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We obtain the solutions of Einstein’s field equations for an anisotropic fluid in a static spherically symmetric metric with off-diagonal elements. We also study the pioneer anomaly with the help of the obtained solutions. First, we derive analytical solutions to study sudden change in gravity in the radial and tangential directions of a non-homogeneous gravitational system by considering Π as a constant. Then we find other solutions by considering Π as a function of r in the space of gravitating object. We extend our solutions in the numerical limits to verify the unusual behavior of gravity at larger distances for the inhomogeneous system. We show a sudden increase in radial pressure for 𝑟𝜖[0, 20] as well as the tangential pressure for 𝜃𝜖[0, 𝜋], which may be treated as a factor of pioneer anomaly. We obtain the anomalous acceleration 2.493 × 10−11𝑚/𝑠 2 at a distance of 20 AU from the Sun, which has better accuracy than other theoretical calculations when it is compared to the observed value. We also derive an expression for cosmological constant in terms of 𝑟. We establish that the cosmological constant is a function of 𝑟, which seems to be variable but its variability diminishes for large values of 𝑟. The results of this study are interesting and quite new. The selected spherically symmetric metric with off-diagonal elements provides a modified method to observe the phenomena of general relativity.

We obtain the solutions of Einstein's field equations for an anisotropic fluid in a static spherically symmetric metric with off-diagonal elements. We also study the pioneer anomaly with the help of the obtained solutions. First, we derive analytical solutions to study sudden change in gravity in the radial and tangential directions of a non-homogeneous gravitational system by considering Π as a constant. Then we find other solutions by considering Π as a function of r in the space of gravitating object. We extend our solutions in the numerical limits to verify the unusual behavior of gravity at larger distances for the inhomogeneous system. We show a sudden increase in radial pressure for 𝑟𝜖[0, 20] as well as the tangential pressure for 𝜃𝜖[0, 𝜋], which may be treated as a factor of pioneer anomaly. We obtain the anomalous acceleration 2.493 × 10-11𝑚/𝑠2 at a distance of 20 AU from the Sun, which has better accuracy than other theoretical calculations when it is compared to the observed value. We also derive an expression for cosmological constant in terms of 𝑟. We establish that the cosmological constant is a function of 𝑟, which seems to be variable but its variability diminishes for large values of 𝑟. The results of this study are interesting and quite new. The selected spherically symmetric metric with off-diagonal elements provides a modified method to observe the phenomena of general relativity. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate harmonic functions on vector bundle manifolds endowed with the class of spherically symmetric metrics. We will study three classes of harmonic functions on total spaces of vector bundles. We attempt to establish the link between harmonic function theories on the base and total space. [ABSTRACT FROM AUTHOR]

This paper is devoted to study the geometry of vector bundle manifolds equipped with spherically symmetric metrics. We will compute the curvature tensor, the sectional curvature, the Ricci curvature tensor and the scalar curvature. We will then characterize spherically symmetric metrics of constant sectional curvature. Moreover, we will establish some rigidity results regarding the scalar curvature and the Ricci curvature. Finally, we investigate geodesics using the fundamental tensors of a submersion. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we find necessary and sufficient conditions under which a spherically symmetric metric with isotropic S-curvature or isotropic E-curvature is invariant under conformal transformations. As an application, we solve one of the open problems presented by Shen and find a class of metrics of isotropic E-curvature which is not of isotropic S-curvature. [ABSTRACT FROM AUTHOR]

In this article, we show that a number of well-known time-dependent, spherically symmetric solutions of the Einstein's field equations sourced by a stiff, perfect fluid with a cosmological constant can be generalised into a solution with arbitrary metric functions. This metric can be applied to construct stiff, perfect fluid metrics with (or without) a cosmological constant. We also explore the possibility that this metric may allow us to generate a singularity-free, spherically symmetric cosmological model. [ABSTRACT FROM AUTHOR]

The isoperimetric problem is one of the fundamental problems in differential geometry. By using the method of the calculus of variations we show that the circle centered at the origin in B 2 (1) is a proper maximum of the isoperimetric problem in a 2-dimensional Finsler space of Funk type. We also obtain the formula of area enclosed by a simple closed curve in a spherically symmetric Finsler plane. [ABSTRACT FROM AUTHOR]

One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant (or scalar) curvature. In this paper, we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature. In particular, we find equations that characterize Finsler warped product metrics of constant flag curvature. Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics. As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the circle centered at the origin in B 2 (δ ξ) is a proper maximum of the isoperimetric problem in a 2-dimensional Randers space endowed with 3-parameter family of non-locally projectively flat Finsler metrics of non-constant isotropic S -curvature. [ABSTRACT FROM AUTHOR]

In this paper, we present a complete list of spherically symmetric nonstatic spacetimes along with the generators of all Noether symmetries of the geodetic Lagrangian for such metrics. Moreover, physical and geometrical interpretations of the conserved quantities (conservation laws) corresponding to each Noether symmetry are also given. [ABSTRACT FROM AUTHOR]

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $$E\longrightarrow M$$ , over a Riemannian manifold M, when E is endowed with a metric connection. The tangent bundle of E admits a canonical decomposition and thus it is possible to define an interesting class of two-weights metrics with the weight functions depending on the fibre norm of E; hence the generalized concept of spherically symmetric metrics. We study its main properties and curvature equations. Finally we focus on a few applications and compute the holonomy of Bryant-Salamon type $${\mathrm {G}_{2}}$$ manifolds. [ABSTRACT FROM AUTHOR]

Different types of T-solutions are investigated. The conditions at which one region of space-time can be described only by a statistic R-solution and another region can be described only by a T-solution are obtained. The common metric for R- and T-solutions is obtained where the spatial and temporal variables are interchanged. The T-solution which has the same mass function as for the internal static Schwarzschild solution is obtained. [ABSTRACT FROM AUTHOR]

Both Jordan-Brans-Dicke (shortened JBD) theory and Brans-Dicke theory in the Einstein’s frame (shortened EBD) are treated as Brans-Dicke theory. However, we learn that only Pauli metric represents the massless spin-two graviton and thus, should be identified as physical. If one just considers the weak field approximation and Newtonian limit, EBD theory gives the same results with Einstein’s general relativity. So, it is necessary to consider strong field effects and cosmological model. The purpose of this paper is to find the exact spherically symmetric metric in the strong field situation, and deduce the deviation of light path in EBD theory. [ABSTRACT FROM AUTHOR]

In this note, we show that the examples of non-Berwaldian Landsberg surfaces with vanishing flag curvature, obtained in [5] , are in fact Berwaldian. Consequently, Bryant's claim is still unverified. [ABSTRACT FROM AUTHOR]