Gravitation and thermodynamics
Implications of the principles of thermodynamics on the structure of space-time.
Abstract:
This course presents the development of the concepts which were formulated originally in the context of black hole physics and relativistic cosmology and which tackle in these cases the problems posed by the second principle of thermodynamics. The resulting ideas and proposals, which remarkably invoke fundamental aspects of quantum physics, lead to new conceptions on gravitational entropy and have profound implications on the nature of space-time: the holographic principle and the corresponding dimensional reduction, the recently proposed entropic origin of gravity and its recent developments are some of the themes which will be discussed during the lectures.
1. Introduction.
The principles of thermodynamics, entropy, phase space and coarse graining, time symmetry vs. time-asymmetry, the case of Newtonian dynamics, problems posed by general relativity: time-asymmetric dynamical systems, the role of space-time singularities. The concept of the universe as an isolated system and its time-evolution - the importance of cosmological clock-time.
2. Entropy and gravity
Heuristic considerations on the maximal entropy states for particle distributions vs. gravitational collapse and black holes: R. Geroch's thought experiment and its resolution by J. Bekenstein - information theory and black holes. Motivations for the J. Bekenstein-S. Hawking entropy formula - order of magnitude calculations - the Unruh effect. Hints to the holographic principle.
3. Thermodynamics and cosmology
The cosmological evolution of entropy, R. Penrose's proposals for gravitational entropy - the role of the Weyl curvature tensor - the importance of tidal effects - H. Bondi's thought experiment - further recent developments. Thermodynamical constraints on cyclic cosmological models - recent alternatives to the Standard Big Bang theory.
4. The holographic principle
The L. Susskind process, holographic bounds. Holography and dimensional reduction vs. Quantum Field Theory - gravity and unitarity. E. Verlinde's proposal for the entropic origin of gravity - further heuristic evidence and recent developments.