Transcript Black Holes and Elementary Particles

Are Black Holes
Elementary Particles?
Y.K. Ha
Temple University
2008
75 years since Solvay 1933
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In physics, there are two
theoretical lengths
• Classical size
• Quantum size
•
Compton
• Classical radius
wavelength
of
a
of an object given
particle given by
by its classical
quantum
theory
mechanics
2
Electron
•
Classical radius:
2
e
r
2
mc
2.82  10
13
cm
• Quantum length:


mc
2.42  10
10
cm
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General Criterion
• If the classical
radius of an
object is larger
than its Compton
wavelength, then
a classical
description is
sufficient.
• If the Compton
wavelength of an
object is larger
than its classical
size, then a
quantum
description is
necessary.
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Black Holes
• Schwarzschild
radius:
2GM
R
2
c
• Proportional to
mass
• Compton
wavelength:


mc
• Proportional to
inverse mass
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Planck Mass
M Pl 
c
5
 2.2 x10 gm
G
• At the Planck mass, the Schwarzschild
radius is equal to the Compton
wavelength and the quantum black hole
is formed.
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Planck Length
l Pl 
G
 33
. x10 cm
3  16
c
• Quantum black holes are the smallest
and heaviest conceivable elementary
particles. They have a microscopic size
but a macroscopic mass.
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Dual Nature
• Quantum black holes are at the
boundary between classical and
quantum regions.
• They obey the macroscopic Laws of
Thermodynamics and they decay into
elementary particles.
• They can have a semi-classical
description.
8
Quantum Gravity?
• There is a total lack of evidence of any
quantum nature of gravity, despite
intensive efforts to develop a quantum
theory of gravity.
• Is is possible that quantum gravity is
not necessary?
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In General Relativity

ds  g ( x)dx dx
2

• Spacetime is a macroscopic concept.
• Is Einstein’s equation similar in nature
to Navier-Stokes equation in fluid
mechanics as a macroscopic theory?
10
Nuclear Force
• Energy levels are quantized in nuclei,
but nuclear force is not a fundamental
force.
• The fundamental theory is Quantum
Chromodynamics of quarks and gluons.
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Graviton
• A hypothetical spin-2 massless particle.
• The existence of the graviton itself in
nature remains to be seen.
• At best it propagates in an a priori
background spacetime.
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Wave Equation
 1 
 
2
 2 2   h  0
 c t

2
• The gravitational wave equation, from
which the graviton idea is developed, is
inherently a weak field approximation
in general relativity.
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Detectability
• It is physically impossible to detect a
single graviton of energy   .
• Detector size has to be less than the
Schwarzschild radius of the detector.
RS  R
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Classical Gravity
• We take the practical point of view that
gravitation is entirely a classical theory,
and that general relativity is valid down
to the Planck scale.
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Spacetime
• This means that spacetime is
continuous as long as we are above the
Planck scale.
• At the Planck scale, quantum black
holes will appear and they act as a
natural cutoff to spacetime.
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What is an elementary particle?
An elementary particle is a logical
construction.
• Are black holes elementary particles?
• Are they fermions or bosons?
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Present Goal
• To construct various fundamental
quantum black holes as elementary
particles, using the results in general
relativity.
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Black Hole Theorems:
1.
2.
3.
4.
5.
Singularity Theorem 1965
Area Theorem 1972
Uniqueness Theorem 1975
Positive Energy Theorem 1983
Horizon Mass Theorem 2005
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Horizon Mass Theorem
For all black holes: neutral, charged or
rotating, the horizon mass is always
equal to twice the irreducible mass
observed at infinity.
M (r )  2 Mirr
Y.K. Ha, Int. J. Mod. Phys. D14, 2219 (2005)
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Black Hole Mass
• The mass of a black hole depends on
where the observer is.
• The closer one gets to the black hole,
the less gravitational energy one sees.
• As a result, the mass of a black hole
increases as one gets near the horizon.
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Asymptotic Mass
M
• The asymptotic mass is the mass of a
neutral, charged or rotating black hole
including electrostatic and rotational
energy.
• It is the mass observed at infinity.
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Horizon Mass
M (r )
• The horizon mass is the mass which
cannot escape from the horizon of a
neutral, charged or rotating black hole.
• It is the mass observed at the horizon.
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Irreducible Mass
M irr
• The irreducible mass is the final mass
of a charged or rotating black hole
when its charge or angular momentum
is removed by adding external particles
to the black hole.
• It is the mass observed at infinity.
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Surprising Consequence !
• The electrostatic and the rotational
energy of a general black hole are all
external quantities.
• They are absent inside the black hole.
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Charged Black Hole
• A charged black hole does not carry
any electric charges inside.
• Like a conductor, the electric charges
stay at the surface of the black hole.
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Rotating Black Hole
• A rotating black hole does not
rotate.
• It is the external space which is
undergoing rotating.
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Significance of Theorem
• The Horizon Mass Theorem is crucial
for understanding Hawking radiation.
3
c
T
8kGM
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Energy Condition
M (r )  M 
• Black hole radiation is only possible if
the horizon mass is greater than the
asymptotic mass since it takes an
enormous energy for a particle released
near the horizon to reach infinity.
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Photoelectric Effect
hf  Ekmax  
• The incident photon must have a
greater energy than that of the ejected
electron in order to overcome binding.
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Hawking Radiation
• No black hole radiation is possible if
the horizon mass is equal to the
asymptotic mass.
• Without black hole radiation, the
Second Law of Thermodynamics is
lost.
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Quantum Black Holes
•
•
•
•
•
•
Mass - Planck mass
Radius - Planck length
Lifetime - stable & unstable
Spin - integer & half-integer
Type - neutral & charged
Other - Area & intrinsic entropy
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Black Hole Types
Spin-0
unstable
M (r )  M 
Spin-1
unstable
M (r )  M 
Spin-1/2
unstable
M (r )  M 
Planck-charge
stable
M (r )  M 
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Spin-0
• A Planck-size black hole created in
ultra-high energy collisions or in the
Big Bang.
• Disintegrates immediately after it is
formed and become Hawking radiation.
• Observable signatures may be seen
from its radiation.
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Planck-Charge
QPl 
G M Pl
• A Planck-size black hole carrying
maximum electric charge but no spin.
• It is absolutely stable and cannot emit
any radiation.
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Spin-1/2
• A Planck-size black hole carrying
angular momentum  / 2 and charge

