Report

Black Holes Matthew Trimble 10/29/12 History • Einstein Field Equations published in 1915. • Karl Schwarzschild: physicist serving in German army during WW1. • Solved EFE for a non- rotating, spherical source, and wrote a paper on quantum theory while suffering from pemphigus on Russian front. • His solution is called the Schwarzschild Metric. Schwarzschild Metric Schwarzschild Metric • Same metric can describe non- rotating black holes. • r*: Schwarzschild radius- the event horizon of the black hole. • r*= 2GM/c^2 • Observers outside cannot view events inside. • 3km for the Sun, 9mm for the Earth. Black Hole Formation • Once matter is compressed smaller than r*, collapse occurs, forming a black hole. • The kind of pressures needed to do this are typically found in Type II Supernova explosions. • r* is the point at which an object’s escape velocity is c, meaning nothing can come back out. Vacuum Energy • In empty space, pairs of particle-antiparticle pairs appear and annihilate on the Planck timescale: 5.39X10^-44 s • Because this happens so quickly, this does not violate the Uncertainty Principle. • The short lifetime gives these particles the name Virtual Particles. Hawking Radiation • Near a black hole, time is dilated enough that these virtual particles last longer than the Planck timescale. • One particle can be released away from the black hole, while the other falls in. • By measuring positive energy particles, the particle with negative energy had to fall into the singularity, lowering the mass and energy of the black hole. Shrinking • Because the blackbody temperature is inversely proportional to the mass, the Hawking Radiation causes the black hole to shrink. • This proportionality also means that a very massive black hole radiates weakly, and can easily overcome this loss through accretion. Mini Black Holes • With a very small M, these Hawking radiate very quickly, meaning they will evaporate long before they have a chance to accrete matter and grow large. Bekenstein-Hawking Entropy • Derived using the blackbody temperature of Hawking radiation. • Entropy is also proportional to the number of microstates. • For a black hole, these microstates are the number of ways a quantum black hole could be formed. • The B-H Entropy method agrees with M theory’s prediction of the quantum states in a black hole. Falling Inside a Black Hole • Observer’s P.o.V: you freeze at the event horizon, along with anything else the black hole has every accreted. • Your P.o.V: you’re time is the proper time (no redshift), so you go right past r*. • This is because the r*/r is a coordinate singularity, not a physical singularity. Eddington-Finkelstein Coordinates • Singularity at r=r* vanishes. • The ln|r-r*| term in the coordinates defines a one way membrane. • For advanced coordinates, particles can only fall in. • For retarded coordinates, particles can only move out, theoretically defining a White Hole. Conclusion • Karl Schwarzschild was more dedicated to physics than you ever will be. • Black Holes are interesting objects that require an abstract way of thinking in order to explain them mathematically. References • http://en.wikipedia.org/wiki/Schwarzschild_metric • http://en.wikipedia.org/wiki/Vacuum_energy • http://en.wikipedia.org/wiki/Einstein_field_equation s • http://en.wikipedia.org/wiki/Karl_Schwarzschild • “Relativity, Gravitation, and Cosmology”, Second Edition, Ta-Pei Cheng • PHZ4601 Lecture Notes, Fall 2012, Dr. Owens