Related papers: Quadrupolar metrics
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 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 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 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…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
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,…
The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…
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…
Two distinct non-singular interior models that describe anisotropic spherical configurations are presented in this work. We develop the Einstein field equations and the associated mass function in accordance with a static spherical…
In this work we present an exact solution of the Einstein-Maxwell field equations describing compact, charged objects within the framework of classical general relativity. Our model is constructed by embedding a four-dimensional spherically…
We investigate the physical properties of equilibrium sequences of non-self-gravitating surfaces that characterize thick disks around a rotating deformed compact object described by a stationary generalization of the static q-metric. The…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
Einstein's theory of general relativity predicts that the only stationary configuration of an isolated black hole is the Kerr spacetime, which has a unique multipolar structure and a spherical shape when non-spinning. This is in striking…
In the present investigation compact stellar models are dealt with in the framework of the modified gravity theory, specifically of $f(\mathbb{T},\mathcal{T})$ type. We have considered that the compact objects are following a spherically…
In the standard Einstein's theory the exterior gravitational field of any static and axially symmetric stellar object can be described by means of a single function from which we obtain a metric into a four-dimensional space-time. In this…
In this work, we report a new exact solution of Einstein's field equations for static spherically symmetric anisotropic matter distributions on the background of paraboloidal spacetime by assuming a quadratic equation of state. The model…
A new class of solutions describing analytical solutions for compact stellar structures has been developed within the tenets of General Relativity. Considering the inherent anisotropy in compact stars, a stable and causal model for…