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Black Hole Physics Black Hole Entropy, Hawking Radiation and Information Paradox 王卓骁 Major: planetary formation THCA Student Seminar Advisor: Doug Lin 2017/11/24 Outline • Over view of black hole physics • Black hole thermodynamics, black hole entropy • Hawking radiation • Information paradox • Recent ambitious hypothesis: Over view of black hole physics • 1784, first idea about black hole, John Michell and Laplace • 1915, general relativity built by Einstein, curvature V.S. matter • 1916, Schwarzschild got the general spherically symmetric, vacuum solution 2GM r = s c2 Over view of black hole physics Event Horizon 2GM r = s c2 Event Horizon Over view of black hole physics Event Horizon • What is event horizon? Schwarzschild solution e.g. world line light cone • Far away observer: space timeslope boundary, “point of no return” Schwarzschild Coordinates. Red line denoted outgoing light rays, while blue for ingoing. Fig. by Quinzacara 2014 Over view of black hole physics Event Horizon • What is event horizon? Schwarzschild solution e.g. • Far away observer: space time boundary, “point of no return” Equivalence Principle. • Traveling astronaut: nothing strange when passing through credit: Andrew Hamilton (JILA) t⇤ = t (r⇤ r) ± − Eddington-Finkelstein Coordinates. Red line denoted outgoing light rays, while blue for ingoing. Fig. by Quinzacara 2014 Over view of black hole physics Stellar evolution Chandrasekhar, 1931 < 1.4 M☉ Oppenheimer, 1939 < 3 M☉ credit: http://chandra.harvard.edu/xray_sources/stellar_evolution.html Over view of black hole physics • 1960s, Kerr solution, Newman solution, no-hair theorem • 1967, pulsar discovered, compact objects became realistic • 1970s, Bardeen, Bekenstein, Carter, Hawking led to BH thermodynamics. Involving QFT, Hawking radiation emerged. • 1972, Cygnus X-1, ~14.8 M☉ • 1974, Sgr A* galactic center (SMBH) Late mid 20th, Golden age Hint for Black hole thermodynamics Entropy? (m1+m2)^2 > m1^2+m1^2 Area theorem: Event horizon area always increase credit: Dan Todd Black hole thermodynamics Classical thermodynamics Bardeen, Bekenstein, Carter, Hawking, 1973 温度 交换 平衡 为什么kappa, determined by m j q c4 = 4GM • 0th: Stationary black hole has constant surface gravity (by GR) T Constant temperature • 1st: M E Energy conservation • 2nd: Horizon area increasing A S Entropy increasing • 3rd: surface gravity cannot achieve 0 Finite process cannot approch 0K Can we specify black hole temperature and entropy? Thermal radiation? SH ? TH ? Hawking radiation Quantum Field Theory credit:Dan Todd Hawking radiation Quantum Field Theory Implies black body radiation Hawking radiation Temperature Blackbody radiation • Certain temperature TH = /2⇡ • what if comparing to CMB (negligible?) • mass loss -> evaporation credit: https://universe-review.ca/R15-17-relativity06.htm Hawking radiation Entropy • Black hole entropy SBH = A/4 • using energy, temperature, entropy relation from classical view • questions arisen… • Inner texture? —> General relativity violation? • Information lost? —> Quantum mechanics violation? No-hair theorem Hawking radiation • Only 3 values characterizing BH • M, J, Q • Hawking radiation only depends on • Information seems lost Really annoyed so many physicists credit: Vishveshwara Paradoxes Hawking radiation Preserved <Equivalence Principle> Break conserved <information> destroyed credit: Jen Christiansen Information paradox Quantum Entanglement Emitting particle mutually entangled credit: http://www.eoht.info/page/Quantum+entanglement Susskind 1993 Information paradox 1st try: Hawking Radiation does carry info credit: Matt Strassler Emitting particle should entangled with both in fallings and previous emits Information paradox 2nd try: snip in fallings and emits Maldacena 1997, holography Firewall Hypothesis Polchinski 2012 credit: Matt Strassler Equivalence principle: free-fall should feel the same as floating in empty space Information paradox 2nd try: snip in fallings and emits I’m sorry that no one has gotten rid of the firewall. But please keep trying. Firewall Hypothesis Polchinski 2012 Information paradox 3rd try: ER=EPR Spacetime entangled with gravity ER = EPR Maldacena 2013 • ER, Einstein Rose bridge • EPR, Quantum Entanglement • In falling particles connected with emitting particles by wormhole Summary • Black hole thermodynamics, BH temperature, entropy • Hawking radiation, information paradox • Firewall hypothesis, ER=EPR hypothesis • Future prospect: ongoing Event Horizon Telescope project.
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