The purpose of the ICRAG was to showcase both research and international collaborations in central Asian countries in the area of Astrophysics in particular in General Relativity and Relativistic Astrophysics. Due to the assistance provided by the local, regional, and international scientific community, central Asian countries saw great success over the last 3 decades in developing and establishing new highly functional and competitive scientific groups specialized in General Relativity & Relativistic Astrophysics in Uzbekistan, Kazakhstan, and Kyrgyzstan. The main purpose of the ICRAG was to celebrate and highlight research and other academic achievements of Central Asia countries.

The venue for the ICRAG-2021 was Ulugh Beg Astronomical Institute, Uzbekistan. The biggest success of the event was that it brought together scientists from central Asian regions working in the area of astrophysics with specialization in General Relativity and Relativistic Astrophysics. The conference provided scientists opportunities to (1) exchange current status of research on the subject of the conference and (2) strengthen ongoing research collaborations with the international institutions.

Over 90 researchers attended the conference with substantial involvement of scientists from Uzbekistan, Kazakhstan, Kyrgyzstan, Pakistan, China, and India. There was also a good number of participants from USA, The Netherlands, Germany, Italy, Japan, and Czech Republic.

Presenters working in the most current subject of the conference were asked to write original or review articles to be published in a special issue of the Arabian Journal of Mathematics. About 20 invited speakers accepted the invitation to contribute. The papers are classified into two categories, (i) mathematical physics & general relativity and (ii) relativistic astrophysics. Based on these two categories, the journal decided to dedicate a special issue publish these papers.

A brief overview of the articles appearing in the special issue under the topic “Mathematical Physics & General Relativity” is as follows.

The first paper entitled “Constraints in inflationary magnetogenesis” by Yuri Shtanov discusses popular models of inflationary and early post-inflationary magnetogenesis and presents model-independent upper bounds on the strength of the resulting magnetic fields imposed by the considerations of weak coupling, back-reaction, and Schwinger effect.

The second paper “Scalarized black holes” by Jose Luis Blazquez-Salcedo, Burkhard Kleihaus, and Jutta Kunz discusses several types of scalarized black holes and their properties.

The third paper entitled “Wormhole solutions with NUT charge in higher curvature theories” by Rustam Ibadov, Burkhard Kleihaus, Jutta Kunz, and Sardor Murodov discusses wormholes with a Newman–Unti–Tamburino (NUT) charge that arises in theories, where a scalar field is coupled to a higher curvature invariant as a Gauss–Bonnet term and as a Chern–Simons term. The domain of existence for a given NUT charge is then delimited by the set of scalarized nutty black holes, a set of wormhole solutions with a degenerate throat, and a set of singular solutions.

In fourth article entitled “Collapse of quasi-two-dimensional symmetrized Dresselhaus spin-orbit coupled Bose-Einstein condensate" by Sh. N. Mardonov, a discussion is given of the collapse process of quasi-two-dimensional Bose–Einstein condensate with symmetrized Dresselhaus spin–orbit coupling. It is observed that at a sufficiently strong spin–orbit coupling, the arising spin-dependent velocity compensates the attraction between particles and can prevent the collapse of the condensate. As a result, spin-orbit coupling can lead to a stable condensate rather than the collapse process.

The fifth article on “Boson stars with negative Gauss-Bonnet coupling" under this topic is presented by Sardor Tojiev and discusses asymptotically flat and anti-de Sitter (AdS) boson star in (4+1)-dimensional Gauss–Bonnet gravity. The dependence of the mass, the charge, and the radius of the boson star on the model parameters, such as Gauss–Bonnet coupling \(\alpha \), cosmological constant \(\Lambda \), and gravitational constant \(\kappa \) os explored. The basic properties of the solutions of boson stars have been studied for the different negative values of Gauss–Bonnet coupling.

