Regular Article - Theoretical Physics
Karmarkar scalar condition
Departamento de Matemática Aplicada and Instituto Universitario de Física Fundamental y Matemáticas, Universidad de Salamanca, Salamanca, Spain
2 Escuela de Física, Universidad Industrial de Santander, Bucaramanga, Colombia
3 Departamento de Física, Universidad de Los Andes, Mérida, Venezuela
Accepted: 9 February 2020
Published online: 21 February 2020
In this work we present the Karmarkar condition in terms of the structure scalars obtained from the orthogonal decomposition of the Riemann tensor. This new expression becomes an algebraic relation among the physical variables, and not a differential equation between the metric coefficients. By using the Karmarkar scalar condition we implement a method to obtain all possible embedding class I static spherical solutions, provided the energy density profile is given. We also analyse the dynamic adiabatic case and show the incompatibility of the Karmarkar condition with several commonly assumed simplifications to the study of gravitational collapse. Finally, we consider the dissipative dynamic Karmarkar collapse and find a new solution family.
© The Author(s) 2020
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