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Transcript of 20 Blackholes
7/21/2019 20 Blackholes
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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