Could go all hypothetical here and suggest
Krasnikov tubes(?)
(Paper here:
A Superluminal Subway: The Krasnikov Tube)
AIUI, Krasnikov tubes are (hypothetical) ‘spacetime tunnels’ which allow for superluminal travel without violating causality, but only for round trips and with much larger energy requirements than say, the (hypothetical) Alcubierre drive.
I'm still trying to figure out the spacetime diagram for one, so I can't explain it yet .. any takers?:
View attachment 296553
Here is a brief description of your attached diagram.
The upper horizontal line is the space axis; the left hand thin vertical line is the time axis for the space-time diagram
The left hand thick vertical line represents the world line or trajectory in space-time of a point of departure (say Earth), the right hand thick vertical line is the destination.
Since the Earth’s orbit is very small compared to the width of the U shape it can be approximated to be spatially in the same position as is the point of destination.
As a result both the Earth and destination point are travelling vertically downwards as they are only moving in time and not in space.
The oblique line which forms the base of the U shape is the world line of a spaceship travelling from Earth to its destination inside the tube.
This is where things get complicated as light cones become distorted and tilted in gravitational fields.
I’ll use an example of a black hole.
In flat space-time the light cones have an undistorted shape and form 45⁰ angles in space-time diagrams as explained in my previous post.
In gravitational fields or using the equivalence principle in which a frame is being accelerated, the speed of light is no longer constant in accelerated frames and the light cones become distorted.
In this diagram the cylinder is a stationary black hole moving only in time.
The surface of the cylinder is the event horizon of the black hole, the vertical axis of the cylinder is the physical singularity.
At distances well away from the black hole, space-time is flat and the light cone is undistorted.
As photons approach the event horizon the light cones become progressively more distorted due to gravity.
For both black holes and a Krasnikov tube since travel is only possible into the future only the forward light cones are considered.
Outside the Krasnikov tube the forward light cones are not distorted as they are in flat space-time.
The two points outside the Krasnikov tube in the space-time diagram are the vertices of the undistorted forward light cones.
Without going into the maths inside the Krasnikov tube the light cones are distorted as illustrated.
I hope this clarifies your attached diagram which is a 180⁰ rotation of the axes when compared to the last diagram in my post.