Transcript Black Holes : A lecture to 6th Formers

Black Holes
Ruth Gregory
Durham Centre for Particle Theory
Who am I?
• I did my A levels back in the 80’s: Physics,
Chemistry and Maths.
• Then went to Cambridge, degree in Maths and
PhD in Theoretical Physics
• Spent 5 years as a researcher in Chicago
• Back to the UK as a fellow, now a Professor
• Research in gravity, cosmology and extra
dimensions
• One child (son) in pre-GCSE year
Outline
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What is a black hole?
How can we see them?
Hawking radiation
Extra dimensions and mini black holes
What is a black hole?
CLASSICAL
QUANTUM
So much mass that escape velocity exceeds the speed of light
Newton’s Law
Inverse square law of gravity
Gives escape velocity
Get v=c if
1 m v2 = GMm
2
r
r = 2GM/c2
Event horizon
How big is a black hole?
The solar system has a range
of different sized objects.
The sun is just a little too
small to form a black hole,
but suppose we squashed it how big would that black
hole be?
Solar event horizon
r = 2GM/c2
G = 6.67 x 10 -11
M = 2 x 10 30 Kg
c = 3 x 10 8 ms-1
r = 3 km
Stellar mass black hole
.
Einstein’s Relativity:
Modern physics owes its roots to
the way we think of space and
quantum mechanics). Instead of
quantities, space and time are
spacetime.
Einstein, who revolutionized
time (as well as giving us
two separate and absolute
part of the same canvas:
In Special Relativity,
spacetime is flat, but
in General relativity
it is curved.
Einstein’s theory of General Relativity relates matter to
curvature, and since curvature is about things not being
straight, it tells us that matter effects motion : GRAVITY.
QuickTim eﾪ and a
GIF decom pressor
are needed t o see t his pict ure.
The fundamental observable of spacetime
gravity is distance, so we write things in
terms of the spacetime metric:
s)2 = f2(x,y) [ (x)2 + (y)2 ]
This example alters Pythagoras,
but what if we apply this to
stars?
Gravitational redshift
The first thing Einstein tells us is that time is slowed in a
gravitational field.
E = h  1GM/r)
As r gets bigger, the gravitational
term becomes smaller and so 
gets smaller to compensate. This
means light is redshifted
But the photon frequency counts ticks of the clock, so time is s l o w e d d o w n
Schwarzschild
Newtonian physics also gives us redshift, but it is Einstein’s
perspective that tells us time is slowing down. It also tells us
space warps around any massive object.
The spacetime around a star or planet or black hole is known
as the SCHWARZSCHILD SOLUTION.
The distance from the planet or star is stretched by the same
amount as time is shrunk. What does this mean in practice?
Tidal Forces
Tidal forces arise because gravitational acceleration is not
constant, but falls off as you move away from the star or
black hole. So a falling object will be accelerated faster
closer to the black hole.
This tidal acceleration
goes like
GM
r3
QuickTim eﾪ and a
GIF decom pressor
are needed t o see t his pict ure.
Spaghettification!
For objects close to a
black hole, this is proportional
to the inverse square of the
event horizon radius.
An astronaut falling into the
black hole will be stretched out
like a piece of spaghetti!
Orbiting a
black hole
.2
r = 2GM L2 + 2GML2
r
r2
c2 r3
Standard
gravitational
attraction
Centrifugal repulsion
Can see the shape of
orbits by plotting
this RHS as V( r )
General
relativistic
attraction
Some orbits and their potentials
By altering angular momentum, can get stable orbits at different
radii. A stable circular orbit lies at a minimum of V. At
r=6GM/c2 the minimum becomes a point of inflection. This is
the innermost stable orbit and can be observed.
Accretion disc
Most black holes are in a binary system, i.e. where there is a
companion star. This star can then literally get sucked apart by the
black hole.
Cygnus X1:
Observing accretion discs
This makes accretion discs
very violent environments,
with gases being heated
up to very high
temperatures. These
radiate in the X-ray band
at a temperature related to
the orbital radius.
So we can measure the innermost stable orbit!
The impossible Planet?
