Structure of anisotropic fuzzy dark matter black holes

Abstract Building on the Einasto dark matter (DM) density parameterizations, this study explores the possibility of constructing DM black holes (BHs) within the formalism of the Starobinsky gravity model. This approach extends the solutions characterizing the non-commutative mini BHs and introduces DM as the fundamental material constituting the BH. Assuming an anisotropic fluid configuration, we demonstrate the existence of different BH models subject to the 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 rescaled mass $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ξ</mml:mi> </mml:math> . To achieve this, we begin by considering a de Sitter-like equation of state (EOS) wherein $$\varepsilon =-P_{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:mrow> </mml:math> . Interestingly, the resulting BH solution not only shares a similar horizon structure with a Reissner-Nordström BH but also replaces the central singularity with a regular de Sitter core through the mechanism of quadratic $$f(\textrm{R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mtext>R</mml:mtext> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> corrections. We further explore the possibility of using a nonlocal EOS instead of the previous one. This alternative approach allows us to construct a fuzzy DM stellar droplet. However, the radial pressure $$P_{r}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:math> remains negative in this case. More precisely, we explore the possibility of these findings informing the existence of moderately massive DM-BHs within the galactic structures. Such objects could have played a role in the early stages of galactic formation. Furthermore, we delve into the intriguing possibility of these moderately massive DM-BHs acting as the central objects within galaxies.

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