_{1}

The observed correlation of the angular momenta
*L*
^{ik}
and magnetic moments
*μ** _{lm}*
of celestial bodies (the Sun, planets and stars) was discussed by many authors but without any explanation. In this paper
,
a possible explanation of this phenomenon is suggested. It is shown that the function
satisf
ies
Maxwell equations and can be considered as a function which determines the electro-magnetic properties of rotating heavy bodies. The

*R*

_{iklm}is the Riemann tensor, which determines the gravitational field of the body,

*r*

_{g}is the gravitational radius of the body, and η is the constant which has to be determined by observations. The field Φ

_{lm}describes the observed correlation. It explains the stability of magnetic field of white dwarfs and neutron stars despite the ohmic dissipation. The function Φ

_{l0}

_{}describes the electric field created by rotating heavy bodies. The presented theory does not contradict any existed experiments and observations.

The common accepted theory on the origin of the magnetic field of stars and planets is based on the assumption that the field is maintained by hydro-magnetic dynamo. Indeed, it is possible to select the appropriate motions inside the celestial bodies which can support the dynamo action. The assumed motions do not contradict the existing models of stars and planets. The numerical calculations of the magnetic field confirm the dynamo model. Unfortunately, there are no certain evidences on motions inside the bodies and the theory is based on more or less true assumption on these motions. Ne- vertheless, it seems that the general approach to the problem is true, through some important data remain unexplained. Some problems are connected with the existing correlation of the angular momenta of the rotation and magnetic moments of celestial bodies.

P. M. Blackett [

However, recent observations show that the

The motions of matter inside different bodies have to be very different. However, observations show the similar connection of magnetic moments and angular momenta for absolutely different bodies. The observed dependence of the logarithm

Here

the observed values, within groups of stars of the corresponding class, reaches two orders of magnitude, but almost linear dependence of the mean values extends to twenty orders of magnitude and much more if the galaxy as a whole is included.

The

The plotted points span a range of some 20 orders of magnitude in both

We will consider below only the case of single stars. The case of binary stars needs a separate investigation. Our result also describes approximately the

To explain the

Class | Number | B_{p} | σ_{B} | A | σ_{A} | C.C. |
---|---|---|---|---|---|---|

Cool stars | 54 | 1.091 | 0.062 | 0.76 | 0.566 | 0.925 |

Solar system | 8 | 0.924 | 0.083 | −0.645 | 0.349 | 0.976 |

Hot stars | 171 | 0.571 | 0.058 | 5.442 | 0.616 | 0.602 |

(Hot stars-SG) | −167 | −0.383 | −0.05 | −7.355 | −0.528 | −0.51 |

Isolated white dwarfs | 14 | −0.119 | 0.355 | 8.731 | 2.004 | −0.096 |

Isolated pulsars | 429 | −0.559 | 0.061 | 7.115 | 0.328 | −0.405 |

Cataclysmic variable | 19 | −1.008 | 0.097 | 14.481 | 0.676 | −0.93 |

Binary pulsars | 32 | −1.167 | 0.04 | 9.613 | 0.221 | −0.983 |

purpose consider the anti-symmetric second rank tensor:

Here

Here

Angular momentum

Using Bianchi identities and contracted Bianchi identities:

where

where

The result (7) is not identical to the four dimensional divergence law for the energy-momentum tensor:

The so called “electromagnetic components of the Riemann tensor” were considered in many papers (see, for example, the paper of B. Mashhoom and references there) [

Let us consider the simplest case of a heavy spherical body having the mass

We will consider the case of a weak field and use the linear approximation. Inside the body:

The metric of rotating bodies depends on angular momentum (the Kerr metric, for example). However, the dependence of the metric

Using (1) and (8) we can see that outside the body the

We can see from (5)-(11) that there exists an antisymmetric tensor

The estimate value of the

Astrophysical objects have both poloidal and toroidal magnetic fields. The toroidal field is easily created from poloidal field by differential rotation of the convective matter inside the body. Such rotation inside the body is common for most astrophysical objects, but the creation of the poloidal field needs complicated cyclonic motions.

The magnetic energy of the body is quadratic with respect to

The electric field created by the body rotation is determined, according to the expression (1), as:

The stationary electric field is created in the system if the metric of the system contains terms with

The field of white dwarfs and neutron stars is usually explained as a relict field conversed during the star contraction. If the initial surface field of a star with radius

Motions inside the bodies could be important not only for dynamo actions but also for the

Unfortunately, there are no direct evidences on the internal structures of celestial bodies, although some qualitative estimations are apparently true. The Earth solid inner core, the mantle and the liquid core are rotating with slightly different angular velocities, and have the axis of rotation slightly inclined towards each other. Interiors of white dwarfs and neutron stars is much more inhomogeneous than the Earth interior. In particular, the shift of the point for isolated white dwarfs in the table presented above, could be due to the different rotation of the different internal layers which was not taken into account in the presented table. The internal structures of massive white dwarfs and neutron stars contain superfluid layers which provide different rotation of different internal regions. These layers can rotate independently of the matter on the star surface. It is possible that the magnetic field of neutron stars is determined mostly by the rotation of the star interior, which is much heavier than the surface layers and could rotate opposite to the surface layers. This may explain the negative sign of the coefficient

The existence of the motions inside celestial bodies which create the dynamo action does not contradict to the possibility of the universal field created by the body rotation.

It was shown by L. Ferarro, et al. (2015) [^{11} years.” The similar result was obtained by Y. Sang and G. Chanmugam (1987) [

Astronomical data show that there exists correlation of the magnetic moments and angular momenta for all celestial bodies. It is impossible that the correlation of such a mechanical property, as the angular momentum

Dolginov, A. (2016) Electromagnetic Field Created by Rotation of Celestial Bodies. Journal of Modern Phy- sics, 7, 2418-2425. http://dx.doi.org/10.4236/jmp.2016.716208