Related papers: Ultra Compact Stars: Reconstructing the Perturbati…
We reconstruct compactly supported potentials with only half a derivative in $L^2$ from the scattering amplitude at a fixed energy. For this we draw a connection between the recently introduced method of Bukhgeim, which uniquely determined…
In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…
This paper is a continuation of the previous one [Journal xx, xxxxx (2022)]. Here, we reformulate the same J-matrix theory by regularizing the inverse square singular potential. The objective is to restore rapid convergence of the…
We study relativistic stars in the context of scalar tensor theories of gravity that try to account for the observed cosmic acceleration and satisfy the local gravity constraints via the chameleon mechanism. More specifically, we consider…
Using the Hubble parameter as new `inverse time' coordinate ($H$-formalism), a new method of reconstructing the inflaton potential is developed also using older results which, in principle, is applicable to any order of the slow-roll…
We analytically investigate a new family of horizonless compact objects in vector-tensor theories of gravity, called ultracompact vector stars. They are sourced by a vector condensate, induced by a non-minimal coupling with gravity. They…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for…
We consider Sturm-Liouville operators on geometrical graphs without cycles (trees) with singular potentials from the class $W_2^{-1}$. We suppose that the potentials are known on a part of the graph, and study the so-called partial inverse…
Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
Using the formalism of general relativity for axially symmetric gravitational fields and their sources - rotating compact stars - a perturbation theory with respect to angular velocity is developed and physical quantities such as mass,…
This investigation delves into the ringdown signals produced by semiclassical stars, which are ultra-compact, regular solutions of the Einstein equations incorporating stress-energy contributions from quantum vacuum polarization. These…
We review basic ideas and basic examples of the theory of the inverse spectral problems.
We study the properties of ultra-compact spherically symmetric dark matter sector star objects, being the solution of Einstein equations with two $U(1)$-gauge fields. One of them is the ordinary Maxwell field, while the auxiliary gauge…
The energy spectra and composition of ultra-high energy cosmic rays are changing in a course of propagation in the expanding Universe filled with background radiation. We developed a numerical code for solution of inverse problem for…
The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…
The primordial power spectrum describes the initial perturbations in the Universe which eventually grew into the large-scale structure we observe today, and thereby provides an indirect probe of inflation or other structure-formation…
In this work we construct an ultracompact star configuration in the framework of Gravitational Decoupling by the Minimal Geometric Deformation approach. We use the complexity factor as a complementary condition to close the system of…