These are three of the most intriguing things in Physics and they are all connected to each other.
Before we look at their connection lets take a look at each individually.
What are they?
According to Einstein a black hole is a region of space in which the gravitational field is so powerful that nothing can escape its pull after it has fallen past its event horizon. It's gravitational pull is so strong that no light can escape so this renders the hole's interior invisible, and indistinguishable from the black space around it. This is why we call them Black Holes. It was originally thought that nothing at all could escape from its clutches but it was proven by Stephen Hawking that they would actually emit a specific type of radiation (Hawking Radiation).
Are there different types?
The simplest type of black hole is one that has mass but no charge nor angular momentum. These are often called Schwarzschild black holes.
What are the parts of a black hole?
A black hole consists of:
An Event horizon:
The event horizon of a black hole is the point of no return. Once an object passes this point there is no escape from the black holes gravitational pull.
A gravitational singularity
According to general relativity, there is a space-time singularity at the centre of a spherical black hole.
A Photon sphere
This is a spherical boundary that traps photons in a circular orbit. Light can escape from a photon sphere.
An elliptical region located outside a rotating black hole.
How can a black hole be found?
A black hole may reveal its presence despite its invisible interior, by it's interaction with matter orbiting around it's event horizon and it emitting Hawking radiation.
How are they formed?
There are believed to be different ways in which black hole are formed.
It is believed that most Black holes are formed when some very dense stars go nova. When a star's fuel is running low and it is cooling down it's internal pressure is insufficient to resist it's own gravity so it collapses in on it's self. This is known as gravitational collapse. During the creation of the universe just after the big bang there is believed to have been objects with enough density to collapse in this way and form black holes.
It is believed by some that they could be formed in high energy collisions. (This is the theory that made people believe that the Large Hadron Collider could create a black hole and destroy the earth.) There is no evidence to support or disprove this theory. We will have to wait and see what happens.
What are they?
These are a theoretical "tunnel" that connects two distant points in space. They are also known as "Einstein-Rosen bridges".
The theory behind them
This is where the connection between Black Holes and Wormholes comes in.
An Einstein-Rosen bridge is a theoretical connection between a Black Hole and a theoretical White Hole.
An Einstein-Rosen bridge would be an unstable wormhole ad as such it would be a non-traversable wormhole.
Kip Thorn came up with a theory to create a traversable wormhole by holding the "throat" of a Schwarzschild wormhole/ Einstein-Rosen bridge open with exotic matter (material that has negative mass/energy). These "Traversable Wormholes" are known as Morris-Thorne wormholes.
Since the Kip Thorns discovery that Morris-Thorne wormholes could exist others have come up with other traversable wormholes as solutions to the equations of general relativity.
This is the one area of theoretical physics that seems to fascinate everyone. It also brings up a lot of questions. None of which are that easy to answer.
Is time Travel Possible?
Which the answer would be not at the moment. And not without rewriting Special Relativity.
What would happen if we could travel into the past and we changed something that happened?
Your guess is as good as anyone's, but there is a theory.
The Grandfather Paradox:
If you traveled back in time and killed your biological grandfather before he met your grandmother, one of your parents (and by extension the you yourself) would never have been conceived. This would imply that you could not have traveled back in time after all, which in turn implies your grandfather would still be alive, and you would have been conceived allowing you to travel back in time and kill your grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox.
The way that this paradox has been sorted is by introducing the theory of Parallel universes, and saying that if you did go back in time and killed your grandfather you would create a point in time where reality split creating two paths one where your grandfather is killed and you are never born, the other staying as it was before you went back in time.
Now let take a look at the connection that black holes and wormholes have with time travel.
Stephen Hawking once said "If black holes can be manipulated or manufactured in the lab to act as a time machine, then surely someone, somewhere in the universe must have developed the capability by now? Or at least, one day, someone will. So then where are they?'
This statement seamed to some to have dispelled the theory that time travel would one day be possible, but Frank Tipler came up with an explanation to why we have never met a time traveler by showing that a time travel device using artificially created black holes would only allow travel back to a time after its own construction, meaning that if this was the only way we could do it then we would never meet a time traveler as the time machine has not been invented yet.