Are Black Holes Elementary Particles? Y.K. Ha Temple University 2008

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Are Black Holes Elementary Particles? Y.K. Ha Temple University 2008. 75 years since Solvay 1933. Classical size Classical radius of an object given by its classical theory. Quantum size Compton wavelength of a particle given by quantum mechanics.

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### Are Black Holes Elementary Particles?Y.K. HaTemple University2008

75 years since Solvay 1933

Classical size

Classical radius of an object given by its classical theory

Quantum size

Compton wavelength of a particle given by quantum mechanics

In physics, there are two theoretical lengths
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.

General Criterion

Proportional to mass

Compton wavelength:

Proportional to inverse mass

Black Holes
Planck Mass
• At the Planck mass, the Schwarzschild radius is equal to the Compton wavelength and the quantum black hole is formed.
Planck Length
• Quantum black holes are the smallest and heaviest conceivable elementary particles. They have a microscopic size but a macroscopic mass.
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.
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?
In General Relativity
• Spacetime is a macroscopic concept.
• Is Einstein’s equation similar in nature to Navier-Stokes equation in fluid mechanics as a macroscopic theory?
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.
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.
Wave Equation
• The gravitational wave equation, from which the graviton idea is developed, is inherently a weak field approximation in general relativity.
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.
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.
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.
What is an elementary particle?

An elementary particle is a logical

construction.

• Are black holes elementary particles?
• Are they fermions or bosons?
Present Goal
• To construct various fundamental quantum black holes as elementary particles, using the results in general relativity.
Black Hole Theorems:
• Singularity Theorem 1965
• Area Theorem 1972
• Uniqueness Theorem 1975
• Positive Energy Theorem 1983
• Horizon Mass Theorem 2005
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.

Y.K. Ha, Int. J. Mod. Phys. D14, 2219 (2005)

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.
Asymptotic Mass
• 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.
Horizon Mass
• 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.
Irreducible Mass
• 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.
Surprising Consequence !
• The electrostatic and the rotational energy of a general black hole are all external quantities.
• They are absent inside the black hole.
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.
Rotating Black Hole
• A rotating black hole does not rotate.
• It is the external space which is undergoing rotating.
Significance of Theorem
• The Horizon Mass Theorem is crucial for understanding Hawking radiation.
Energy Condition
• 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.
Photoelectric Effect
• The incident photon must have a greater energy than that of the ejected electron in order to overcome binding.
• 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.
Quantum Black Holes
• Mass - Planck mass
• Lifetime - stable & unstable
• Spin - integer & half-integer
• Type - neutral & charged
• Other - Area & intrinsic entropy
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.
Planck-Charge
• A Planck-size black hole carrying maximum electric charge but no spin.
• It is absolutely stable and cannot emit any radiation.
Spin-1/2
• A Planck-size black hole carrying angular momentum and charge

and magnetic moment .

• It is unstable and it will decay into a burst of elementary particles.
Spin-1
• A Planck-size rotating black hole with angular momentum but no charge.
• It will also decay into a burst of elementary particles
Micro Black Holes
• Microscopic black holes with higher mass and larger size may be constructed from the fundamental types.
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.
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.
GZK Effect
• Interaction of protons with cosmic microwave background photons would result in significant energy loss.
• Energy spectrum would show flux suppression above eV.
• 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.
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.
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.
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.
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

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.