Ricci Curvature of Finsler Metrics by Warped Product
Abstract
In the present work, we consider a class of Finsler metrics using the warped product notion introduced by Chen, Shen and Zhao [1], with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.
Degree
Ph.D.
Advisors
Shen, Purdue University.
Subject Area
Mathematics|Theoretical physics
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