Lecture 10: Black Holes

1
(No Transcript)
2
A huge great enormous thing, like like
nothing. A huge big well, like a I dont
know like an enormous big nothing ... Piglet
describes the Heffalump, in Winnie the Pooh by
A.A. Milne
3
Dark stars

• Rev. John Michell (1783)
• If there really should exist in nature any
  bodies whose density is not less than that of
  the sun, and whose diameters are more than 500
  times the diameter of the sun their light
  could not arrive at us.
• Pierre Simon Laplace (1796)
• There exist in the heavens therefore dark
  bodies, as large as and perhaps as numerous as
  the stars themselves.

4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
Calculation of escape velocity
Rocket escapes when K.E. ? P.E.
K.E.
P.E.
8
Calculation of Schwarzschild radius
Karl Schwarzschild (1876-1916)
9
Schwarzschild radii for different objects
10
Earth as a depression in the space-time fabric
Albert Einstein (1879-1955)
11
A black hole is an infinite abyss in space-time
12
Structure of a black hole
13
Recall singular behaviour of electrons electric
field

• E Q / (4pe0r2)
• It is infinite when r 0. Quantum field
  theorycomes to the rescue

14
Photon orbits around a black hole
15
Falling into a black holetime dilation
16
Spaghettification!
17
Singularity theorem

• Every black hole must have a singularity inside
  itself

18
Naked singularity

• A singularity that is not inside a black hole
  (not surrounded by an event horizon), and
  therefore can be seen by someone outside it

Roger Penrose (b1931)
19
Cosmic censorship hypothesis

• The laws of physics prevent naked singularities
  from forming when a star collapses

20
No-hair theorem

• A black hole has almost no hair its only hair
  are its
• mass
• angular momentum
• electric charge

21
John A. Wheeler (b1911)
22
Types of black holes

• Schwarzschild (1916)
• mass
• Reissner-Nordström (1916, 1918)
• mass, electric charge
• Kerr (1963)
• mass, angular momentum
• Kerr-Newman (1965)
• mass, angular momentum, electric charge

23
Space-time diagram
24
Schwarzschild black hole
25
Reissner-Nordström black hole
26
Kerr black hole
27
Wormhole
28
Energy extraction from a Kerr black hole
29
Virtual particles

• In quantum theory, there is an intrinsic
  uncertainty in energy and time ?E ?t h/4p
• This implies the existence of virtual particles
  even in a vacuum
• Virtual particles appear in pairs, consisting of
  a particle and its corres-ponding antiparticle

30
Hawking radiation

• One partner of a virtual-particlepair could fall
  into a black hole, carrying negative energy with
  it
• Effectively, the black hole appearsto be
  emitting particles and losingmass!

Stephen W. Hawking (b1942)
31
But this effect is very tinyfor normal black
holes

• For a solar mass black hole
• Temperature 10-7 K
• Lifetime 1067 years (age of universe 1010
  years)
• Since T ? 1/M, this effect is morepronounced for
  small black holes
• Mini black holes created duringthe Big Bang?

32
Binary black hole system
33
Microlens event
34
Black hole in globular cluster
35
Disk in galaxy NGC 7052
36
NGC 4438
37
Galaxy NGC 6251 nucleus
38
M87