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Supermassive black holes can capture or disrupt stars that come sufficiently close. This article reviews the dynamical processes by which stars or stellar remnants are placed onto loss-cone orbits and the implications for feeding rates. The capture rate is well defined for spherical galaxies with nuclear relaxation times that are shorter than the galaxys age. However, even the dense nucleus of the Milky Way may be less than one relaxation time old, and this is certainly the case for more massive galaxies; the capture rate in such galaxies is an initial-value problem with poorly-known initial conditions and the rate can be much higher, or much lower, than the rate in a collisionally relaxed nucleus. In nonspherical (axisymmetric, triaxial) galaxies, torquing of orbits by the mean field can dominate perturbations due to random encounters, leading to much higher capture rates than in the spherical geometry, particularly in (massive) galaxies with long central relaxation times. Relativistic precession plays a crucial role in mediating the capture of compact remnants from regions very near to the black hole, by destroying the orbital correlations that would otherwise dominate the torques. The complex dynamics of relativistic loss cones are not yet well enough understood for accurate estimates of compact-object (EMRI) capture rates to be made.
A new so-called `gravitational loss-cone instability in stellar systems has recently been investigated theoretically in the framework of linear perturbation theory and proved to be potentially important in understanding the physical processes in cent
A gap in phase-space, the loss cone (LC), is opened up by a supermassive black hole (MBH) as it disrupts or accretes stars in a galactic centre. If a star enters the LC then, depending on its properties, its interaction with the MBH will either gener
Geometric Mean Market Makers (G3M) such as Uniswap, Sushiswap or Balancer are key building blocks of the nascent Decentralised Finance system. We establish non-arbitrage bounds for the wealth process of such Automated Market Makers in the presence of
Galactic winds are associated with intense star formation and AGNs. Depending on their formation mechanism and velocity they may remove a significant fraction of gas from their host galaxies, thus suppressing star formation, enriching the intergalact
Signal propagation in the non equilibirum evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determ