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We present a stationary generalization of the static $q-$metric, the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. It possesses three independent parameters that are related to the mass,…
This paper studied the relativistic accretion thick disc model raised by a deformed compact object that slightly deviated from spherical up to the quadrupole moment by utilising $\rm q$-metric. This metric is the simplest asymptotically…
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…
External matter distributions can substantially reshape the strong field environment of compact objects, yet this effect is usually neglected in idealized isolated models. In this work, we investigate geometrically thin, optically thick…
We present approximate exterior and interior solutions of Einstein's equations which describe the gravitational field of a static deformed mass distribution. The deformation of the source is taken into account up to the first order in the…
We investigate the Zipoy-Voorhees metric ($q-$metric) as the simplest static, axially symmetric solution of Einstein's vacuum field equations that possesses as independent parameters the mass and the quadrupole moment. In accordance with…
An infinite family of exact solutions of the electrovacuum Einstein-Maxwell equations is presented. The family is static, axially symmetric and describe thin disks composed by electrically polarized material in a conformastatic spacetime.…
One crucial problem in relativistic astrophysics is that of the nature of black hole candidates. It is usually assumed that astrophysical black holes are described by the Schwarzschild or Kerr space-times; however, there is no direct…
In this paper, the dynamical equations and junction conditions at the interface between adjacent layers of different elastic properties for an elastic deformable astronomical body in the first post-Newtonian approximation of Einstein theory…
Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such…
Astrophysical compact objects are studied in the context of quadratic non-metricity gravity. The solutions to the gravitational field equations, which include fluid components, are analyzed to investigate the density and pressure properties…
We investigate the interior Einstein's equations in the case of a static, axially symmetric, perfect fluid source. We present a particular line element that is specially suitable for the investigation of this type of interior gravitational…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
An exact solution of Einstein's equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the…
We consider the circular motion of test particles in the gravitational field of a static and axially-symmetric compact object described by the $q$-metric. To this end, we calculate orbital parameters of test particles on accretion disks…
Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a…
We study the observational properties of a class of exact solutions of Einstein's field equations describing stationary, axially symmetric, rigidly rotating dust (i.e. non interacting particles). We ask the question whether such solutions…
This paper studies the oscillation properties of relativistic, non-self-gravitating tori in the background of a distorted deformed compact object. This work concentrates on the static and axially symmetric metric containing two quadrupole…
This is the second article of a sequence of research on deformations of Q-curvature. In the previous one, we studied local stability and rigidity phenomena of Q-curvature. In this article, we mainly investigate the volume comparison with…