Maldacena J. Black Holes and Holography in String Theory. 2004

8/6/2019 Maldacena J. Black Holes and Holography in String Theory. 2004

1/30

Black Holes andBlack Holes andHolography inHolography in

String TheoryString Theory

Juan MaldacenaJuan Maldacena

Institute for Advanced StudyInstitute for Advanced Study

Paris 2004


2/30

Why?Why?

Gravitational force decreases with distance. If the velocity is largeGravitational force decreases with distance. If the velocity is largeenoughenough we can escape,we can escape, e.g. spacecrafts sent to other planets, etc.e.g. spacecrafts sent to other planets, etc.

Everything that goes up comes down againEverything that goes up comes down again

Only if it goes slower thanOnly if it goes slower than vvee ==

v less than vv less than vee v greater than vv greater than vee

NewtonNewtons Gravitys Gravity

11Km/s !11Km/s !


3/30

Consider an object so massive and so small that its escape velocity isConsider an object so massive and so small that its escape velocity is

larger than the speed of light.larger than the speed of light.

Black hole: no light can come out of it.Black hole: no light can come out of it.

The black hole size depends on the mass:The black hole size depends on the mass:

RRBH, sunBH, sun = 3 Km= 3 Km

RRBH, earthBH, earth = 1 cm= 1 cm

RRBH, usBH, us = smaller than any distance we can measure today.= smaller than any distance we can measure today.

Laplace ~ 1800

Black Holes in Newtons Gravity


4/30

Special RelativitySpecial Relativity

The speed of light is the maximum speed at whichThe speed of light is the maximum speed at which

information travels.information travels.

Physics is the same no matter how fast an observer isPhysics is the same no matter how fast an observer is

moving. In particular, all observers measure the same speed ofmoving. In particular, all observers measure the same speed of

light.light.

Space and time are related. How we perceive time dependsSpace and time are related. How we perceive time depends

on how fast we move.on how fast we move.

Time flows differently for observers that are movingTime flows differently for observers that are moving

relative to each other.relative to each other.

Einstein 1905


5/30

Equivalence PrincipleEquivalence Principle

The motion of a particle in a gravitational field is independent ofThe motion of a particle in a gravitational field is independent of

the mass of the particle.the mass of the particle.

Aristotle: Heavy objects fall faster.Aristotle: Heavy objects fall faster.

Galileo: All objects fall in the same way once we removeGalileo: All objects fall in the same way once we remove

the effects of the air resistance.the effects of the air resistance.


6/30

General RelativityGeneral Relativity

NewtonNewtons theory does not obey special relativity.s theory does not obey special relativity.

Einstein: space-time is curved.Einstein: space-time is curved.

A heavy mass curves space-time and the motion of a light particleA heavy mass curves space-time and the motion of a light particle

just follows thejust follows the shortestshortest line along that space-time.line along that space-time.

Gravity is due to space-time curvature.Gravity is due to space-time curvature.

Einstein 1915


7/30

Gravity changes the flow of timeGravity changes the flow of time

If we have two observers in a curved space-time, time canIf we have two observers in a curved space-time, time can

flow differently for each of those observers.flow differently for each of those observers.

Top floor

First floor Time flows slower

By one part in 1015

(one in one quatrillion).


8/30

Examples: Redshift factor at:Examples: Redshift factor at:

Surface of the sun: 1Surface of the sun: 12 102 10-6-6

Surface of the earth: 1Surface of the earth: 18 108 10-10-10

Surface of a neutron star: 0.7Surface of a neutron star: 0.7

(flow of time at some position)(flow of time at some position)Redshift factor =Redshift factor =(flow of time far away )(flow of time far away )

An observer far from a heavy mass sees time going faster than anAn observer far from a heavy mass sees time going faster than anobserver close to it.observer close to it.

Redshift FactorRedshift Factor


9/30

rr

Karl Schwarzschild found the space-time outside a massive object.Karl Schwarzschild found the space-time outside a massive object.

One finds precisely how time slows down:One finds precisely how time slows down:

RedshiftRedshift

11

Black hole radiusBlack hole radius

? STAR EXTERIOR


10/30

Black HolesBlack Holes

Can an object have a size smaller than the black hole radius?Can an object have a size smaller than the black hole radius?

