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## General Relativity and Applications 4. Black Holes

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**General Relativity and Applications4. Black Holes**Edmund Bertschinger MIT Department of Physics and Kavli Institute for Astrophysics and Space Research**“It was like a hole in the sky…” – Iman Farid**Above: The moon occulting the sun (29 March 2006, APOD 31-Mar-06). Left: A black hole occulting Saturn (simulated). (Cover photograph, Exploring Black Holes)**In my entire scientific life, extending over forty-five**years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity provides theabsolutely exact representation of untold numbers of black holes that populate the universe. Subrahmanyan Chandrasekhar, The Nora and Edward Ryerson Lecture, 22 April 1975**What is a black hole?**A massive spacetime curvature singularity, Surrounded by an event horizon (a point or ring of infinite density and tidal acceleration) (a spacetime boundary between causally disconnected regions of the universe)**Outline**The Astrophysics of Black Holes • Two varieties (small, super-large) • How do we recognize a black hole? The Physics of Black Holes The Fun of Black Holes**Black Holes in the Universe**Most basic property: mass Galactic Nuclei: 106 to 109 Msun Dead stars: 3 to 15 Msun**The biggest nearby black hole: Sgr A***Center of our galaxy: radio source Sgr A* Distance: 8 kpc = 8000 pc, 1pc = 3.3 lt-yr Highly obscured in optical Dense central star cluster visible in infrared Photo/illustration from A. Tanner, UCLA**Stellar Dynamics of Sgr A***• M = combined mass (BH + star) • a = semimajor axis of stellar orbit • P = orbital period • Star S0-2 has a=920 AU, P=14.5yr • M = 3.7x106 solar masses (20%) A. Ghez et al. (2005) From R. Genzel et al., Max-Planck-Institut für extraterrestrische Physik**How do we know it’s a black hole?**No firm proof yet: Black holes are indistinguishable from Newtonian bodies at large distances r: Lack of alternative: Any plausible alternative would lead quickly to gravitational collapse**Pinning down a black hole:Observe it close in**Accretion disk Angular momentum and dissipation forces gas falling toward the BH to orbit in a disk Friction causes the gas to slowly spiral in toward the BH, and makes the gas very hot so it glows. The problem: Relativistic disks are much too distant to resolve! Figure from STScI**The Anatomy of Black Holes**Indirectly looking close in: Emission from inner accretion disk or jets Figure from NASA/ GSFC Imagine**Black Hole vs. Neutron Star:Surface or Event Horizon?**Neutron stars are brighter and have X-ray bursts from thermonuclear explosions on their surfaces. BH do not. Garcia et al. 2001 Chandra X-Ray Observatory**Relativistic Jets**From NRAO/AUI: R. Perley, C. Carilli, J. Dreher We don’t know how the jets form! Magnetic fields? BH spin? From NRAO/AUI and STScI: D. Merritt and R. Ekers Did jets change direction when black holes collided?**Gamma-Ray Bursts**GRB 990123 Long-duration (> 2s) GRBs caused by relativistic jets of a newly born BH, pointing toward earth 20-50 keV 50-100 keV 100-300 keV >300 keV Figure from NASA/ SkyWorks Digital 0 50 100 seconds Figure from NASA CGRO/BATSE**Outline**The Astrophysics of Black Holes The Physics of Black Holes • Orbits • Light cones and Penrose diagram • Event horizon The Fun of Black Holes**Gravity as both an effect of curvature and as a force.**In flat spacetime, freely-falling bodies follow paths of maximal proper time. Einstein equivalence principle: the same is true in curved spacetime (geometry). Geometry/force duality: Gravity is a force and torque in local Lorentz frames**f**Orbits in Newtonian Physics Conserved quantities:**Orbital dynamics from E, L**In Lecture 3, Veff(R) was introduced to deduce the expansion R(t) of the universe!**Orbital periods**Veff r E/m For bound Kepler orbits, both r and f are periodic functions of t with identical periods. Consequence: Bound orbits are Closed ellipses!