On Darboux rotation axis of lightlike curves

In this paper, by used Frenet trihedron for a lightlike curve, the motion of Darboux rotation axis is seperated to two simultaneous rotation motions. These rotation motions are that tangent and normal vectors of lightlike curve rotate around each other. But, the angular speeds of them are different. Then, by doing the similar operations, we obtain that Darboux axis rotates around spacelike vector of Frenet trihedron of the lightlike curve and this spacelike vector rotates around Darboux axis. Consequently, we obtain the series of Darboux vectors by this way. So, simple mechanisms can be formed.

COLLAPSE AND DISPERSAL IN MASSLESS SCALAR FIELD MODELS

The phenomena of collapse and dispersal for a massless scalar field have drawn considerable interest in recent years, mainly from a numerical perspective. We give here a sufficient condition for the dispersal to take place for a scalar field that initially begins with a collapse. It is shown that the change of the gradient of the scalar field from a timelike to a spacelike vector must be accompanied by the dispersal of the scalar field. This result holds independently of any symmetries of the spacetime. We demonstrate the result explicitly by means of an example, which is the scalar field solution given by Roberts. The implications of the result are discussed.

Classical energy emission by a point dipole

The classical Larmor formula [Formula: see text] for the energy-emission rate R of a point particle with charge e moving with acceleration aλ is extended to include the energy-emission rate of a point dipole whose dipole moment is characterized by a spacelike vector sα.