When this was first discovered it was thought that it wasWhen this was first discovered it was thought that it was

something unphysical, that maybe objects could never becomesomething unphysical, that maybe objects could never become

that small.that small.

Later it was understood that:Later it was understood that:

1)1) Some stars can collapse into a black hole.Some stars can collapse into a black hole.

2)2)

An observer who is falling into the black does not feel anything specialAn observer who is falling into the black does not feel anything special

as he crosses the horizonas he crosses the horizon

3)3) There are some objects in the sky that are probably black holes.There are some objects in the sky that are probably black holes.


11/30

The Horizon and BeyondThe Horizon and Beyond

The surface where time slows to a halt is called a horizon.The surface where time slows to a halt is called a horizon.

If you cross it you do not feel anything special, but you cannot comeIf you cross it you do not feel anything special, but you cannot come

back out again.back out again.

Once you cross the horizon, you continue to fall in and you are crushedOnce you cross the horizon, you continue to fall in and you are crushed

into ainto a singularity.singularity. This is a region of very high space-time curvatureThis is a region of very high space-time curvaturethat rips you apart.that rips you apart.

singularitysingularity

horizonhorizon


12/30

Real Black HolesReal Black Holes

Black holes can form in astrophysical processes. Some stars are soBlack holes can form in astrophysical processes. Some stars are so

massive that collapse into black holes.massive that collapse into black holes.

Black holes produced through these processes are of the followingBlack holes produced through these processes are of the following

types:types:

1)1) Black holes that collapse from stars with masses of the orderBlack holes that collapse from stars with masses of the order

of a few times the mass of the sunof a few times the mass of the sun(( rrhh ~ 10 km )~ 10 km )

2)2) Black holes in the center of galaxies with masses of the order of aBlack holes in the center of galaxies with masses of the order of a

billion times the mass of the sun.billion times the mass of the sun.(( rrhh ~ 3 10~ 3 10

99 km ~ size of the solar system )km ~ size of the solar system )


13/30

How Do We See Them?How Do We See Them?

In principle we could see them by seeing how they deflectIn principle we could see them by seeing how they deflectlight, etc.light, etc.

In practice these black holes are surrounded by some gasIn practice these black holes are surrounded by some gas

and this gas heats up in a characteristic way as it falls inand this gas heats up in a characteristic way as it falls in

and astronomers see the radiation coming from this hot gas.and astronomers see the radiation coming from this hot gas.


14/30


15/30

The final shape of a black hole as seen from the outsideThe final shape of a black hole as seen from the outside

is independent of how we make it (up to the total mass,is independent of how we make it (up to the total mass,charge and angular momentum).charge and angular momentum).

Total area of the horizon always increases. Total mass of black holesTotal area of the horizon always increases. Total mass of black holesdoes not necessarily increase.does not necessarily increase.

Gravity waves

Universality

Area law:

Gravity waves


16/30

White Black Holes!White Black Holes!

The laws of quantum mechanics imply that black holes emit thermalThe laws of quantum mechanics imply that black holes emit thermal

radiation.radiation.

Smaller black holes have a higher temperature.Smaller black holes have a higher temperature.

What is this temperature for black holes of different masses?What is this temperature for black holes of different masses?

TTsunsun == 3.6 103.6 10-7-7 KK

TTearthearth = 0.1 K= 0.1 K

TTM=10M=10 KgKg = 7000 K (would look white )= 7000 K (would look white )1818

Hawking 1973


17/30

Why?Why? Pair creationPair creation

particleparticle

Anti-particleAnti-particle

In the presence of a horizonIn the presence of a horizon

particleparticleAnti-particleAnti-particle

In flat spaceIn flat space

horizon


18/30

The Life and Death of a Black HoleThe Life and Death of a Black Hole

Black hole emits radiationBlack hole emits radiation looses energylooses energy has a finite lifetime (if nohas a finite lifetime (if no

additional matter is falling in)additional matter is falling in)

Lifetime for various black holes:Lifetime for various black holes:

Mass of the sunMass of the sun much longer than the age of the universemuch longer than the age of the universe

Our mass ( 100 Kg )Our mass ( 100 Kg ) aa millisecond.millisecond.

Mass of 10Mass of 101212 Kg (mass of a mountain)Kg (mass of a mountain) age of the universe.age of the universe.

