Karmarkar scalar condition

Abstract

In this work we present the Karmarkar condition in terms of the structure scalars obtained from the orthogonal decomposition of the Riemann tensor. This the 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 Kamarkar 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.

Radiating-collapsing models satisfying Karmarkar condition

“…the (2.58)-(2.59) reduce to those obtained here using anisotropy together with the Karmarkar condition. Thus, although we had chosen ∆ for the mathematical simplicity, the results obtained are physically significant and in agreement with those obtained in [25].…”

“…Recently, the Karmarkar scalar condition has been used for the nonstatic system, where they found two class of solutions [25]. One of their solutions is that of a horizon free radiating collapse For the collapsing phenomena Θ should be negative throughout the collapse which is confirmed from the figure that as the collapse starts at t = −100, Θ has zero value and it starts decreasing till the collapse reaches its end state at t = 0.…”

Charged anisotropic compact objects obeying Karmarkar condition

“…Both electric charge q(r) and electric field E(r) must be strictly positive and increasing functions with radius, meaning that at the origin both must be null ı.e, q(0) = E(0) = 0. From expressions (35) and (37) the electric field is given by…”

Gravitationally collapsing stars in f(R) gravity

“…In [57], it has been shown that for the static case, Karmarkar condition together with the pressure isotropy yields the Schwarzschild [72] like form of the metric functions. Also, it has been shown that these set of gravitational potentials are the special class of those found in [73]. Thus, although we have assume this particular form of (36) for the mathematical simplicity, represents the physically viable solutions.…”