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 Lec 20: Black Holes 1

Black Holes

Lecture 20

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 Lec 20: Black Holes 2

Lecture Topics Schwarzchild radius

black hole radius

The density of black holes

Properties of black holes

allin! into a black hole

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 Lec 20: Black Holes "

#akin! a $%ark Star& Suppose the escape 'elocity of an ob(ect was

e)ual to the speed of li!ht*

 R s = Schwarzchild radius

Puttin! in nu+bers:

 M  R   3s  =  Rs  in km

 M  in solar masses

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 Lec 20: Black Holes ,

%roppin! rocks Suppose we drop a rock fro+ 'ery far out in

space* How fast is it !oin! when it hits-

The potential ener!y of the ball is:

#. / +ass distance fro+ center of

arth

  + +ass of rock

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 Lec 20: Black Holes 3

4ra'itational Potential ner!y The potential ener!y difference between

two points surroundin! a +ass is:

21  R

GMm

 R

GMm PE    −=∆

5hen /2 67 infinity 8'ery lar!e distance9

/2 7 /1

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 Lec 20: Black Holes

Potential ⇒ ;inetic ner!y The kinetic ener!y of the rock when it hits is:

where ' 'elocity of the rock at i+pact

  + +ass of the rock*

This ; co+es fro+ the con'ersion of P

into ; 8by !ra'ity9*

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 Lec 20: Black Holes <

=on'ertin! P to ;  >ll the P the rock had when it started is

con'erted to ; at i+pact*

which +eans

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 Lec 20: Black Holes ?

The scape @elocity /e'erse the proble+:

5hat is the +ini+u+ speed upward the rock

+ust ha'e to escape the earth* Ats the sa+e as if you let if fall 8only !oin! the

other way9C

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 > Black Hole is Born

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Black holes bend space

=lip fro+ $Space 1DDD& E bad 0s Scii series

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 Lec 20: Black Holes 11

How bi! are black holes-Fb(ect #ass 8#sun9 /s

Star 10 "0 k+

Star " D k+

Sun 1 " k+

arth " G 106

  D ++

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 Lec 20: Black Holes 12

How dense are black holes- The a'era!e density of a black hole is:

but

#ore +assi'e black holes are less denseC

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 Lec 20: Black Holes 1"

%ensities 8contd9 or a black hole with M = M 

 sun*

ρ = 2 x 1016 g/cm3 

or M = 10 M  sun

*

ρ  2 x 1014 g/cm3 

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 Lec 20: Black Holes 1,

@ery #assi'e Black Holes Suppose we could +ake a black hole a

bi! as the solar syste+. e*! /s  ,0 >*

Then # 2 G10D #sun

and ρ  0*003 !Ic+"  8C9

 6 > 2 G10D #sun black hole can not be

for+ed by a sin!le star*

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5arped Space Ti+e

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 Lec 20: Black Holes 1

The 'ent Horizon The e'ent horizon 

is located at /s*

 >nythin! inside thee'ent horizon is

!one fro+ si!ht

fore'er 8nothin! canescape9*

/s

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'ent

Horizon

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 Lec 20: Black Holes 1?

Ti+e %ilation

/ecall that clocks run slower on the

surface of the earth than on a +ountain

top* @iewed fro+ space clocks slow down

as they approach the e'ent horizon*

 >t the e'ent horizon. the clock stopsC

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 Lec 20: Black Holes 1D

4ra'itational /edshift

The !ra'itational redshift !ets lar!er

and lar!er as ob(ects approach the

e'ent horizon* >t the e'ent horizon the redshift

beco+es infiniteC

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allin! in

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 Lec 20: Black Holes 21

allin! into a black hole

Black Hole

 >

$>& falls in while$B& stays outside*

5hat happens if you fall in-

B

=lock

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 Lec 20: Black Holes 22

Black Hole

Person > fallin! into BH

  Person outside BH sees

1* Photons fro+ > redshifted*

2* =lock > slow down*"* Person > stretched and

  ripped apart by tidal forces*

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 Lec 20: Black Holes 2"

