Anisotropic relativistic fluid spheres: an embedding class I approach
Abstract
Abstract In this work, we present a new class of analytic and well-behaved solution to Einstein’s field equations describing anisotropic matter distribution. It’s achieved in the embedding class one spacetime framework using Karmarkar’s condition. We perform our analysis by proposing a new metric potential $$g_{rr}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>g</mml:mi><mml:mrow><mml:mi>rr</mml:mi></mml:mrow></mml:msub></mml:math> which yields us a physically viable performance of all physical variables. The obtained model is representing the physical features of the solution in detail, analytically as well as graphically for strange star candidate SAX J1808.4-3658 ( $$Mass=0.9 ~M_{\odot }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>M</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>0.9</mml:mn><mml:mspace/><mml:msub><mml:mi>M</mml:mi><mml:mo>⊙</mml:mo></mml:msub></mml:mrow></mml:math> , $$radius=7.951$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>d</mml:mi><mml:mi>i</mml:mi><mml:mi>u</mml:mi><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn>7.951</mml:mn></mml:mrow></mml:math> km), with different values of parameter n ranging from 0.5 to 3.4. Our suggested solution is free from physical and geometric singularities, satisfies causality condition, Abreu’s criterion and relativistic adiabatic index $$\varGamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Γ</mml:mi></mml:math> , and exhibits well-behaved nature, as well as, all energy conditions and equilibrium condition are well-defined, which implies that our model is physically acceptable. The physical sensitivity of the moment of inertia ( I ) obtained from the solutions is confirmed by the Bejger−Haensel concept, which could provide a precise tool to the matching rigidity of the state equation due to different values of n viz., $$n=0.5, 1.08, 1.66, 2.24, 2.82$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>0.5</mml:mn><mml:mo>,</mml:mo><mml:mn>1.08</mml:mn><mml:mo>,</mml:mo><mml:mn>1.66</mml:mn><mml:mo>,</mml:mo><mml:mn>2.24</mml:mn><mml:mo>,</mml:mo><mml:mn>2.82</mml:mn></mml:mrow></mml:math> and 3.4.