Falling into a black hole

One of the most fascinating things about black holes is what
happens to objects/suicidal astronauts that fall into them, andhow
this compares with the way things look to an observer watching
from a safe distance. Let us first consider what it would be like if
you were unlucky enough to fall in to one.One aspect of gravity that has not been mentioned so far is the
tidal force. We know that the gravitational pull of a body becomes
weaker the further away we are fromit. Surely it then follows that,
just by standing on the ground, your feet should feel a stronger
pull due to the Earth’s gravity than your head, which is further
away from the surface. This is in fact true, but the difference in the
gravitational field of the Earth is so tiny over such a small distance
that you would never feel it. We can, on the other hand, clearly see
the tidal effects of the Moon’s gravity on the Earth. This is because
the side of the Earth facing the moon feels a stronger gravitational
pull than the opposite side which gives rise, as the Earth spins,
to the daily tides of the seas from which the tidal force derives its
name.
When it comes to black holes the gravitational force is
changing much more dramatically and you are able to feel the
tidal effect even along the length of your body. This becomes
unbearably strong and will ultimately rip you to shreds long before
you are finally crushed at the singularity.
A small black hole, of the order of several solar masses, has
tidal forces so extreme that any astronaut venturing too close
would be killed long before he or she has even crossed the event
horizon! Not very nice is it? You would think that you might at least be given the chance to get close to the horizon without too
much trouble. Luckily we have good reason to believe that there
exist black holes with masses millions of times that of the Sun.
Such supermassive black holes have much gentler tidal forces and
one could easily cross the event horizon of such a hole without
feeling any discomfort. As you continue to free fall towards the
singularity the tidal forces will gradually grow in intensity. Thus
although you will eventually be ripped apart then crushed to a
point of infinite density at least you can now do a little sightseeing
on your way down.
Throughout this book you might have gathered7 that I have
been trying to postpone the discussion of gravity’s weird effect
on time until the next section. I cannot, however, do black holes
justice without relaxing my resolve on this a little. Inside a black
hole space and time are so warped that the distance from the
event horizon to the singularity is not a distance in space in the
normal sense (in the sense that it can be measured in kilometres
or some other appropriate unit of length). Instead it becomes a
time direction. Basically the radial distance to the centre of the
hole is interchanged with the time axis! Just a minute, you think,
we have been discussing the size of black holes in terms of their
Schwarzschild radius which is most definitely measured in units
of length. The difference is that the Schwarzschild radius is a
radius as viewed from outside the hole. Imagine observing a black
hole against a bright backdrop that would clearly highlight its
dark horizon, such as a luminous gas nebula. The distance across
this black disc is its diameter, or twice its Schwarzschild radius.
Once inside the black hole things are very different.
This interchange of space and time explains why any object
falling into a black hole has no choice but to move inwards towards
the singularity. Physicists liken this to the unavoidable way we
move in time towards the future. What is more, since you can get
no further once you have reached the singularity, this point must
mark the end of time itself! This is where black hole singularities
differ from the Big Bang which is a singularity that marks the
beginning of time. They are more like the Big Crunch singularity (the one that marks the end of space and time if there were enough
matter in the Universe to cause it to collapse in on itself).
The time it takes to reach the singularity from the horizon,
as measured by someone falling in, is proportional to the mass
of the black hole. Thus for a hole with ten times the mass of the
Sun it would take just one ten-thousandth of a second to hit the
singularity, whereas for a supermassive black hole it could take
several minutes.
A question that is often asked is whether an astronaut falling
through the event horizon of a black hole notices anything different
(assuming it is a big enough hole for the astronaut to survive the
tidal forces). The answer is no. The only way you could find out
whether you had crossed the horizon (notice how that astronaut
has now become you? don’t take it personally, I don’t even know
you and would not wish such an end on anyone) would be if you
tried to halt your fall and climb back out again by firing your rocket
engines to push yourself back up away from the centre of the hole.
According to the Russian astrophysicist and leading black hole
expert, Igor Novikov, just another of the weird aspects of black
hole physics and a consequence of the way time is warped is that
by trying to do this (firing your rockets to escape from the hole)
you will reach the singularity even quicker than if you had left
your engines off!
This is certainly very counter-intuitive but he explains it in the
following way. Remember that without the rocket engines firing
you are in free fall and not feeling any gravitational force (apart
from the tidal forces of course). By pointing your rocket away
from the singularity and firing the engines you will feel a force
of acceleration upwards and, due to the principle of equivalence,
this is like feeling the effects of a gravitational field. However,
because of the way space and time are mixed up inside a black
hole you continue to fall at the same rate as before. It is just that
now your time will slow down. This is known as gravitational
time dilation and I will discuss it in Chapter 6. It means that a fall
from the horizon to the singularity that would have taken you, say,
ten seconds, might now seem like just five seconds. Weird!
While writing this chapter, I mentioned to my wife, Julie, that
I had reached the part where I describe what it is like inside a black hole. “Very dark, I expect” was her deadpan and profound reply.
In fact it is not completely dark since the light from the outside
Universe still gets in. The difference is that the light becomes bent
and focused into a small bright patch. It would be like a view of the
receding light from the entrance to a dark tunnel as you venture
deeper inside the hole.
Let us now consider what a distant observer sees when an
object falls into a black hole that, for simplicity, is assumed not
to be spinning. Imagine now that you are in your space ship,
hovering at a safe distance outside the event horizon. You witness
a colleague falling in towards the horizon. Rather than seeing him
falling faster and faster until he suddenly disappears through the
horizon, the rate of his fall seems to slow down more and more
as he approaches the horizon until he finally stops, frozen, just
outside it. This apparent slowing down of a falling object is due to
the way gravity affects the rate of flow of time. In fact time literally
slows down in gravitational fields and this is most noticeable in the
strong field outside a black hole.
If the astronaut has calculated that he will pass through the
event horizon at twelve o’clock precisely according to both of your
previously synchronized watches, then you can, via a powerful
telescope, observe the time shown on his watch as he falls. You
will see the hands on his watch slow down as he approaches the
horizon until they finally stop at twelve o’clock exactly. In fact, at
the horizon time stands still. Sometimes it is (wrongly) suggested
that you would see him frozen outside the horizon forever. In fact,
his image will very quickly fade away and he will disappear. This
is not because you have ‘seen’ him fall through the horizon, but
rather because the light reaching you fromhim has been redshifted
to such long wavelengths that it quickly goes beyond the visible
spectrum. This redshift is not quite the same as that due to receding
distant galaxies whose light is Doppler shifted. Now there is an
additional affect due to the slowing down of time near the horizon
that makes the light appear to you to have a lower frequency
and thus a longer, redshifted, wavelength. The falling astronaut,
however, has a different concept of the rate at which time is flowing
and calculates that he falls towards the hole faster and faster.