The Gravothermal Instability at all scales: from Turnaround Radius to Supernovae

The gravitational instability, responsible for the formation of the structure of the Universe, occurs below energy thresholds and above spatial scales of a self-gravitating expanding region, when thermal energy can no longer counterbalance self-gravity. I argue that at sufficiently-large scales, dark energy may restore thermal stability. This stability re-entrance of an isothermal sphere defines a turnaround radius, which dictates the maximum allowed size of any structure generated by gravitational instability. On the opposite limit of high energies and small scales, I will show that an ideal, quantum or classical, self-gravitating gas is subject to a high-energy relativistic gravothermal instability. It occurs at sufficiently-high energy and small radii, when thermal energy cannot support its own gravitational attraction. Applications of the phenomenon include neutron stars and core-collapse supernovae. I also extend the original Oppenheimer--Volkov calculation of the maximum mass limit of ideal neutron cores to the non-zero temperature regime, relevant to the whole cooling stage from a hot proto-neutron star down to the final cold state.Comment: Minor amendments to match published versio

Binary black hole growth by gas accretion in stellar clusters

We show that binaries of stellar-mass black holes formed inside a young protoglobular cluster, can grow rapidly inside the cluster's core by accretion of the intracluster gas, before the gas may be depleted from the core. A black hole with mass of the order of eight solar masses can grow to values of the order of thirty five solar masses in accordance with recent gravitational waves signals observed by LIGO. Due to the black hole mass increase, a binary may also harden. The growth of binary black holes in a dense protoglobular cluster through mass accretion indicates a potentially important formation and hardening channel

Relativistic Gravothermal Instabilities

The thermodynamic instabilities of the self-gravitating, classical ideal gas are studied in the case of static, spherically symmetric configurations in General Relativity taking into account the Tolman-Ehrenfest effect. One type of instabilities is found at low energies, where thermal energy becomes too weak to halt gravity and another at high energies, where gravitational attraction of thermal pressure overcomes its stabilizing effect. These turning points of stability are found to depend on the total rest mass $\mathcal{M}$ over the radius $R$. The low energy instability is the relativistic generalization of Antonov instability, which is recovered in the limit $G\mathcal{M} \ll R c^2$ and low temperatures, while in the same limit and high temperatures, the high energy instability recovers the instability of the radiation equation of state. In the temperature versus energy diagram of series of equilibria, the two types of gravothermal instabilities make themselves evident as a double spiral! The two energy limits correspond also to radius limits. So that, stable static configurations exist only in between two marginal radii for any fixed energy with negative thermal plus gravitational energy. Ultimate limits of rest mass, as well as total mass-energy, are reported. Applications to neutron cores are discussed.Comment: 30 pages, 21 figures; references added; minor changes to match published versio

Binary Black Hole Growth by Gas Accretion in Stellar Clusters

We show that binaries of stellar-mass black holes formed inside a young protoglobular cluster, can grow rapidly inside the clusters core by accretion of the intracluster gas, before the gas may be depleted from the core. A black hole with mass of the order of eight solar masses can grow to values of the order of thirty five solar masses in accordance with recent gravitational waves signals observed by LIGO. Due to the black hole mass increase, a binary may also harden. The growth of binary black holes in a dense protoglobular cluster through mass accretion indicates a potentially important formation and hardening channel

The Cosmological Black Hole

We briefly review the recent novel solution of General Relativity, we call the cosmological black hole, firstly discovered in [Roupas, Z. Eur. Phys. J. C 82, 255 (2022)]. A dark energy universe and a Schwartzschild black hole are matched on a common dual event horizon which is finitely thick due to quantum indeterminacy. The system gets stabilized by a finite tangential pressure applied on the dual horizon. The fluid entropy of the system at a Tolman temperature identified with the cosmological horizon temperature is calculated to be equal with the Bekenstein-Hawking entropy.Comment: Talk given in the 11th International Conference on Mathematical Modelling in Physical Science