and
magnetic
moment
.
3Q / 2

Pl
• It is unstable and it will decay into a
burst of elementary particles.
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Spin-1
• A Planck-size rotating black hole with
angular momentum  but no charge.
• It will also decay into a burst of
elementary particles
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Micro Black Holes
2
2
 GM 
 Q
 J

  G    
 c 
 c
 M
2
• Microscopic black holes with higher
mass and larger size may be
constructed from the fundamental
types.
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Black Hole Area
2
2 2

8G M
Q
J c

A
1 1
4
2 
2
4

c
GM
G M

2
2
4GQ

4
c




2
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Quantization
• Quantization of the area of black holes
is a conjecture, not a proof.
• Unphysical spins (transcendental and
imaginary numbers) not found in
quantum mechanics would appear.
• Integer and half-integer spins do not
result in quantization of area.
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Ultra-High Energy Cosmic Rays
Theoretical Upper Limit
• K. Greisen, End to the Cosmic Ray
Spectrum, Phys. Rev. Lett 16 (1966) 748
• G.T. Zatsepin and V.A. Kuzmin, Upper
Limit of the Spectrum of Cosmic Rays, JETP
Lett. 4 (1966) 78.
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GZK Effect
• Interaction of protons with cosmic
microwave background photons would
result in significant energy loss.
• Energy spectrum would show flux
suppression above 6  1019 eV.
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Cosmic Ray Experiments
AGASA
• A dozen
events above
GZK limit
possibly
detected.
Hi-Res
• GZK effect
observed.
• There is no
correlation
with nearby
sources.
Pierre-Auger
• GZK effect
observed.
• Correlation
with AGN
sources.
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GZK Paradox
• Why are some cosmic ray energies
theoretically too high if there are no
near-Earth sources?
• Quantum black holes in the
neighborhood of the Galaxy could
resolve the paradox posed by the GZK
limit on the energy of cosmic rays from
distant sources.
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Annihilation
• Quantum black holes carrying
maximum charges are absolutely
stable.
• They can annihilate with opposite ones
to produce powerful bursts of
elementary particles in all directions
with very high energies.
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Dark Matter
• Planck-charge quantum black holes
could act as dark matter in cosmology
without having to resort to new
interactions and exotic particles
because they are non-interacting
particles.
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Planck-Charge Black Holes
• Their electrostatic repulsion exactly
cancels their gravitational attraction.
• There is no effective potential between
them at any distance.
• The net energy outside the black hole
is identically zero.
• They behave like a non-interacting gas.
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Conclusion
• Quantum black holes could have a real
existence and play a significant role in
cosmology.
• They would be indispensable to
understanding the ultimate nature of
spacetime and matter.
• Their discovery would be revolutionary
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Gerard `t Hooft,
Of fabulous fame.
Ploughing the quantum field,
He set it aflame.
When those gauge particles,
Leaping from virtual to real.
Telling the Yang-Mills saga,
It is a dream come true.
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