Person fallin! in sees

Af person a $paused& while fallin! in then he

would see: =lock B is runnin! 'ery fast*

Photons co+in! fro+ person B and the rest of the

uni'erse are blueshifted* @isible photons beco+e J6rays and γ 6raysC

The tidal forces will be 'ery bad for the personfallin! into the black hole*

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 Lec 20: Black Holes 2,

Tides

Tidal forces are due to the difference in

the !ra'itational force across an ob(ect*

Kear a black hole !ra'ity chan!es 'eryrapidly with distance* neutron stars tooC

Tides pull on the ob(ect and stretch it inthe direction of the star*

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 Lec 20: Black Holes 23

Tides

Black Hole

Tides pull the two people

towards the outer walls*

People lyin! in 12 ft*

spaceship near the walls*

%istance Tidal orce

fro+ BH 8 !s 9

3000 k+ 1*2

1000 k+ 1,,  100 k+ 1*,G103

  20 k+ 1*?G10<

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 Lec 20: Black Holes 2

=irclin! a Black Hole

Frbitin! lyin! alon!

e'ent horizon

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 Lec 20: Black Holes 2<

 >re black holes dan!erous-

BHs dont !o around scoopin! up

people and stars*

Fnly if you !et 'ery close to one is therea proble+*

/eplacin! the sun with a 1 #sun black

hole would not chan!e the orbits of theplanetsC But wed ha'e a proble+ keepin! war+*

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5hats on the other side-

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The sin!ularity

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 Lec 20: Black Holes "0

/ele'ance of Black Holes

Black holes can be for+ed when a

+assi'e star collapses

#core 7 , #sun  8star: # 7 13 #sun9 =enter of the #ilky 5ay 8our 4alaGy9

 > 2G10 #sun black hole

=enters of Muasars

Black holes up to 2G10D #sun 

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 Lec 20: Black Holes "1

An6=lass Muestion

19 5hat is the radius of a 1.000.000 #sun black hole 8in

k+9-

a9 10  b9 "0 c9 "G10  d9 "G10< 

⇑ 

 M  R s

  ×=   3

 R s in km, M  in M sun

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 Lec 20: Black Holes "2

An6=lass Muestion

19 5hat is the radius of a 1.000.000 #sun black hole 8in

k+9-

a9 10  b9 "0 c9 "G10  d9 "G10< 

⇑ 

29 5hat is the e'ent horizon of a Black Hole-

a9 Place where tides rip thin!s apart

b9 Place fro+ which nothin! can escapec9 Place to !o for a drink

d9 Place where photons are e+itted

⇒

 M  R s

  ×=   3

 R s in km, M  in M sun

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 Lec 20: Black Holes ""

Kearin! a Black Hole

 >pproachin! $nterin!&

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 Lec 20: Black Holes ",

The i+pact 'elocity

Puttin! in so+e nu+bers

  #earth  G 102, k!

  /earth ,00 k+ *,G10 +

  4 *<G10611 K6+2Ik!2  8+"Ik!Is29

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 Lec 20: Black Holes "3

scape 'elocity

scape 'elocity is the speed an ob(ect wouldneed to escape fro+ a celestial body*

The escape 'elocity depends on +ass*

Ga+ples: arth: 11*2 k+Isec 823.000 +ph9

#oon: 2*, k+Isec

1 k+ asteroid: 1*" +Isec 8you could (u+p off itC9

Sun: 1? k+Isec 5hite %warf: 000 k+Isec CC

How hi!h can the escape 'elocity !et-

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 Lec 20: Black Holes "

%ark Stars

/e'* Nohn #itchell 6 1<?"

 >n ob(ect +ore +assi'e than the Sun

could ha'e an escape 'elocity !reaterthan the speed of li!htC

Today we call this ob(ect a black hole* >n ob(ect fro+ which no li!ht can escape*

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"<

#akin! a $%ark Star&

Suppose the escape 'elocity of an ob(ect wase)ual to the speed of li!ht*

 R s = Schwarzchild radius