Pisin Chen

Pisin Chen

Department of Physics and Graduate Institute of Astrophysics &

Leung Center for Cosmology and Particle Astrophysics National Taiwan University

NTU Joint Physics Colloquium, May 10, 2016

General relativity predicts the existence of black holes

Curvature

×

Karl Schwarzschild

Event Horizon (事件視界):

Schwarzschild = 黑盾

ds² = - 1- 2GM c²r

æèç ö

ø÷ c²dt² + 1- 2GM c²r

æèç ö

ø÷

-1

dr² + r²

(

)

1

0 ® ¥

Diverges:

r_h º 2GM c²

Schwarzschild radius

The first black hole solution (1916):

Non-rotating BH

Golden Age of classical black hole 1963 – 1973

Roy Kerr

ds² = - D

r^{2 dt - asin}

2qdf

( )

⁽

⁾

r² = r² + a² cos²q, r₀² = r² + a², D = r² - 2Mr + a²

Spinning black hole solution (Roy Kerr, 1963)

Interstellar

Three types of black holes

Supermassive BH (millions to billions of solar mass)

Stellar size BH (several to tens of solar mass)

Primordial BH (induced around Big Bang)

Black hole thermodynamics

1972 – 1973

Black hole thermodynamics

• Zeroth Law: The surface gravity of a non- rotating black hole is constant.

• First Law: The change of total energy equals to that of the area, angular momentum, and charge:

• Second Law: The area of the BH surface can only increase in time.

• Third Law: Zero surface gravity BH does not exist.

In another word, cannot be zero.

dE = k

8 p ^dA + WdJ + FdQ dA

dt ³ 0

k

Black hole entropy

• Bekenstein-Hawking entropy:

S

= k

A 4l

E = k

T

Jacob Bekenstein (1947-2015) Ludwig Boltzmann (1844-1906)

Tomb of Boltzmann in Vienna, Austria

S = k logW

Entropy

2

law of thermodynamics

Quantum mechanics Gravity

General relativity Thermodynamics

Geometry

S

= k

A 4l

Black hole entropy: an amazing equation!

Worse yet, S is NOT proportional to the BH volume, but its surface area!

Hawking evaporation: Linking

GR, QM, and Stat Mech in one stroke

r

= 2GM

c

g = GM r

k

T

= c

8 p GM = g

2 p c

Black hole evaporation

T

M

?

Frolov, V. V. P., Novikov, I. D. (1998). Black hole physics: basic concepts and new developments (Vol. 96). Springer

Lifetime of black holes

• Hawking temperature:

• Stefan-Boltzmann law:

Lifetime of BH: Solar mass BH=10⁶⁷ years

Age of the universe = 1.38 x 10¹⁰ years

E

A = s T

µ 1 M

A = 4 p r

µ M

Black hole surface area:

BH evaporation rate inversely proportional to

mass squared:

dM

dt µ 1

M

John Wheeler (who invented the name Black Hole):

“What would happen if I drop my coffee into a black hole?”

No-hair theorem

The information loss problem

Can Hawking radiation carry out

information after all?

Recommend reading

BH Complementarity Principle

The basic requirement of natural law is that it is consistent with causality.

New Scientist, Oct. 2006,

Leonard Susskind, Lárus

Thorlacius, John Uglum, “The Stretched Horizon and Black Hole Complementarity”

An elephant falls toward a BH

A sees it indefinitely approaches the horizon.

B sees instead that it pass through

A sees it get thermalized and radiated.

B sees it continue to its doom.

Quantum entanglement

“A quantum whole is not simply the sum of its parts”.

A B

Schrödinger:“Verschrankung”(1935) as a result of discussing with Einstein

“Quantum entanglement is not just a property of QM, it is THE character of QM. It fundamentally breaks QM from classical physics.

What is quantum entanglement?

Thermodynamics:

Entropy Disorder

Quantum Informatics:

Entanglement Entropy How tangled the system is

Monogamy of quantum entanglement

From Shannon entropy to von Neumann entropy

John von Neumann

Claude Shannon (1916-2001)

Page Time Old Black Hole Young

Black Hole

Information

Entanglement entropy

Pure state black hole

S

Don Page

When would BH entanglement entropy come out?



AMPS firewall paradox

In 2012, four physicists (AMPS) argued that the 3

basic assumptions that led to the BH complementarity principle, namely,

1. Unitarity

2. Local quantum field theory 3. No drama

cannot be all consistent. They suggested that the

“most conservative” solution would be that there

exists a firewall on the BH surface, anything falls into BH would be burned into ashes.

AMPS firewall paradox

• Ahmed Almheiri, Donald Marolf, Joseph Polchinski, James Sully,

“Black Holes:

Complementarity or Firewalls?”, JHEP 1302 (2013) 062.

