Spherically symmetric ’t Hooft–Polyakov monopoles

A general analytic spherically symmetric solution of the Bogomol’nyi equations is found. It depends on two constants and one arbitrary function on radius and contains the Bogomol’nyi–Prasad–Sommerfield and Singleton solutions as particular cases. Thus all spherically symmetric ’t Hooft–Polyakov monopoles with massless scalar field and minimal energy are derived.

New Model of 4D Einstein–Gauss–Bonnet Gravity Coupled with Nonlinear Electrodynamics

New spherically symmetric solution in 4D Einstein–Gauss–Bonnet gravity coupled with nonlinear electrodynamics is obtained. At infinity, this solution has the Reissner–Nordström behavior of the charged black hole. The black hole thermodynamics, entropy, shadow, energy emission rate, and quasinormal modes of black holes are investigated.

A new nonlinear electrodynamics and electrically charged regular black holes

A regular static, spherically symmetric electrically charged black hole solution of general relativity coupled to a new theory for nonlinear electrodynamics is presented. This theory has the interesting feature that, at far distances from the black hole, in the weak field limit, the theory reduces to Maxwell Lagrangian with Heisenberg–Euler correction term of quantum electrodynamics. The singular center of the black hole is replaced by flat, de Sitter, or anti de Sitter space, if the spacetime in which the black hole is embedded is asymptotically flat, de Sitter, or anti de Sitter, respectively. Requiring the correspondence to Heisenberg–Euler Lagrangian at large distances, in the weak field limit, we find that (i) a minimum mass is required for the formation of an event horizon for the regular static, spherically symmetric solution of the theory, and, (ii) the mass of the solution must be quantized. We also study the basic thermodynamic properties of the black hole solution and show that they are qualitatively similar to those of Reissner–Nordström black hole.

Charged throats in the Hořava–Lifshitz theory

A spherically symmetric solution of the field equations of the Hořava–Lifshitz gravity–gauge vector interaction theory is obtained and analyzed. It describes a charged throat. The solution exists provided a restriction on the relation between the mass and charge is satisfied. The restriction reduces to the Reissner–Nordström one in the limit in which the coupling constants tend to the relativistic values of General Relativity. We introduce the correct charts to describe the solution across the entire manifold, including the throat connecting an asymptotic Minkowski space-time with a singular 3+1 dimensional manifold. The solution external to the throat on the asymptotically flat side tends to the Reissner–Nordström space-time at the limit when the coupling parameter, associated with the term in the low energy Hamiltonian that manifestly breaks the relativistic symmetry, tends to zero. Also, when the electric charge is taken to be zero the solution becomes the spherically symmetric and static solution of the Hořava–Lifshitz gravity.

An analytical model for the Maxwell radiation field in an axially symmetric galaxy

The Maxwell radiation field is an essential physical characteristic of a galaxy. Here, an analytical model is built to simulate that field in an axisymmetric galaxy. This analytical model is based on an explicit representation for axisymmetric source-free Maxwell fields. In a previous work, the general applicability of this representation has been proved. The model is adjusted by fitting to it the sum of spherical radiations emitted by the composing “stars.” The huge ratio distance/wavelength needs to implement a numerical precision better than the quadruple precision. The model passes a validation test based on a spherically symmetric solution. The results for a set of “stars” representative of a disk galaxy indicate that the field is highest near the disk axis, and there the axial component of E {\bf{E}} dominates over the radial one. This work will allow us in the future to check if the interaction energy predicted by an alternative theory of gravitation might be a component of dark matter.

Structure of the compact astrophysical objects in the conformally-unimodular metric

A spherically symmetric solution for a gravitational field is considered in the conformally-unimodular metric. The reason for the study of this particular gauge (i. e., conformally-unimodular metric) is its relation to the vacuum energy problem. That aim connects it to other physical phenomena (including black holes), and one could argue that they should be considered in this particular class of metrics. As the vacuum solutions, so the incompressible liquid ones are investigated. In the last case, the nonsingular «eicheon» appears as a non-point compact static object that possessed different masses and structures. Such objects are a final product of the stellar collapse, with the masses exceeding the Tolman – Oppenheimer – Volkoff limit. The term «eicheon» refers to the fundamental G. Weyl’s paper «Gravitation und Elektrizität», published, in particular in the book «Das Relativitätsprinzip. Eine Sammlung von Originalarbeiten zur Relativitätstheorie Einsteins» (Berlin, 2018), where he introduced the concept of gauge invariance (German Eichtheorie) firstly in its relation to the unified field theory. Using this term to describe the compact nonsingular astrophysical objects emphasizes the decisive role of the gauge fixing by the unimodular metric. Besides, the connotation with Eichel (acorn) stresses the twofold internal structure of an object: as a point-like in the unimodular metric and a surface in the Schwarzschild one. The radial geodesic lines are investigated in the conformally-unimodular metric, as well.

Wormholes in 4D Einstein–Gauss–Bonnet gravity

Recent times witnessed a significant interest in regularizing, a $$ D \rightarrow 4 $$D→4 limit, of EGB gravity initiated by Glavan and Lin [Phys. Rev. Lett. 124, 081301 (2020)] by re-scaling GB coupling constant as $$\alpha /(D-4)$$α/(D-4) and taking limit $$D \rightarrow 4$$D→4, and in turn these regularized 4D gravities have nontrivial gravitational dynamics. Interestingly, the maximally or spherically symmetric solution to all the regularized gravities coincides in the 4D case. In view of this, we obtain an exact spherically symmetric wormhole solution in the 4D EGB gravity for an isotropic and anisotropic matter sources. In this regard, we consider also a wormhole with a specific radial-dependent shape function, a power-law density profile as well as by imposing a particular equation of state. To this end, we analyze the flare-out conditions, embedding diagrams, energy conditions and the volume integral quantifier. In particular our −ve branch results, in the limit $$\alpha \rightarrow 0$$α→0, reduced exactly to vis-$$\grave{a}$$a`-vis 4D Morris-Thorne of GR.

Testing Generalized Einstein-Cartan-Kibble-Sciama Gravity Using Weak Deflection Angle and Shadow Cast

In this paper, we use a new asymptotically flat and spherically symmetric solution in the generalized Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity to study the weak gravitational lensing and its shadow cast. To this end, we first compute the weak deflection angle of generalized ECKS black hole using the Gauss–Bonnet theorem in plasma medium and in vacuum. Next by using the Newman-Janis algorithm without complexification, we derive the rotating generalized ECKS black hole and in the sequel study its shadow. Then, we discuss the effect of the ECKS parameter on the shadow of the black hole and weak deflection angle. In short, the goal of this paper is to give contribution to the ECKS theory and look for evidences to understand how the ECKS parameter effects the gravitational lensing.