10 BlackHoles

8/10/2019 10 BlackHoles

1/28

10 - Relativity & Black Holes


2/28

Problem:

Some aspects of electromagnetism dont ork rig!t "nless

t!ere is a preferred frame of reference - i#e# of motion

$s t!ere% $s it t!e material' t!at lig!t propagates in - t!e

aet!er'%

1887 Michelson &

Morley Experiment

speed of light in a

vacuum is independentof the motion of the

source!

Consequence:all observers

measure the

same speed

of light,

regardless oftheir motion

w.r.t. the light

source!!!!


3/28

Ramification:

(lt!o"g! relativevelocities

add)s"btract for most

common ob*ects+

THIS IS T T"#$

%" &I'HT! ,!e

speed of a lig!t

so"rce coming

toard yo" is t!e

same as one going

aay from yo"#


4/28

ot!er points

$f p!ysical las' are

"niversal+ everyone

s!o"ld be able toderive t!e same sets

of las+ even if t!ey

dont see e.actly t!e

same t!ing#

/vents' t!at

appear

sim"ltaneo"s

in one frame of

reference may

not appear so

in anot!er#


5/28

1905 Einstein published his first paper on

the special theory of relativity. In it are 2

postulates:

1. The speed of light in a vacuum is constant for

all observers

2. Every observer derives the same physical

laws

/instein realied t!at eton !ad not really defined time'

in a consistent ay: it is not an absol"te' 2"antity+ b"t m"st

be defined in terms of observable 2"antities#


6/28

Consequences of Relativity

Time Dilation

Suppose you flew a rocket ship parallel to a perfectly

reflecting mirror, and shown a flashlight beam out the

widow so that it came right back to the flashlight.

=2

( )

2

=42

2,ime for lig!t to !it mirror & ret"rn:


7/28

Now suppose you were stationary on the ground where the

mirror is mounted. What would you see?

t=2

=

2

2 +

2

2

2 =42

2 +

22

2

so t2 = ( )

2

+ 22

2 2 1

2

2

?

??

?

??

= ( )2

2 =( )

2

1 2

2?

??

?

??

=

1 2

2

,!e rate t!at time

passes for t!e to

observers of t!e

same event is

different33

,ime dilation' - time

passes more sloly!en traveling fast+

compared to a

stationary'

observer


8/28

Observer in the Rocket:

Outside Observer:

The outside observer will see the clock time of the ship advance 1

sec for every 2.3 sec that his own clock ticks. The stationary

observer sees the ships clock running slower!

B"t t!e observer on t!e rocket sees t!e person on t!e gro"nd

travel past at a !ig! speed+ and the observer on the ship must

see the same thing occurring to the clock of the outside observer!

= 1

t= 1

1

2

= 0.9=

1

10.81 =

1

0.192.3


9/28

(not!er conse2"ence: 4engt! 5ontraction

6b*ects appear to be compressed along t!eir direction

of motion33

(nd+ as it! time+ t!e observer on t!e train see t!e

orld aro"nd t!em compresses along t!e same line ofmotion33


10/28

1

1 ( )2

= (ll t!ese effects get

bigger)smaller it!

0#0 1#0

0#1 1#0070#7 1#177

0#8 1#99

0#; #;strictly speaking it is t!e

moment"m+ not t!e mass?@


11/28

6t!er eird t!ings:

,o on o"tside

observer+ a traveling

lig!t so"rce seems to

beam' its lig!t

forard

View of

space for astationary

observer

View of

space for a

movingobserver -

sees a

starbow


12/28

$n m"c! t!e same manner t!at t!e time dilation can be

derived+ anot!er direct conse2"ence is t!at matter at rest

!as b"ilt in' energy:

/Amc

ost importantly+ it! t!ese ne clarifications' t!e lasof electromagnetism can be derived correctly3


13/28

So far - applies to v A constant - inertial motion'

Special ,!eory of Relativity >for a specialframe ofreference it! acceleration A 0@

C!at abo"t acceleration% e live in a universe

premeated b+ gravit+, which causesacceleration-. In general, a .

Dor t!e more generalcase e need a more'eneral Theor+ of "elativit+


14/28

6bserved Problem

,!e orbit oferc"ry:

Newtonian Gravity Predicts: 5557.62 arcsec/century

Observed Value: 5600.73 arcsec/century

Difference: 43.11 0.45 arcsec/century too fast!!

This seeming small inconsistency led Einstein to completely change

the way we look at the universe.

(lso tr"e for all planetary orbits+ b"t less so f"rt!er from S"n


15/28

The Principle of Equivalence

The force of gravity is, in most instances, indistinguishablefrom the force due to accelerated motion.


16/28

Deflection of Starlight & Gravitational Lensing

Eistant gala.ies lensed)arped

in appearance by close gala.y

masses


17/28

4ig!t travels along straig!t' lines in a c"rved space-time'

$f t!is ere a soccer

field+ !o o"ld a

soccer ball roll' on it%

4ig!t be!aves similarlytraveling t!ro"g! c"rced

=E space


18/28

Fravitational Reds!ift:

4ig!t loses energy as it travels aay from a so"rce of gravity

/2"ivalent viepoint: time r"ns more sloly

t!e closer yo" are to a so"rce of gravity3


19/28

/lac0 Holesake t!e gravity stronger by cramming

t!e mass into a smaller & smaller vol"me:

event"ally even lig!t cannot escape3


20/28

$ts a case of e.treme c"rvat"re


21/28

on-rotating

>Sc!arsc!ild@

black !ole:

/vents inside t!e

Schwar1schild

"adiuscannot be

seen by a distant

observer - t!is is t!e

$vent Hori1on

Rs =2

2

Rs

= 3

$n "sef"l' "nits:

Every object in the universe has a Schwarzschild radius. But

only if their mass is contained within this limiting distance

do they become a BH.


22/28

Rotating >Gerr@

BH:

6b*ects insidet!e ergosp!ere

co"ld

>s"pposedly@ be

transported toot!er

places)times3

/ven o"tside+

frame dragging'

s!o"ld occ"r

A rotating mass has a tendency to pull space-time along with it


23/28

Frame Dragging at Earth being measured using Gravity Probe B,

launched April 20, 2004. Frame dragging occurs because a

rotating mass has a tendency to pull space-time along with it.
http://einstein.stanford.edu/http://einstein.stanford.edu/


24/28

6bserving Black Holes


25/28

(ccreting Black Holes

(s materialsflos don

toard t!e

black !ole in

t!e form of an

accretion disk+

it does t!e

energy

conversion

t!ing':

Fravitational potential energy kinetic >motion@

energy t!ermal energy radiant energy


26/28

C!ite darf+ ne"tron star+ or black !ole% Ho do e kno%

Size R - arying I-ray emission - cannot occ"r more 2"ickly

t!an it takes lig!t to cross t!e diameter of t!e ob*ect >or elset!e b"rst signal' is as!ed o"t@

Mass - "se binary systems & Geplers =rd 4a3

$s R J RS%

HE 9898 A 5yg I-1 as first knon' BH


27/28

Black !oles s!o"ld also radiate Haking Radiation'


28/28

Travel into a black hole? ot me!

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