My Favorite Black Hole
There are some common misconceptions about black holes.
And often these misconceptions are taught as fact in the schools.
My favorite among these is the contention that if you got
close to a black hole it would tear your body apart by
the differential gravity.
The reason people think this is that it is true for the
most common size of black hole. But not for all black holes.
But before we explore that idea lets nail down some basics.
I will only use two digits of accuracy, because I am dealing
with concepts here.
If you needed to navigate a starship on these calculations
you would need to worry about more digits.
And due to the awkwardness of showing exponents on a web
page I will use engineering notation:
2.0E5 means 2.0 times (10 to the 5th power), or 100,000.
How big is a black hole?
If you know the mass of the black hole and make a couple of
assumptions, the radius is easy to calculate.
The assumptions are that it is uncharged and not spinning.
The first assumption is probably a good one.
It is hard to maintain charge on objects, they
tend to neutralize.
The second assumption is rocky.
But let's assume it for the moment and then
return to that later.
Now our equation is simply
r = M * 1.5E-30 km/kg
How big is a stellar-class black hole?
Let's consider an example, a black hole weighing 10 times our sun.
r = 2.0E31 kg * 1.5E-30 km/kg
r = 3.0E1 km
r = 30 km
Pretty small, huh?
How big would a black hole be if it contained our galaxy?
The Milky Way mass is 5.8E11 solar masses or 12E41 kg.
r = 12E41 kg * 1.5E-30 km/kg
r = 1.7E12 km
That's well outside the orbit of pluto from the sun,
but about 1/5 the distance to the nearest star.
OK, let's take a look at something really big!
How big would a black hole be if it contained the Universe?
The mass of the universe is not well known. Estimates vary
over a range of 10 billion.
But if we take an estimate somewhere in the middle
it is about 1.6E55kg.
r = 1.6E55 kg * 1.5E-30 km/kg
r = 2.4E25 km
That is an interesting number when you consider that the
radius of the observable Universe is only 4.4E23 km.
In other words, the Universe has already formed a black
hole, and we are inside it.
I expect my readers to be writhing at this point.
How can this be?
If we were inside a black hole we would all be crushed
or torn apart by the extreme gravity.
But that brings us back to those misconceptions I mentioned
at the top of the page.
Why are we not torn apart?
Most explanations of black holes say that as an astronaut
approaches the event horizon he will be torn part.
Stephen Hawking called this effect "spaghettification".
And this is true for stellar sized black holes.
Ironically, the bigger the black hole gets the
weaker the effect.
But that page says that as you approach the singularity
you will be torn apart even in very large black holes.
Yes, but there is a problem with that explanation.
The problem is that as you approach and cross the
event horizon the extreme gravity warps time and space.
The warping makes what used to be your z dimention
(the direction toward the center of the black hole)
slowly become your time dimension.
From this we can see that rather than stretching
you in space, the black hole stretches you in time.
What does that mean?
I'm not sure. But it's not physical stretching any more.
What about the singularity they speak of?
That's a tricky one.
But remember that space and time were warped.
And the singularity they are referring to is from
the perspective of an outside observer.
That in itself is a dubious concept since one cannot
observe across an event horizon.
But in any case, in the perspective of the astronaut
going into the black hole (entering our universe)
the dimension of the singularity is timewise.
In other words, to the astronaut the singularity is
a time, not a place.
And that time is in the future.
We just used an estimate of the mass of the Universe.
True. But if you consider that the Universe used to be
smaller, but no less massive, the Universe must
have been a black hole before even if it isn't today.
And when you then consider that there is no way to
escape from a black hole, you have to assume that
we must still be inside it.
But if we are inside a black hole, where is the outside?
The point is that the direction "out" doesn't exist as
a physical direction once you cross the event horizon.
What used to be that direction is now the time dimension,
specifically backwards in time.
So the only "way" out is to go backwards in time.
If the dimension for "out" doesn't exist how can we calculate the size of the Universe?
But we know how old the Universe is: 14 billion years.
And we have a conversion factor between time and distance: light.
The speed of light is considered the universal conversion
factor in all reference frames.
It should be good both inside and outside the black hole.
So measuring the Universe that way we get a radius
that is 14 billion light years across, which is even
smaller than the radius we earlier assumed.
So that also supports the idea that we are in a black hole.
What if the black hole is spinning?
Yes, we assumed it wasn't.
And that affects the shape and size of the event horizon.
But it turns out the effect is small.
If you spin up a black hole, it grows slightly
in the directions perpendicular to the axis.
There is a maximum rotation rate for a black hole.
But even at that maximum, the black hole will fit into
a sphere with twice the radius of an unspinning black hole.
And this also applies to charged black holes.
They will always fit inside a sphere of twice the diameter.
That means the Universe fits even more easily inside of it's
So this does not affect the conclusions we made above.
Why don't we see stuff falling into our Universe from outside?
To see this we have to look in the right "place".
Remember that the z dimension outside is our time dimension.
That means that the event horizon is in our deep past.
So to see the infalling stuff, we have to look at that
How far back?
I'm not sure. But I suspect it is the beginning of time;
specifically the Big Bang.
Copyright © 2009 C Allen Brown
Last modified 11 May 2009