Ricci Curvature of Finsler Metrics by Warped Product

In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), 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.

Author dc:creator

• Marcal, Patricia

Advisor dc:contributor.advisor

• Shen, Zhongmin

• Warped Product
• Finsler Metrics
• Ricci Curvature
• Ricci flat

Statement dc:rights

• Attribution-NonCommercial-ShareAlike 4.0 International

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-sa/4.0/

Language dc:language.iso

en_US

Identifier URI

http://dx.doi.org/10.7912/C2/2410

OAI identifier oai:identifier

oai:scholarworks.indianapolis.iu.edu:1805/22680