Time travel
is nothing special. You’re time traveling right now into the future. Relativity
theory shows higher gravity and higher speed can slow time down enough to allow
you to potentially travel far into the future. But can you travel back in time
to the past?

In this
video I first do a quick review of light cones, world lines, events, light like
curves, time-like curves, and space-like curves in this video so that you can
understand the rest of the video.

A space
like-world line means that the object has to travel faster than light. But
moving anything to the speed of light requires an infinite amount of energy to
accelerate. So this is not possible.

Going faster
than the speed of light can create scenarios that allow you to travel back in
time. But since this is not physically possible, we need to figure out a clever
manipulation of space time. This means we have to solve Einstein’s equations of
General relativity.

The simplest
spacetime is a flat spacetime. The equation for this can be expressed in
Cartesian or spherical coordinates. But to travel back in time we need more
complex spacetime. The first solution ever presented to Einstein’s field
equations was done by Karl Schwarzschild. He formulated non-flat spacetime that
happened to describe a black hole, when no one had ever heard of it.

The r_s term
in this equation is called the Schwarzschild radius. It is the point beyond
which nothing can escape the black hole, because in order to escape, you would
have to go faster than the speed of light, which you cannot do. In this
equation when r is equal to r_s in the dr squared term, we get a zero in the
denominator. This makes the term is undefinable. Its physical meaning is the
event horizon.

Looking at
the light cone of objects falling into the black hole, if the object is far
away, then its cone is upright. As it starts falling into the black hole, it
starts to tilt more and more as it falls further towards the black hole.
Exactly at the event horizon, the light cone lies tilted at 45 degrees. All
future events point to inside of the event horizon, meaning there is no escape
from the black hole even at the speed of light, once you enter the event
horizon.

Eventually
the light cone will point completely towards the singularity at the center.
This means that all future events will lie at the singularity. The singularity
is a future moment in time rather than a point in space.

The
spacetime inside black holes can allow travel back in time. But even if we can
go back in time inside the black hole, the event horizon prevents us from
escaping the black hole. So what good is it going back in time if we are
trapped inside the black hole? It turns out there is a way to escape it.

In 1965 the
Kerr-Newman metric was described by Ezra Newman. It describes a rotating black
hole. There are ways we can remove the event horizon in this metric. When you
do the math, we find that if the black hole is spinning fast enough, the event
horizon disappears. It is then no longer a black hole, but a naked singularity.
A naked singularity is just a singularity with no event horizon.

This is
important is because when you don’t have an event horizon, you can go near the
singularity in the center, but come right back out. There is no event horizon,
that otherwise prevents you from coming out of a black hole.

Now we can
theoretically travel back in time by going around the singularity. This happens
because we can traverse a closed time like curve, which allows world lines from
the future cone to loop around into the past light cone. We can loop our light
cone around the singularity such that our future light cone ends up in the past
light cone of where you started. And now since we are not bound inside the
black hole by the boundary of the event horizon, we can come out of this
spacetime back to about where we started, but at a time BEFORE we started. We
went back in time.

But there
are a few problems. First, theory doesn’t mean reality. Black holes may not be
able to physically rotate fast enough for the event horizon to disappear. The
math works with a test particle with little gravitation, but not at higher
gravity such as that of a human.

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