In the paper on “How do rotating black holes form in higher dimensions” by Naresh Dadhich and Sanjar Shaymatov, it is stated that in Einstein gravity, higher dimensional rotating black holes cannot be formed by gravitational accretion and collapse processes. They could however be formed in pure Gauss–Bonnet/Lovelock gravity where both processes could very well work in the dimension window, \(2N+2\le D \le 4N\). In all critical odd dimensions \(D=2N+1\) and existence of bound orbits, the formation of rotating black holes in higher dimensions is yet another property that singles out pure Lovelock gravity.

A brief overview of the articles appearing in the special issue under the topic “Relativistic Astrophysics” is as follows.

In the first paper entitled “Testing General Relativity with black hole X-ray data: a progress report” by Cosimo Bambi, a review of the research performed by group at Fudan University devoted to application of black hole X-ray data for testing gravity theories including General Relativity (GR) in the strong field regime is given. Astrophysical systems explored are stellar-mass black holes in X-ray binaries or supermassive black holes in active galactic nuclei (AGN) accreting from geometrically thin and optically thick accretion disks.

The second paper entitled “Virial clouds and rotational asymmetry in galactic haloes” by Asghar Qadir and Francesco De Paolis treats baryonic dark matter in galaxies in the form of molecular hydrogen clouds, and discusses a mechanism for observing them. A method of seeing the clouds based on possible observation of temperature asymmetry in the cosmic microwave background towards the M31 galaxy, due to a “Doppler effect” induced by the M31 halo rotation. The observed temperature asymmetry in M31 and other galaxies can be used to study the rotation of galactic haloes and map their dynamics. The development of the ideas to trace the evolution of molecular hydrogen clouds from their formation to the modern day is reviewed.

The third paper “Distinguishing regular and singular black holes in modified gravity” by Aleksandra Demyanova, Javlon Rayimbaev, Ahmadjon Abdujabbarov, and Wenbiao Han explores possible ways of distinguishing regular and singular black holes (BHs) in modified gravity (MOG) called regular MOG (RMOG) and Schwarzschild MOG (SMOG) BHs through observational data from twin-peak quasi-periodic oscillations (QPOs) which are generated by test particles in stable orbits around the BHs. The authors provide comparisons of the innermost stable circular orbit (ISCO) and the orbits where twin peak QPOs with the ratio 3:2 taken place, and show that QPOs cannot be generated at/inside ISCO and there is a correlation between the radius of ISCO and QPO orbits.

The fourth article entitled “Gravitational waves from binary neutron stars” by Luca Baiotti reviews the current global status of research on gravitational waves emitted from mergers of close binary neutron star systems. It is focused on general-relativistic simulations and their application to interpret data from the gravitational-wave detectors, especially in relation to the equation of state of relativistic compact stars.

The fifth article “Quintessential effects on quasi-periodic oscillations in 4D Einstein-Gauss-Bonnet gravity” under this topic is presented by Javlon Rayimbaev, Pulat Tadjimuratov, Bobomurat Ahmedov, and Satimbay Palvanov which discusses dynamics of test particles in the spacetime of a quintessential black hole (BH) in a novel four-dimensional Einstein–Gauss–Bonnet (EGB) theory. Fundamental frequencies such as Keplerian and harmonic oscillations are investigated together with applications to quasi-periodic oscillations (QPOs) where the powerful way to test alternative gravity theories in strong field regime using astrophysical observations of twin-peak QPOs is discussed.

The sixth article “Constraining spacetime deformation based on astrophysical observations from radio pulsars” under this topic is presented by Nozima Juraeva, Javlon Rayimbaev, Kamoliddin Haydarov, Maksud Umaraliyev, and Ahmadjon Abdujabbarov, and devoted to treatment of cut-off for plasma magnetospheric radiations around magnetized neutron stars in the presence of spacetime deformation using deathline conditions of curvature radiations (CR), and inverse Compton scattering (ICS) around deformed neutron stars. Upper limits for the deformation parameter for selected several millisecond pulsars are obtained using the deathline conditions.

The last review article “Development and Perspectives of Relativistic Astrophysics in Uzbekistan” by Bobomurat Ahmedov is devoted to overview the recent research on relativistic astrophysics performed by the Theoretical Astrophysics Group located at Ulug Beg Astronomical Institute of Uzbekistan Academy of Sciences, Tashkent.