Equatorial accretion on the Kerr black hole

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. At infinity the gas obeys the Maxwell-J\"{u}ttner distribution, restricted to the equatorial plane. In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. The accretion slows down the rotation of the black hole. We present preliminary results for a Vlasov gas accretion onto a Kerr black hole moving with a velocity parallel to the equatorial plane.Comment: Accepted to Acta Phys. Pol. B Proc. Suppl. Animated Fig. 1. Talk presented at the 8th Conference of the Polish Society on Relativity (POTOR8), 19-23 September 2022, Banach Center IMPAN, Warsaw, Polan

Equatorial accretion on the Kerr black hole

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. At infinity, the gas obeys the Maxwell–Jüttner distribution, restricted to the equatorial plane. In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. The accretion slows down the rotation of the black hole. We present preliminary results for the Vlasov gas accretion onto the Kerr black hole moving with a velocity parallel to the equatorial plane

Lane-Emden stars, selfgravitating disks and the Sobolev inequality

We estimate the minimal mass of selfgravitating polytropic disks using the famous Sobolev inequality. This bound resembles the well known mass formula for Lane-Emden stars. For ideal gas with the polytropic index n = 3 the minimal mass is not smaller than the Jeans mass. The accuracy of the estimate is verified in a number of numerical examples. The bound works well for heavy selfgravitating disks and is less useful for light disks.Comment: 9 pages, 2 figure

Evaluation of the generalized Fermi-Dirac integral and its derivatives for moderate/large values of the parameters

Approximations with Matlab implementations for the relativistic Fermi-Dirac integral and its partial derivatives are given in this paper. As the numerical tests show, the expansions allow to calculate the functions efficiently and with high accuracy for a large range of parameters. Therefore, our algorithms are expected to be a very useful tool, in combination with other methods, for building reliable and efficient software for computing the functions for all the parameters ranges

Machine learning on the road to unlocking microbiota's potential for boosting immune checkpoint therapy

The intestinal microbiota is a complex and diverse ecological community that fulfills multiple functions and substantially impacts human health. Despite its plasticity, unfavorable conditions can cause perturbations leading to so-called dysbiosis, which have been connected to multiple diseases. Unfortunately, understanding the mechanisms underlying the crosstalk between those microorganisms and their host is proving to be difficult. Traditionally used bioinformatic tools have difficulties to fully exploit big data generated for this purpose by modern high throughput screens. Machine Learning (ML) may be a potential means of solving such problems, but it requires diligent application to allow for drawing valid conclusions. This is especially crucial as gaining insight into the mechanistic basis of microbial impact on human health is highly anticipated in numerous fields of study. This includes oncology, where growing amounts of studies implicate the gut ecosystems in both cancerogenesis and antineoplastic treatment outcomes. Based on these reports and first signs of clinical benefits related to microbiota modulation in human trials, hopes are rising for the development of microbiome-derived diagnostics and therapeutics. In this mini-review, we're inspecting analytical approaches used to uncover the role of gut microbiome in immune checkpoint therapy (ICT) with the use of shotgun metagenomic sequencing (SMS) data