Wormhole Stability
Although the General Relativity equations permit wormholes to exist, they aren't stable long enough for any mass (even a photon) to traverse them. Ultimately they collapse trapping the object attempting to pass through.
At least this is true for all the matter we've discovered so far.
In order to make a worm hole "stable", it needs to be threaded with matter that possesses a property called "Negative Mass".
From the link:
In theoretical physics, negative mass is a hypothetical concept of
matter whose mass is of opposite sign to the mass of normal matter,
e.g. −2 kg. Such matter would violate one or more energy conditions
and show some strange properties, stemming from the ambiguity as to
whether attraction should refer to force or the oppositely oriented
acceleration for negative mass.
Also from the link:
o Positive mass attracts both other positive masses and negative masses.
o Negative mass repels both other negative masses and positive masses.
For two positive masses, nothing changes and there is a gravitational
pull on each other causing an attraction. Two negative masses would
repel because of their negative inertial masses. For different signs
however, there is a push that repels the positive mass from the
negative mass, and a pull that attracts the negative mass towards the
positive one at the same time. Hence Bondi pointed out that two
objects of equal and opposite mass would produce a constant
acceleration of the system towards the positive-mass object, an
effect called "runaway motion" by Bonnor...
Wormhole handles
The matter with negative mass, which holds your wormhole open, also gives it anchor points. If you move the framework of this matter, you also must move the wormhole.
So if you want a plausible wormhole, you must also plan for it to have handles that humans can move around.
Time travel
Whether you like it or not, the introduction of FTL through space, also gives you time travel.
Kip Thorne's discussion of Time Travel and Wormholes:
Thorne takes his wormhole and puts one end in his living room, and the
other aboard a spaceship parked in his front yard. Thorne's wife,
Carolee, hops aboard the spaceship to prepare for a trip. The two
don't have to say goodbye, though, because no matter how far away
Coralee travels, they can see each other through the wormhole. They
can even hold hands, as if through an open doorway.
Carolee starts up the spaceship, heads into space and travels for six
hours at the speed of light. She then turns around and comes back home
traveling at the same speed — a round trip of 12 hours. Thorne watches
through the wormhole and sees this trip occur. He sees Coralee return
from her trip, land on the front lawn, get out of the spaceship and
head into the house.
But when Thorne looks out the window in his own world, his front lawn
is empty. Coralee has not returned. Because she traveled at the speed
of light, time slowed down for her: What was 12 hours for her was 10
years for Thorne back on Earth.
Now, as Thorne and Coralee hold hands through the wormhole, they are
each traveling in time. Coralee has landed on Earth 10 years after she
left, and there she will meet Thorne, 10 years older. But she can
still reach through the wormhole and find Thorne, who is only 12 hours
older. Thorne can step through the wormhole and find himself 10 years
in the future, or his future self can step back 10 years into the
past.
