the premise that the pressure at the axis varies with axial distance z as Re [A( z )e iino(z )], where n ≫ 1, o' is real, and A (z) and o (z) >do not vary rapidly with z The pattern made by the characteristic cones of Poincaré’s equation after repeated reflexions at the boundary proves pertinent. Modes are evaluated, with a proportional error o(n -1 ), for a class of containers that has special symmetries and for eigenfrequencies that produce reflexion patterns with topologies like those found in a sphere. The largest velocities in the modes considered occur near the circles where a characteristic cone touches a boundary.

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