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.

Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks

We construct nonassociative quasi-stationary solutions describing deformations of Schwarzschild black holes, BHs, to ellipsoid configurations, which can be black ellipsoids, BEs, and/or BHs with ellipsoidal accretion disks. Such solutions are defined by generic off-diagonal symmetric metrics and nonsymmetric components of metrics (which are zero on base four dimensional, 4-d, Lorentz manifold spacetimes but nontrivial in respective 8-d total (co) tangent bundles). Distorted nonassociative BH and BE solutions are found for effective real sources with terms proportional to $$\hbar \kappa $$ ħ κ (for respective Planck and string constants). These sources and related effective nontrivial cosmological constants are determined by nonlinear symmetries and deformations of the Ricci tensor by nonholonomic star products encoding R-flux contributions from string theory. To generate various classes of (non) associative /commutative distorted solutions we generalize and apply the anholonomic frame and connection deformation method for constructing exact and parametric solutions in modified gravity and/or general relativity theories. We study properties of locally anisotropic relativistic, optically thick, could and thin accretion disks around nonassociative distorted BHs, or BEs, when the effects due to the rotation are negligible. Such configurations describe angular anisotropic deformations of axially symmetric astrophysical models when the nonassociative distortions are related to the outer parts of the accretion disks.

On the classification of Landsberg spherically symmetric Finsler metrics

In this paper, as an application of the inverse problem of calculus of variations, we investigate two compatibility conditions on the spherically symmetric Finsler metrics. By making use of these conditions, we focus our attention on the Landsberg spherically symmetric Finsler metrics. We classify all spherically symmetric manifolds of Landsberg or Berwald types. For the higher dimensions [Formula: see text], we prove that all Landsberg spherically symmetric manifolds are either Riemannian or their geodesic sprays have a specific formula; all regular Landsberg spherically symmetric metrics are Riemannian; all (regular or non-regular) Berwald spherically symmetric metrics are Riemannian. Moreover, we establish new unicorns, i.e. new explicit examples of non-regular non-Berwaldian Landsberg metrics are obtained. For the two-dimensional case, we characterize all Berwald or Landsberg spherically symmetric surfaces.

On the completeness of total spaces of horizontally conformal submersions

In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.

Conformal vector fields of static spherically symmetric space-times in f(R, G) gravity

Assuming the most general form of static spherically symmetric space-times, we search for the conformal vector fields in [Formula: see text] gravity by means of algebraic and direct integration approaches. In this study, there exist six cases which on account of further study yield conformal vector fields of dimension four, six and fifteen. During this study, we also recovered some well-known static spherically symmetric metrics announced in the current literature.

An Overview of Quasinormal Modes in Modified and Extended Gravity

As gravitational waves are now being nearly routinely measured with interferometers, the question of using them to probe new physics becomes increasingly legitimate. In this article, we rely on a well established framework to investigate how the complex frequencies of quasinormal modes are affected by different models. The tendencies are explicitly shown for both the pulsation and the damping rate. The goal is, at this stage, purely qualitative. This opportunity is also taken to derive the Regge-Wheeler equation for general static and spherically symmetric metrics.

Anisotropic compact stars in non-conservative theory of gravity

We develop anisotropic compact stars in the scenario of non-conservative theory such as Rastall theory. We consider the Krori and Barua static spherically symmetric metrics and find their unknown constants by using the masses and radii of well-known compact stars. We investigate the anisotropic compact star through various physical quantities such as anisotropic behavior, regularity conditions, stability and surface redshift. It is found that the present compact stars are stable and are in the stellar equilibrium form.