Relativistic parametric embedding class I solutions of cold stars in Karmarkar space-time continuum.

• We have obtained a new parametric class of well-behaved solutions in embedding class I. • We use pressure anisotropy and Karmarkar condition for developing viable models of compact stars PSR J1614-2230 and SAX J1808.4-3658. • Our solutions satisfy the following stability conditions i.e., Herrera cracking condition, causality condition, Bondi condition, Zeldovich condition and stable static criteria (Harrison-Zeldovich-Novikov criterion) for both the stars in their respective ranges of parametric class. • Our solutions satisfy all energy conditions and equilibrium condition (TOV equation) which are essential for a physically viable stellar models. The aim of this paper is to explore a new parametric class of relativistic solutions to the Einstein field equations describing a spherically symmetric, static distribution of anisotropic fluid spheres to study the behavior of some of the cold stars in the setting of Karmarkar space-time continuum. We develop models of stellar objects for a range of parameter values of n and analyze their behavior through graphical representation. For each of these models, we have found that the metric potentials are well behaved inside the stellar interior and the physical parameters such as density, radial and tangential pressures, red-shift, radial speed, radial pressure density ratio and energy conditions display a continuous decrease from the center to surface of the stars whereas the mass, anisotropy, adiabatic indexes and compactification factor show a monotonous increase which imply that the proposed solution satisfy all the physical aspects of a realistic stellar objects. The stability of the solutions are verified by examining various stability aspects, viz., Zeldovich criteria, causality condition, Bondi condition, equilibrium condition (TOV-equation) and stable static criteria in connection to their cogency. [ABSTRACT FROM AUTHOR]