Download PHYSICS 015

Stronger Gravity
Black Holes and the
Curvature of Space-Time
Black Holes
The name “black hole” was coined by John
Archibald Wheeler, of Princeton University, in the
1960s. At that time, such objects were matters of
idle speculation, not real astrophysical research.
Here we see Wheeler
with Einstein and
Yukawa, a year before
Einstein’s death.
The Extreme Case
If an object of mass M shrinks to a size given
by the
Schwarzschild radius:
RS = 2 G M / c2
the escape velocity is c (the speed of light),
and neither light nor material particles can
escape.
Some Numbers
Note that Rs is proportional to the mass.
For the Earth, Rs = about 1 cm
For the Sun (300,000 times more massive),
Rs = 300,000 cm = 3000 m = 3 km
For a ten-solar-mass star, Rs = 30 km (bigger
than a neutron star!)
It Doesn’t Stop There!
Once the material attains this small size and enormous
density, nothing can stop the further complete infall.
Gravity overwhelms all resistance; the ‘fall’ continues.
Singularity
As noted, the collapse continues within the
Schwarzschild radius, to zero volume and infinite
density: a singularity – or at least that’s what
the mathematics tells us.
What ‘really’ happens there? Physics can not yet
tell us: we need a theory of quantum gravity, or
perhaps string theory.
http://cjwainwright.co.uk/maths/physicscube/
What is a Singularity?
First, consider burrowing through
the Earth.
It may not be possible for practical
reasons (for example, the extreme
pressure overwhelms our tools) but
there is nothing in principle that
disallows this. You can imagine
making your way, inch by inch.
But in the Singularity…
In a singularity like a black hole, there is no ‘connection’
from one side to the other through the central point.
Imagine climbing down one side of a well, intending later
to climb back up the other – and then discovering there
is no bottom!
Infinitely
Deep!
The points on opposite sides of the hole are always
separated by an infinite distance, if you choose to go
through the hole. (You can of course always go around
the hole, out where space is not so distorted.)
This is because of the infinite elasticity (the ‘stretchiness’)
of space itself.
Trapping People in a Singularity
Running Down is Easy
…but try
climbing!
http://www.physics.queensu.ca/~hanes/Movies/Climbing-Dunes.mp4
The
Behaviour
of Light
Note that light
follows curved
paths, and can
even orbit
the black hole.
An Important Proviso:
The Material has Vanished
- But is Not Gone
Note that the mass is still there!
For objects far away, it has exactly the same
gravitational influence as it always did.
Black Holes Do Not Suck!
Suction is a manifestation
of pressure.
The motor and fan expel
air out the top, creating a
vacuum in the canister.
Air in the room rushes in
through the hose, carrying
dust and dirt with it.
The Fate of the Earth
If the Sun became a black hole, the Earth would not
suddenly get ‘sucked into’ it.
There is no external pressure to push it into the Sun in
the way that air in your bedroom pushes the dust
into the vacuum cleaner.
And the gravity we feel would not change.
Very close to the black hole, however, the situation is
different.
Here’s a Thought Experiment
Move to the moon for your own safety. Now
compress the Earth to the size of an olive, so it
collapses to a black hole. What next?


The moon would continue in its orbit, around
an invisible Earth.
If you looked directly towards the shrunken
Earth, the new black hole would have an
occasional pronounced effect on beams of light
from stars directly behind it. (“lensing”)
Nothing Else Would Change…
But you’d never be able to go home!
There’s no way to ‘re-expand’ the Earth.
Now Suppose You (A Keen Scientist!)
Decide to Look at the Black Hole ‘Close Up’
This is not a good idea!
Let’s Consider Some Numbers
Right now your body is more than 6 million metres
from the centre of the Earth.
This gives rise to an overall
net downward gravitational
force that you experience as
your weight.
But Near a Shrunken Earth
Suppose you descend towards the grape-sized
black hole until your feet are just one metre
from it.
1 metre
What gravitational pull would you now experience?
Obviously a large one, because you are closer to
all the Earth’s mass, but just how big?
Inverse-Square Law
The atoms in your feet are
now only 1 meter from the
material in the hole, rather
than 6 million meters.
Because of the inverse-square law, the force on the atoms
in your feet would be
36 trillion times
( = 6 million x 6 million)
as strong as what they are feeling right now.
That’s Not Necessarily a Problem!
If all your atoms felt the same
force, and if you were
coasting freely through
space, no problem!
(Touching down on a surface
would hurt, though! Your
own weight would crush
you.)
But Your Head is Farther Away!
If you are of average height
(~1.6 metres), your head
would be about 2.6
metres from the hole.
So your head does not feel
as strong a force.
What Matters is the Difference!
Both these forces are unimaginably strong, and
pull you towards the hole.
But the gravitational force on the atoms in your
feet is fantastically stronger than the force on
the atoms in your head.
You’d get ripped apart, atom by atom.
Spaghettification!
This is a tidal effect.
See the ASTR 101 notes for a reminder of tides.]
Meet a Brave Astronaut
Find a volunteer willing to fall into the black hole for
the sake of science.
Watch her go, and ask her to report regularly by radio.
What would we see and learn?
Two Very Different Perceptions
Her experience:
quick and nasty  spaghetti!
Our observation:
infinitely drawn out,
with a slow fade to
invisibility.
Her Signals Arrive Ever More Slowly
(‘News From the Pit’)
The last few escaping photons…
…take forever to get out, and barely make it
at all, losing almost all their energy