**Numerical Integration of Orbits**JKerrOrbits was developed by S. Tuleja, T. Jezo, and J. Hanc based on earlier Schwarzschild integrator of A. Riess and E. Taylor**Orbits around a non-spinning BH:Curved spacetime modifies E,**L, vr Taylor expand v/c << 1, r >> GM/c2 general relativity special relativity t = proper time**Effective Potential for Non-spinning BH**Veff E/m r general relativity 2GM/c2 For details see Lecture Notes 3 and Exploring Black Holes Chapters 3, 4**Perihelion precession**Orbits around a point mass in GR: Two different periods! Pr Pf Orbits do not close! Mercury: 43”/century PSR 1913+16: 8o/year**ct**y x Light Cone My worldline (trajectory) If you pass inside the cone, I can communicate with you! Also, my worldline can never move outside these cones! The cone moves along the trajectory with me! Minkowski diagram without a black hole**h**t=+ r= r=0 t=- x Penrose Diagrams: Spacetime Map Map infinity to boundary of a compact domain: Minkowski diagram becomes a Penrose Diagram. Purpose is to display “light cones” – worldlines of all massive particles must remain inside the cone. Light cones preserved (conformal transformation). Angular coordinates (q,f) not shown in the diagram. Severe distortion near boundary. time space**r=0**t=+ r= r=0 t=- Spherical, Uncharged Black HoleOppenheimer and Snyder, 1939 Penrose diagram: Global geometry Topology Causal structure Event horizon: Once crossed, there is no return! Outwards-directed light rays remain stuck to the event horizon! Central Singularity Event Horizon Worldline of a collapsing star’s surface**The Schwarzschild singularity is a time, not a place**Across the horizon,all of space is crushed, like a big bang singularity in reverse. Spatial geometry of a black hole, From Andrew Hamilton, U. Colorado (Google him to learn about his fantastic simulated BH voyage!)**What happens at the event horizon?**• Classically, nothing. • Event horizon is determined by global, not local, structure • Quantum mechanically, Hawking radiation • Particle vacuum state fluctuates with creation/annihilation of virtual pairs of particles • Negative energy particles fall in, positive energy ones escape, black hole loses mass as blackbody radiation • Completely negligible for astrophysical black holes**How can matter escape from a BH?**Hawking radiation is extremely weak and may never be observed. Yet it raises profound questions of quantum gravity that perhaps only Superstring Theory will be able to answer! Note: Hawking radiation also includes antiparticles! (The particle can fall into the black hole.) • Quantum tunneling produces a Particle-Antiparticle pair from the vacuum! • http://superstringtheory.com/blackh/blackh3.html • Warning: this diagram is misleading because quantum particles are in fact waves!**Outline**The Astrophysics of Black Holes The Physics of Black Holes The Fun of Black Holes**Interstellar travel by BH?**Penrose diagram of a spherical, charged BH (half of Reissner-Nordstrom spacetime). Gravitational repulsion of electric fields causes freely-falling observer to bounce back to increasing r, crossing into another universe! Similar to dark energy! Problem: instability of the second horizon destroys the connections (Poisson and Israel “mass inflation”). Cool diagram from Andrew Hamilton, U. Colorado**Interstellar travel by BH?**Penrose diagram of a spherical, charged BH (half of Reissner-Nordstrom spacetime). Gravitational repulsion of electric fields causes freely-falling observer to bounce back to increasing r, crossing into another universe! Similar to dark energy! Problem: instability of the second horizon destroys the connections (Poisson and Israel “mass inflation”). Cool diagram from Andrew Hamilton, U. Colorado**Nature of the Singularity**• Classical gravity: spacetime geometry near the singularity not fully understood • Oscillatory curvature singularity (Belinsky, Khalatnikov, Lifshitz): “spaghettification” or “eggbeater”? • Spacelike, timelike, or null? • Horizon structure? Singularities without horizons? • Quantum gravity: singularity resolved, but is very small (10-35 m) • Quantum coherence and probability: whence information? Superstring states?**Outstanding Questions**• Are the BH of nature exactly the BH predicted by Einstein’s theory? • How do supermassive BH form? What role do they play in galaxy formation? (G. Kauffmann lectures) • How and why do relativistic jets form? (R. Blandford’s lectures)**More Questions**• What is the nature of the singularity? • What is the quantum mechanical wavefunction of a black hole spacetime? • Are four spacetime dimensions enough to properly describe a black hole? • ???