Geodesics in the Morris-Thorne Wormhole Spacetime
Geodesics in the Morris-Thorne Wormhole Spacetime
The simplest wormhole geometry is given by the line element , see [2]. The parameter defines the size of the throat of the wormhole, and represents the proper length radius.
d=-d+d++d+θd
2
s
2
c
2
t
2
l
2
b
0
2
l
2
θ
2
sin
2
ϕ
b
0
l
Light rays and objects in free motion in four-dimensional spacetimes follow lightlike or timelike geodesics. In general, these geodesics must be computed numerically. However, in the Ellis wormhole spacetime, there is an analytic solution of the geodesic equation in terms of elliptic integral functions. Because of the spherical symmetry and staticity of the metric, it suffices to consider geodesics in the hypersurface . This two-dimensional surface can be embedded in the three-dimensional Euclidean space. The corresponding embedding function reads with =+.
t=constant,θ=
π
2
z(r)=±ln+-1
b
0
r
b
0
2
r
b
0
2
r
2
b
0
2
l
In this application, you can change the throat size , the initial position of the observer, and the initial angle of the geodesic with respect to the local reference frame of the observer.
b
0
r
i
ξ