Tuesday 14 April 2026, 16:00 - 17:00 in HG00.310
Manus Visser (Radboud/RCNP)
Geometric Origin of Black Hole Thermodynamics
In this talk, I review the laws of black hole thermodynamics, emphasizing their geometric origin and their relation to both Lorentzian and contact geometry. I begin with a brief overview of general relativity and black holes. According to the no-hair theorem, stationary and axisymmetric vacuum black hole solutions are fully characterized by only two parameters: mass and angular momentum. This simplicity is reminiscent of equilibrium thermodynamics, where macroscopic states are described by a small number of variables, such as internal energy and entropy. The laws of black hole thermodynamics make this analogy precise. In particular, the first law relates variations of the mass to variations of the horizon area and angular momentum. This suggests a thermodynamic interpretation, further supported by Bekenstein’s proposal to identify the area of the event horizon with the entropy of the black hole. Moreover, the second law of black hole thermodynamics (the Penrose-Hawking area theorem) states that the horizon area can never decrease, closely paralleling the second law of thermodynamics. Finally, I discuss the relation between equilibrium thermodynamics and contact geometry, and show how this framework can be applied to black holes.