The improved description of the planets’ interior is provided. We examine modified gravity effects on Earth-like planets composed iron core and silicate mantle. confirm that mass–radius relations as well density profiles differ with respect to commonly adopted Newtonian models.

The wave equation ?tt?c2?xu(x,t)=e?tf(x,t) in the cone {(x,t):?x??t,x?Rd,t?R+} is shown to have a unique solution if u and its partial derivatives x are L2(e?t) on cone, can be explicit given Fourier series of orthogonal polynomials cone. This provides particular for boundary value problems non-homogeneous which combined with homogeneous obtain full solution.

In this paper, we prove two rigidity results for non-positively curved homogeneous Finsler metrics. Our first main result yields an extension of Hu-Deng's well-known proven the Randers Indeed, that every connected space with non-positive flag curvature and isotropic S-curvature is Riemannian or locally Minkowskian. We extend Szabó's theorem Berwald surfaces show metrics are second to (α,β)-metr...