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Are Black Holes Elementary Particles? Y.K. Ha Temple University 2008 75 years since Solvay 1933 1 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 3 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. 4 Black Holes • Schwarzschild radius: 2GM R 2 c • Proportional to mass • Compton wavelength: mc • Proportional to inverse mass 5 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. 6 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. 7 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? 9 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. 11 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. 12 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. 13 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 14 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. 15 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. 16 What is an elementary particle? An elementary particle is a logical construction. • Are black holes elementary particles? • Are they fermions or bosons? 17 Present Goal • To construct various fundamental quantum black holes as elementary particles, using the results in general relativity. 18 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 19 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 M irr Y.K. Ha, Int. J. Mod. Phys. D14, 2219 (2005) 20 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. 21 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. 22 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. 23 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. 24 Surprising Consequence ! • The electrostatic and the rotational energy of a general black hole are all external quantities. • They are absent inside the black hole. 25 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. 26 Rotating Black Hole • A rotating black hole does not rotate. • It is the external space which is undergoing rotating. 27 Significance of Theorem • The Horizon Mass Theorem is crucial for understanding Hawking radiation. 3 c T 8kGM 28 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. 29 Photoelectric Effect hf Ekmax • The incident photon must have a greater energy than that of the ejected electron in order to overcome binding. 30 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. 31 Quantum Black Holes • • • • • • Mass - Planck mass Radius - Planck length Lifetime - stable & unstable Spin - integer & half-integer Type - neutral & charged Other - Area & intrinsic entropy 32 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 33 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. 34 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. 35 Spin-1/2 • A Planck-size black hole carrying angular momentum / 2 and charge 3QPl / 2 and magnetic moment . • It is unstable and it will decay into a burst of elementary particles. 36 Spin-1 • A Planck-size rotating black hole with angular momentum but no charge. • It will also decay into a burst of elementary particles 37 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. 38 Black Hole Area 2 2 2 8G M Q J c A 1 1 4 2 2 4 c GM G M 2 2 4GQ 4 c 2 39 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. 40 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. 41 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. 42 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. 43 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. 44 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. 45 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. 46 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. 47 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 48 49 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. 50