Newtonian Forms For The Motion Of Particles In Dilaton Spacetime

As one of the foundation stones of modern Physics, general relativity can describle well the physical phenomena of the large scale structure of spcetime, and has been testified by lots of experiments. But with the gradual development of modern Physics and the gradual deepening of Man's knowledge, general relativity are confronted with sach problems as singularity and gravity quantization. Men want to find a theory to overcome these troubles, or even unify the four interactions in nature. Superstring theoty springing up in recent years may provides some edification on these problems.The test of supertring theory, however, needs hight energy to carry out. With the present experimental equipment and technology, this may only be a dream. Nevertheless men may find out some clues to testify supertring theory by observing the universe. In terms of the dilaton spacetimes in supertring theory, it has qualitative different properties from those appearing in general relativity, anyone of its solutions with nonzero electromagnetic field strength must have a nonconstant dilaton, and the apearance of dilaton may arise some observable gravitational effects.If we treat gravitation field as an optic medium, useing the Newtonian forms for the equations of motion of relativistic particles in gravitation field, which connects optics with mechanics, we can deal with some complex problems of particles' motion in gravitation field through familiar methods of Newton mechanics, and simplify the computation .We have generalized this description for the motion of relativistic particles to the Gibbons-Meadaand Garfinkle-Hornedilaton dilaton spaceti'mes in sting theory. By introducing a coordinate transformation, wo express those dilaton metrics with isotropic coordinates, get the effective indexs of these dilaton spacetimes, and acquire the differential equations of motion of relativistic particles. Using these equations of motion, we investigate some classical gravitational effects in dilaton spacetime, such as the bending of light rays, the perihelion advance of planet, the delay of radar echo, and the redshifts.Our work shows that the effects resulting from dilaton may be observableprovided the dilaton is strong enough in these dilaton spacetimes. So to observe the universe can offer the test of sting theory on a certain degree.