Black Holes and Quantum Mechanics

Short course

Speaker: Dr. Walter Tangarife

He recently earned his Ph.D. from the University of Texas at Austin working with the Theory Group lead by the Nobel Prize Steven Weinberg. His research range from Dark Matter in extensions of the Minimal Supersymmetic Standard Model to Applications of AdS/CFT to the black hole information paradox. He will soon join Tel Aviv University as a postdoctoral fellow.

Summary

After a century of Einstein's General Relativity, black holes remain a fascinating laboratory for the understanding of the interaction between gravity and quantum mechanics. For several decades, black hole physics has provided great ideas that have revolutionized the way theorists study space, time and matter. In this set of lectures, we will introduce the most relevant concepts and ideas about black holes. Together with observers at the black hole horizon, we'll discover the main information paradoxes and we'll study how these puzzles have shaped the current theoretical research in high energy physics.

Outline

Lecture 1 - Introduction to Black Holes: The Schwarzschild and the near-horizon geometries. Causal structure of black holes and Penrose diagrams. Real black hole geometry.

Lecture 2 - Quantum mechanics and quantum field theory in curved space-time. Quantum information and entanglement entropy. Geodesic and accelerated observers. First glance to the information paradox.

Lecture 3 - Information paradox. Black hole complementarity. Fast scramblers. Firewalls. Further developments.

Videos

References

• Elementary:
  • Susskind & Lindesay, An introduction to Black Holes, Information and the string theory revolution. 2005.
  • Carroll, Spacetime and Geometry. 2003.
• More advanced:
  • S. Hawking, Particle Creation by Black Holes, Commun.Math.Phys. 43 (1975) 199–220.
  • D. N. Page, Information in black hole radiation, Phys.Rev.Lett. 71 (1993) 3743–3746, [hep-th/9306083].
  • P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 0709 (2007) 120, [arXiv:0708.4025].
  • D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 1306 (2013) 085, [arXiv:1301.4504].
  • T. Jacobson, Introduction to quantum fields in curved space-time and the Hawking effect, [arXiv:gr-qc/0308048].