Harmonic sections of vector bundles with spherically symmetric metrics

We equip an arbitrary vector bundle over a Riemannian manifold, endowed with a fiber metric and a compatible connection, with a spherically symmetric metric (cf. [4]), and westudy harmonicity of its sections firstly as smooth maps and then as critical points of the energy functional with variations through smooth sections.We also characterize vertically harmonic sections. Finally, we give some examples of special vector bundles, recovering in some situations some classical harmonicity results.

Homogeneous perfect fluid collapse in five-dimensional spherically symmetric spacetime

In this paper, the higher-dimensional collapse of homogeneous isotropic perfect fluid is studied by considering the geometry of five-dimensional spherically symmetric metric. Using equations of state for different fields like dust, radiation and stiff fluid with and without cosmological constant [Formula: see text], the gravitational collapse is studied. The results are compared with the usual four-dimensional study in [A. V. Astashenok, K. Mosani, S. D. Odintsov and G. C. Samanta, Int. J. Geom. Methods Mod. Phys. 16, 1950035 (2019)]. It is found that the collapse rate is faster in five-dimensional spacetime as compared to four-dimensional case supporting the cosmic censorship hypothesis.

On Projectively Flat Finsler Warped Product Metrics of Constant Flag Curvature

In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these metrics by warped product. Using the obtained equations, we manufacture new locally projectively flat Finsler warped product metrics of vanishing flag curvature. These metrics contain the metric introduced by Berwald and the spherically symmetric metric given by Mo-Zhu.

Exact charged black hole solutions in D-dimensions in f(R) gravity

We consider Maxwell-f(R) gravity and obtain an exact charged black hole solution with dynamic curvature in D-dimensions. Considering a spherically symmetric metric ansatz and without specifying the form of f(R) we find a general black hole solution in D-dimensions. This general black hole solution can reduce to the Reissner–Nordström (RN) black hole in D-dimensions in Einstein gravity and to the known charged black hole solutions with constant curvature in f(R) gravity. Restricting the parameters of the general solution we get polynomial solutions which reveal novel properties when compared to RN black holes. Specifically we study the solution in $$(3+1)$$ ( 3 + 1 ) -dimensions in which the form of f(R) can be solved explicitly giving a dynamic curvature and compare it with the RN black hole. We also carry out a detailed study of its thermodynamics.

A higher dimensional cosmological model for the search of dark energy source

With due consideration of reasonable cosmological assumptions within the limit of the present cosmological scenario, we have analyzed a spherically symmetric metric in 5D setting within the framework of Lyra manifold. The model universe is predicted to be a DE model, dominated by vacuum energy. The model represents an oscillating model, each cycle evolving with a big bang and ending at a big crunch, undergoing a series of bounces. The universe is isotropic and undergoes super-exponential expansion. The value of Hubble’s parameter is measured to be [Formula: see text] which is very close to [Formula: see text], the value estimated by the latest Planck 2018 result. A detailed discussion on the cosmological parameters obtained is also presented with graphs.

THE GENERALIZED SPHERICALLY-SYMMETRIC METRIC

Four parameter group of transformations containing rotations and time translations is consi[1]dered due to spherical symmetry and stationarity of the space-time metric. It is found that there exists such a quartet of Killing vector fields which constitute the Lie algebra of the transforma[1]tion group and in which space-like vectors are not orthogonal to the time-like one. The metric corresponding to the Lie algebra of Killing vectors is composed. It is shown that the metric is non-static.

Static wormhole solutions and Noether symmetry in modified Gauss–Bonnet gravity

In this paper, we analyze static traversable wormholes via Noether symmetry technique in modified Gauss–Bonnet $$f(\mathcal {G})$$f(G) theory of gravity (where $$\mathcal {G}$$G represents Gauss–Bonnet term). We assume isotropic matter configuration and spherically symmetric metric. We construct three $$f(\mathcal {G})$$f(G) models, i.e, linear, quadratic and exponential forms and examine the consistency of these models. The traversable nature of wormhole solutions is discussed via null energy bound of the effective stress–energy tensor while physical behavior is studied through standard energy bounds of isotropic fluid. We also discuss the stability of these wormholes inside the wormhole throat and conclude the presence of traversable and physically stable wormholes for quadratic as well as exponential $$f(\mathcal {G})$$f(G) models.

Anisotropic solution for compact objects in f(𝒢,𝒯) gravity

In this paper, we consider a new solution to discuss the physical aspects of anisotropic compact celestial bodies in the background of [Formula: see text] theory. We take static spherically symmetric metric to describe the internal region of the stellar objects and apply the embedding class-I method to get the metric solution corresponding to a specific [Formula: see text] model. By matching the interior and exterior geometries at the boundary, we find the values of unknown constants. We check the stability and viability of the resulting solution through various parameters that include energy bounds, causality condition, Herrera’s condition, role of adiabatic index, redshift and compactness factor. The graphical interpretation is done for some particular compact star candidates, i.e. LMC X-4, Cen X-3, 4U 1820-30 and Vela X-1. We conclude that our model provides physically acceptable structure of the considered compact objects and is also stable.

Existence of realistic stellar objects in Rastall gravity with linear equation of state

In this paper, we have discussed the anisotropic matter configuration to explore the existence of realistic stellar objects in non-conservative theory named as Rastall theory of gravity. We have assumed a static spherically symmetric metric with linear equation of state (EoS) to formulate the dynamical equations. The Durgapal and Banerji transformation is employed to investigate the gravitational behavior of compact objects. In this regard, a particular gravitational potential is selected to solve the system of dynamical equations numerically. We compared change in behavior of physical quantities like energy density, anisotropy parameter, and radial and tangential pressures by plotting three particular cases. With the help of physical analysis, it can be seen that the solutions of compact spheres hold physical acceptability criteria and depict stability.