Could be observed if it was formed at the big bang.Could be observed if it was formed at the big bang.


19/30


20/30

Heat and EntropyHeat and Entropy

HeatHeat

motion of the microscopic components of the system.motion of the microscopic components of the system.

We can measure the number of microscopic degrees of freedom by theWe can measure the number of microscopic degrees of freedom by the

entropyentropy of the systemof the system

First law of thermodynamicsFirst law of thermodynamics relates entropy and the specific heat.relates entropy and the specific heat.the more energy needed to raise the temperaturethe more energy needed to raise the temperature the more entropythe more entropy

How does the heat of the black hole arise? What isHow does the heat of the black hole arise? What is movingmoving on a black hole?on a black hole?

Compute entropy from the first law:Compute entropy from the first law:

hNG

horizontheofAreaS

4=

233 )10( cm

horizontheofAreaS

=

Bekenstein, Hawking


21/30

Black holes and the Structure of Space-timeBlack holes and the Structure of Space-time

Black holes are independent of what forms them. TheirBlack holes are independent of what forms them. Their

thermal properties only depend on gravity and quantumthermal properties only depend on gravity and quantum

mechanics. This should be explained by a theory of quantummechanics. This should be explained by a theory of quantum

gravity.gravity.

Roughly speaking, the black hole entropy should come fromRoughly speaking, the black hole entropy should come from

the motion of thethe motion of the space-time quanta,space-time quanta, from the elementaryfrom the elementary

quanta (or atomsquanta (or atoms) that make space and time.) that make space and time.

Understanding precisely these thermal aspects of black holes,Understanding precisely these thermal aspects of black holes,we learn something about the quantum structure of space-time.we learn something about the quantum structure of space-time.


22/30

Information LossInformation Loss

We can form a black hole in many different ways, but it alwaysWe can form a black hole in many different ways, but it always

evaporates in the same way.evaporates in the same way.

The principles of quantum mechanics imply that there should beThe principles of quantum mechanics imply that there should bea precise description of black holes.a precise description of black holes.

There should be subtle differences in what comes out of a black hole,There should be subtle differences in what comes out of a black hole,

depending on how we made it.depending on how we made it.

Hawking


23/30

Black holes in string theoryBlack holes in string theory

We understand some simple black holes

Collection of D-branes

And strings.

Entropy: Number of ways to arrange the strings and D-branes.

Strominger, Vafa


24/30

Holography and Black HolesHolography and Black Holes

Entropy = Area = volumeEntropy = Area = volume

Usual optical hologram:Usual optical hologram: 2d surface encodes the information2d surface encodes the information

about the three dimensional shape of an objectabout the three dimensional shape of an object

/

Holography in quantum gravity:

Number of degrees of freedom to describe a region grows

like the area of the region

t Hooft, Susskind


25/30

Holography in String Theory

We can describe the interior of some space-times in terms of a

theory at the boundary.

Theory at the boundary is a relatively simple theory of particles


26/30

Negatively curved space

BoundaryInterior


27/30

Negatively curved space-time

Light trajectory

Particle trajectory

Time

Particles living in the interior attracted to the center


28/30

Interior Boundary

Particles living on the

Boundary describe anobject in the interior

Black holes are described by

a large number of particles on the

boundary

Gravitational physics in the interior Described in an alternative

way by interacting particles living on the boundary.


29/30

Interior

Particles on the boundary could describe very complex objects

Space-time and everything in it emerges dynamically out of the

interaction of the particles living on the boundary.Photo Credit & Copyright: Jason Ware


30/30

ConclusionsConclusions

Black holes are fascinating objects where the effects of space-timeBlack holes are fascinating objects where the effects of space-time

curvature are dramatic.curvature are dramatic.

Black holes combined with quantum mechanics provide veryBlack holes combined with quantum mechanics provide very

interesting challenges to our understanding of space-time.interesting challenges to our understanding of space-time.

String theory is capable of putting together the classical andString theory is capable of putting together the classical and

quantum aspects of black holes. There is no information loss.quantum aspects of black holes. There is no information loss.

We are getting very novel and interesting ways of describing spaceWe are getting very novel and interesting ways of describing spacetime.time.

Documents

Maldacena J. Black Holes and Holography in String Theory. 2004