From the picture, the black hole subtends an angle of 1˚ in the sky
r = tan 1o ≈ 1
d
50
r
d
GM ≈ c2 x 10-5 ≈ 105 m s-2 m-1
d3
r2
for a stellar mass black hole
Fairly impossible!
But for a galactic super black hole, r ≈ 1010 m, and the tidal forces
are 10-8 m s-2 m-1, which is similar to that on earth.
Milky Way Black Hole
QuickTim eﾪ and a
YUV420 codec decom pressor
are needed t o see t his pict ure.
Although X-ray observations give us
the most concrete evidence of black
holes, the most spectacular
confirmation is that of stellar motion at
our galactic core. This houses a black
hole of 3 million solar masses! We see
it by the rapid motion of stars orbiting
around a black empty space.
How else might we see a black hole?
Hawking Radiation
Back in the early 1970’s it was realised that if a black hole was
truly black, then it had to carry entropy. Entropy measures
disorder, and it always increases in any physical process.
But if a black hole was a thermodynamic object, then surely it
had to be a black body: it had to radiate.
Bekenstein put forward values of entropy and temperature
needed to make thermodynamics work, Hawking showed how
to do this using quantum field theory.
Heisenberg Uncertainty
A unique feature of Quantum Mechanics is the uncertainty
principle, which tells us we cannot precisely simultaneously
measure position and velocity, or time and energy. This means
that empty space is not really empty, but has lots of particles
and anti-particles continually pair creating and annihilating.
E t ≤ h/2
e+
x
x
e
t ≤ h
≈ 10 -21 s
4mec2
Pair creation in curved space
Near the event horizon, it
is possible that one of the
particles gets drawn into
the black hole, while the
other escapes. The particle
which has been captured
has negative energy with
respect to an observer at
infinity, and so the black
hole loses mass.
The black hole appears to be emitting particles, and a full calculation
shows this emission is thermal: the black hole is radiating.
Black holes aren’t black!
A black hole is a true black body, and radiates at the Hawking
temperature:
TH =
h c3
8GMkB
So a solar mass black hole has a temperature of about 60 nK!
But very small black holes have high temperatures, and
evaporate very quickly. Can these be formed?
LHC
The Large Hadron Collider at CERN in Geneva is being run in
right now. This will collide protons at huge energies, and will
test our theories of fundamental particles. But it will also be able
to look for mini black holes…..
Atlas detector at LHC:
look carefully for the
experimenter!
Mini Black Holes
Typically, black holes have to form
when matter is highly concentrated, to
within its Schwarzschild radius. But
what if we can change this equation?
Braneworlds and extra dimensions
change the balance by making gravity
stronger. We only think it is weak
because we are trapped in four
spacetime dimensions.
Why extra Dimensions?
Like Einstein we seem
obsessed with finding a “unified”
description of nature.
The Standard Model works well
for particle physics, but Gravity
seems stubbornly classical.
AE: “God does not play at dice”
NB: “Stop telling God what to do!”
Quantum Forces
The other major development of last century was
Quantum Physics (again pioneered by Einstein) which
explains all the small-scale forces of nature, and can
include electromagnetism:
• Weak Nuclear Force (allows nucleons to interact
with electrons, also explains radioactivity)
• Strong Nuclear Force (keeps nuclei together)
• Electromagnetism
String Theory
Replaces particles by strings:
QuickTim eﾪ and a
GIF decom pressor
are needed t o see t his pict ure.
..and can explain gravity
in the same breath as
quantum theory…
But needs TEN dimensions!
Time and relative dimensions in space?
What does 10 dimensions mean?
We are used to 3 space and 1 time dimension, but there is no reason
to have only 4 dimensions, other than that is what we see. We are
allowed to have more dimensions, if we can find a way to hide
them. A bit like the TARDIS!!
• Make them small (Kaluza-Klein)
• Glue ourselves to a sheet (braneworld)
There’s a black hole in my lab!!
Because braneworlds make gravity stronger, black holes form
more easily! But we would have seen signals in supernova if
they were going to form at LHC.
Summary
 Black holes are fun objects to study in Einstein’s GR
 They are so compact and heavy, they literally tear space apart
 We have good evidence for black holes from X-ray observations
 …and also from orbiting stars at our own galactic core.
 Black holes can also radiate, and evaporate!
 Maybe mini-black holes can form in the lab