- #1

GR191511

- 76

- 6

since we are interested in the Newtonian limit,we restrict our attention to the spatial part of the geodesic equation,i.e.when a=##\alpha####\quad ##,and we obtain,by using ##\frac{d\tau}{dt}=1+O(\varepsilon^2)##:

##\frac {\partial^2 x^\alpha} {\partial t^2}+\Gamma^\alpha{}_{bc}\frac{dx^b}{dt}\frac{dx^c}{dt}(1+O(\varepsilon))=0##.##\quad ##I wonder how the auther gets "(1+O(##\varepsilon##))"?