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## Black Holes

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### The End of Space and Time Topics Introduction Black Holes Static Rotating Detection Summary Introduction Gravity (1600s) Introduction 1783 John Michel, a ... – PowerPoint PPT presentation

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Title: Black Holes

1
Black Holes
• The End of Space and Time

2
Topics
• Introduction
• Black Holes
• Static
• Rotating
• Detection
• Summary

3
Introduction Gravity (1600s)
All objects fall at the same rate
But how can this be?
4
Introduction
• 1783
• John Michel, a Cambridge professor, noted that a
sufficiently massive and compact star could have
an escape speed vesc that exceeds that of light,
in which case light would be unable to escape
from it.

5
Introduction II
• 1907
• Einstein had a crucial insight
• A person falling off a building experiences no
gravity!
• The happiest thought of my life

6
Introduction III
• This insight led Einstein to propose the
• Principle of Equivalence
• A local frame of reference (for example, the
inside of a small elevator) in free fall is
indistinguishable from a local frame of reference
in free space.

7
Introduction IV
Principle of Equivalence
8
Introduction V
• Einstein's great leap of imagination
• He suggested that objects in a gravitational
field move as they do, not because of a
mysterious force called the force of gravity,
but, because the space and time in which they
move is warped by the presence of matter and
energy.
• Consequently, objects of differing mass fall
towards the ground with the same acceleration
because they follow the same space-time
contours.

9
Gravity as Curved Spacetime
• Spacetime
• Is warped by matter and energy
• All objects
• Experience the same hills and valleys of
spacetime.

10
Introduction General Relativity (1915)
Bending of star-light by the Sun
Sir Arthur Eddington Eclipse Expeditions 1919
11
The Schwarzschild Solution (1916)
• Karl Schwarzschild
• Karl Schwarzschild found the first exact solution
of Einstein's equations.
• It describes the space-time geometry around any
spherical object.

http//scienceworld.wolfram.com/biography/photo-cr
edits.htmlSchwarzschild
12
Static Black Holes
Photon sphere
Event horizon
Escape speed light speed
3RS/2
RS
RS is called the Schwarzschild Radius RS 3 km
for the Sun
Singularity A boundary in space and time
13
Time-Warps Near the Event Horizon
• Time-Warps
• The event horizon is a one-way boundary You can
enter, but in the words of a famous song, You
can check out anytime you like but you can never
leave
• Moreover, from the viewpoint of a traveler who
crosses the event horizon the crossing occurs in
a finite amount of time.
• But from the viewpoint of someone far from the
black hole, the traveler takes an infinite amount
of time to cross!

14
Space-Warps Near the Event Horizon
15
• Rotating Black Holes
• Black holes have two
• special boundaries
• Event Horizon
• Stationary Limit
• For static holes these boundaries coincide, but
• differ for holes that rotate.

Fig. 14-7, p.284
16
Detecting Black Holes Or how to find the grin
of the Cheshire cat
Fig. 14-8, p.285
17
The Grin of Cygnus X-1
Fig. 14-10a, p.286
18
Fig. 14-11, p.288
19
Super-Massive Black Holes
Galaxy M87 Distance 50 million ly Length of
jet 4000 ly MassBH 2 billion M? RadiusBH 3km
x 2 billion 6 billion km 40 AU
20
Summary
• The finite speed of light allows, in principle,
the existence of objects from which light cannot
escape.
• In Einsteins theory of gravity the latter is
explained as a warping of space and time of which
black holes are the extreme examples.
• Evidence is mounting suggesting, amazingly, that
such objects actually exist.