This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterization preference relation the corresponding minimal solution in terms of generalized oriented distance function sup-inf type. establish continuity associated an existence result solution. Painlevé–Kuratowski convergence solutions family scalar problems to

As it became well known in the past years, Einstein-scalar-Gauss-Bonnet (EsGB) theories evade no-hair theorems and allow for scalarized compact objects including black holes (BH). The coupling function that defines theory is main character process nature of scalarization. With right choice, becomes an extension general relativity (GR) sense any solution to GR field equations remains a EsGB theo...

Method of deviation was introduced in [1] for drawing implicit curves. This paper develops algorithms for drawing lines and conic sections using method of deviation. All computations are performed in integer mode. The lines and conic sections drawn are compared with those drawn using mid point algorithm.

We determine all point-sets of minimum size in PG(2, q), q odd that meet every external line to a conic in PG(2, q). The proof uses a result on the linear system of polynomials vanishing at every internal point to the conic and a corollary to the classification theorem of all subgroups of PGL(2, q).

For large q we characterize the (q + 1)-sets in PG(2, q), q odd, having more than 0.326q nuclei on a conic. In the process more information about the structure of (q + 1)-sets having a large number of nuclei on a conic is obtained.

We study the linear instability and nonlinear dynamical evolution of Reissner-Nordstr\"om (RN) black hole in Einstein-Maxwell-scalar theory asymptotic flat spacetime. focus on coupling function $f(\phi)=e^{-b\phi^2}$ which allows both scalar-free RN solution scalarized solution. first present system parameters during dynamic scalarization. For parameter regions where spontaneous scalarization o...

We study the process of fully nonlinear dynamical scalarization starting from a charged black hole or naked singularity in asymptotically flat spacetime Einstein-Maxwell-dilaton theory. Initially dilaton field is negligible compared to gravitational and Maxwell field. Then experiences an immediate growth, later it oscillates with damping amplitude finally settles down finite value. For hairy de...

We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In slow rotation approximation $a\ll1$ with parameter $a$, GB term is given by a for Schwarzschild hole, whereas CS takes linear $a$. The tachyonic instability represents onset spontaneous scalarization. use (2+1)-dimensional hyperboloidal foliation method to show considering...