Einasto-core generalization of the Dymnikova regular black hole metric

Abstract In this work, we develop an Einasto-core generalization of the Dymnikova regular black hole metric, motivated by the flat density profile and the Einasto-type density distribution used in modeling dark matter halos and galactic structures. Replacing the exponential source term in the Dymnikova metric with an Einasto-type profile defined by the parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , we obtain a new, regular class of asymptotically flat and spherically symmetric configurations. We derive the corresponding spacetime metric by employing the Einstein field equations with an anisotropic stress-energy tensor as the matter source. Our analysis confirms that a family of regular black hole solutions can be constructed for arbitrary values of the Einasto index $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and for a broad range of mass parameters M .The resulting configuration smoothly interpolates between a de Sitter core at the center and a Schwarzschild-like exterior at large radii, preserving the regular character of the geometry. It is observed that the interpolation of different shape parameter values leads to distinct self-gravitational, anisotropic populations of cosmic objects with unique physical characteristics. The non-singular and viable nature of the obtained solution is examined through the finiteness of the scalar curvature.