• Ahmed Almheiri, Donald Marolf, Joseph Polchinski, Douglas Stanford, James Sully,

“An Apologia for Firewalls”, JHEP 1309 (2013) 018.

x 𝜙

The energy of a quantum field at a location x

depends on the variation of the field value there.

The value of the quantum field needs not be continuous on a boundary across which the spacetime is not continuous.

Nature 496, 20 – 23, April 4 2013.

General relativity:

For a sufficiently large BH, whose curvature is small, objects should pass its horizon

uneventfully－“No Drama”

AMPS firewall ：

The requirement that Hawking radiation can bring information out from BH would result in the notion of firewall.

Conflict between QM and GR!

Quantum Mechanics

vs. General Relativity

Solution 1: Horizon does not exist

• Media: Hawking said BH does not exist (2014).

• Actually what Hawking said was, Event Horizon may not exist, the only thing real is the Apparent Horizon.

• Apparent horizon can trap matter and lights, but as the BH evaporates, they will be released.

• However, the notion of apparent horizon depends on the choice of the coordinates, and so it’s not an invariant

statement.

Solution 2: Quantum entanglement is actually equivalent to wormholes

ER (Einstein–Rosen) =EPR (Einstein–Podolsky–Rosen)

＝

Wormhole

Solution 3: Decoding BH information would take extremely long time

The existence of

firewall can only be

revealed when the BH information is

decoded, but thqt will take a time longer

than BH’s lifetime.

D. Harlow, P. Hayden,

“Quantum Computation vs. Firewalls”, JHEP 06

(2013) 085,

[arXiv:1301.4504 [hep- th]].

Solution 4: BH Remnant stores the

missing information

Generalized uncertainty principle

- Gravitational correction to QM

GPU leads to BHR

• Generalized uncertainty principle argues for the existence of a minimum length (Planck length)

• Repeating what Hawking did using standard UP, invoking GUP to BH evaporation.

Hawking evaporation would come to a stop when BH radius reaches Planck length

Black hole remnant

• BHR can be a throat to the “bag of gold”, a

wormhole, a large interior volume.

Naked Black Hole Firewalls

Molecular-type Workshop on Black Hole

Information Loss Paradox, YITP, Kyoto, May 2015

Hideki Yukawa Memorial Hall

Yukawa Institute for Theoretical Physics

How would firewalls become naked?

• As a quantum process, fluctuations are inevitable in Hawking radiation.

• BH’s backreaction to these fluctuations would

“teleologically” cause the migration of the event horizon inside of where it would be.

• The supposed firewall would therefore be observable to distant observers, or “naked”.

• On the other hand, stellar size BHs are large and have small curvatures; therefore GR should work.

• So the notion of firewalls is not as conservtive as AMPS argued.

A conceptual Penrose diagram illustrating the formation of a Schwarzschild black hole from a collapsing null shell, and its subsequent Hawking evaporation. Here, the event

horizon (r_EH) has been shifted inward some distance from the adiabatic horizon (r_AdH) due to a quantum fluctuation. This renders the firewall (denoted by the dashed curve that appears after the Page time t_Page) naked. The apparent horizon (r_ApH) is also shown for comparison, but light rays can escape from inside it, since the black hole is shrinking.

Kyoto Ginkakuji Temple (銀閣寺)

Kyoto Ginkakuji Temple (銀閣寺)

Kyoto Philosopher Path

Kyoto Philosopher Path (哲學之道)

Kyoto Philosopher Path (哲學之道)

A conceptual design of the

accelerating plasma mirror experiment

Unruh Effect vs. Hawking Effect

Proposed Unruh effect experiment

(Chen-Tajima, 1999)

Plasma wakefield acceleration

Tajima-Dawson (1979)- Laser driven

Chen-Dawson-Huff-Katsouleas (1985)- Particle beam driven

CORE-U, Hiroshima 57

SLAC & LBL- Acceleration of O(100) GeV/m observed!

AWAKE- A new experiment at CERN

Relativistic Plasma Mirror

Bulanov, Esirkepov, Tajima (2003)

CORE-U, Hiroshima 58

Reflected laser pulse Lorentz-boosted and tighter-focused.

Plasma mirror can also be created

by laser bouncing off the target

Plasma wakefield in the nonlinear

regime acts like a tunami

Accelerating plasma mirror

• Born relativistic

• Laser velocity in plasma can be accelerated and therefore its wakefield

• Acceleration can increase in time and stop abruptly

62

What can it offer?

What it cannot offer?

• Being in flat space, unitarity preserved: no loss of information

• No singularity either

• Investigation of correlation of partner modes and possible final outburst of energy

霍京粒子

真空微擾量子態偶合纒結 能量爆衝? 伙伴粒子

真空微擾振盪

視界 電漿反射鏡的世界缐

How would accel. plasma mirrors reveal the

secrets of black hole information loss paradox?

？

Summary – The war continues to rage

2016

Firewalls would be naked