Περίληψη:

I will discuss recent results of Gravitational Statistical Mechanics. I will show that if an ideal, self-gravitating gas with constant rest mass is sufficiently heated up, it becomes subject to a novel relativistic gravothermal instability, which occurs at high energy and small radii, even if the rest mass satisfies the Newtonian weak-field approximation. In the one hand, thermal energy tends to stabilize a gas with respect to self-gravity, but on the other, being a form of mass-energy, it gravitates as well. According to Tolman-Ehrenfest effect, the temperature profile is inhomogeneous at thermal equilibrium in General Relativity. I find that there is always a
threshold beyond which thermal energy cannot support its own gravitational attraction. Applications of the phenomenon include neutron stars and core-collapse supernovae. I generalize the Oppenheimer-Volkov calculation of the mass limit to the whole non-zero temperature regime. Secondly, I will present the novel Gravitational Phase Transitions I identified together with collaborators Scott Tremaine, Bence Kocsis. Under conditions of spherical or axial symmetry in a stellar cluster, the thermodynamic relaxation of stellar orbits' angular momentum progresses much faster than the relaxation of the rest degrees of freedom. The angular momentum vectors reach a state of internal thermal equilibrium, resembling the relaxation of spins in paramagnetic systems. Analogous phase transitions of the first and second kind are identified. Finally, I will discuss the growth and hardening of binary black holes due to accretion of primordial gas in proto-globular clusters. In collaboration with Demosthenes Kazanas, we have shown that binary black holes can grow to masses relevant to recent LIGO's observations, at the order of 35 solar masses or more during the first few Myrs of the life of a proto-globular cluster, while they get significantly harder during this process.