The effective potential in Newton's, Einstein's theories and beyond

• Marek A. Abramowicz (CAMK, Poland, Silesian University in Opava, Czech Republic, Göteborg University, Sweden)

I shortly describe the concept of the effective potential in Newton's theory and claim that even if one does not know Einstein's general relativity, one may correctly guess the topology of the potential in Einstein's theory from Newton. This allows one to discover, without Einstein's equations, all "relativistic effects" in particles' and photons' motion around compact objects in the strong field limit. I speculate that the same may be true for quantum effects in strong gravity: even without knowing Quantum Gravity (QG) theory, one may guess all classes of all the QG effects, potentially observable in particles' and photons' motion around compact Quantum Gravity objects. This may be relevant for interpreting the EHT images (in particular secondary rings) and the LIGO-Virgo results (in particular ringdowns and echoes).

Collapse of two-dimensional spin-orbit coupled Bose-Einstein condensate

• Shukhrat Mardonov (Ulugh Beg Astronomical Institute)

A finite-size quasi-two-dimensional Bose-Einstein condensate collapses if the attraction between atoms is sufficiently strong. Here we present a theory of collapse for condensates with the interatomic attraction and spin-orbit coupling. We consider two realizations of spin-orbit coupling: the axial Rashba coupling and the balanced, effectively one-dimensional Rashba-Dresselhaus one. In both cases spin-dependent “anomalous” velocity, proportional to the spin-orbit-coupling strength, plays a crucial role. For the Rashba coupling, this velocity forms a centrifugal component in the density flux opposite to that arising due to the attraction between particles and prevents the collapse at a sufficiently strong coupling. For the balanced Rashba-Dresselhaus coupling, the spin-dependent velocity can spatially split the initial state in one dimension and form spin-projected wave packets, reducing the total condensate density. Depending on the spin-orbit-coupling strength, interatomic attraction, and initial state, this splitting either prevents the collapse or modifies the collapse process. These results show that the collapse can be controlled by a spin-orbit coupling, thus extending the domain of existence of condensates of attracting atoms.

Conference photo Turn on your camera and smile!

Light ray as charge distinguisher of black holes in nonlinear electrodynamics

• Bobir Toshmatov (Ulugh Beg Astronomical Institute, Tashkent)

It is well-known fact that a light ray does not follow the null geodesics of spacetime in nonlinear electrodynamics, instead it follows the null geodesics of so-called effective spacetime. Moreover, in general relativity coupled to the nonlinear electrodynamics the spacetime cannot possess both electric and magnetic charges at the same time. By combining these two phenomena, we aim to discover possibility whether it is possible to distinguish the type of charge of the spacetime, via the motion of light ray in it. The results show that if the spacetime is solution of general relativity coupled to the nonlinear electrodynamics, one cannot distinguish its type of charge (magnetic or electric) through the motion of light ray around it.

Dynamical analysis approaches in spatially curved FRW spacetimes

• Morteza Kerachian (Charles University, Czech Republic)

In this work we perform dynamical analysis of a broad classes of barotropic fluids and a non- minimally coupled real scalar fields in the Friedmann-Robertson-Walker (FRW) spacetime frame- work. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid’s energy den- sity. The second part of our study concerns the dynamics of an unspecified positive potential in a spatially curved FRW spacetime. For each of these cosmological models we define a new set of dimensionless variables and a new evolution parameter. In the frameworks of these general setups, we have recognized several general features of these systems, like symmetries, invariant subsets and critical points, and provide their cosmological interpretation. The last part of our work provides some examples to show how these two general setups can be used.

Accretion disks with radial heat advection

• Michal Bursa

The talk will discuss thermal solutions of a thin accretion disk model with magnetic fields and a radial gradient of entropy.

Conference Closing

• Martin Urbanec