Einstein clusters as models of inhomogeneous spacetimes

Szybka, Sebastian J.; Rutkowski, Mieszko

doi:10.1140/epjc/s10052-020-7948-0

“…In this work, we shall focus on an old method developed by Einstein to construct spherically symmetric solutions using the anisotropic matter distributions known as the Einstein clusters [13]. Moreover, this idea was used to explain dark matter in terms of Einstein clusters by Boehmer and Harko [14] and Lake [15], as well as other related studies [16][17][18]. Recently Cardoso et al [19] used the Einstein cluster to construct a space time geometry using the Hernquist-type distribution and a black hole in the center.…”

Section: Introductionmentioning

confidence: 99%

Black holes surrounded by Einstein clusters as models of dark matter fluid

Jusufi¹

2022

Preprint

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We construct a novel class of spherically symmetric and asymptotically flat black holes and naked singularities surrounded by anisotropic dark matter fluid with the equation of state (EoS) of the form Pt = ωρ. We assume that dark matter is made of weakly interacting particles orbiting around the supermassive black hole in the galactic center and the dark matter halo is formed by means of Einstein clusters having only tangential pressure. In the large distance from the black hole we obtain the constant flat curve with the upper bound for the dark matter state parameter ω ∼ < 10 −7 . To this end, we also check the energy conditions of the dark matter fluid outside the black hole/naked singularity, the deflection of light by the galaxy, and the shadow images of the Sgr A black hole using the rotating and radiating particles. For the black hole case, we find that the effect of dark matter fluid on the shadow radius is small, in particular the angular radius of the black hole is shown to increase by the order 10 −4 µarcsec compared to the vacuum solution. For the naked singularity we obtain significantly smaller shadow radius compared to the black hole case. Finally, we study the stability of the S2 star orbit around Sgr A black hole under dark matter effects. It is argued that the motion of S2 star orbit is stable for values ω ∼ < 10 −7 , however further increase of ω leads to unstable orbits.

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“…Magli [15] presented a general class of time-dependent spherically symmetric solutions of Einstein's equations with zero radial pressure, and later on, Gair [16] discussed all possible kinds of evolution of the shells constituting the cluster. Einstein clusters have also been studied as a toy model for small-scale inhomogeneous spacetimes by Szybka and Rutkowski [17].…”

Section: Jcap04(2024)070mentioning

confidence: 99%

Modelling Einstein cluster using Einasto profile

Acharyya,

Banerjee,

Kar

2024

J. Cosmol. Astropart. Phys.

0

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We demonstrate a general relativistic approach to model dark matter halos using the Einstein cluster, with the matter stress-energy generated by collisionless particles moving on circular geodesics in all possible angular directions and orbital radii. Such matter, as is known, allows an anisotropic pressure profile with non-zero tangential but zero radial pressure. We use the Einasto density profile for the Einstein cluster. Analytical studies on its properties (metric functions) and stability issues are investigated. Further, to establish this model (with the Einasto profile) as one for a dark matter halo, we use the SPARC galactic rotation curve data and estimate the best-fit values for the model parameters. General relativistic features (beyond the Keplerian velocities) such as the tangential pressure profile, are quantitatively explored. Thus, Einstein clusters with the Einasto profile, which tally well with observations, may be considered as a viable model for dark matter halos.

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Black holes surrounded by Einstein clusters as models of dark matter fluid

Jusufi

¹

2023

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We construct a novel class of spherically symmetric and asymptotically flat black holes and naked singularities surrounded by anisotropic dark matter fluid with the equation of state (EoS) of the form $$P_t=\omega \rho $$ P t = ω ρ . We assume that dark matter is made of weakly interacting particles orbiting around the supermassive black hole in the galactic center and the dark matter halo is formed by means of Einstein clusters having only tangential pressure. In the large distance from the black hole we obtain the constant flat curve with the upper bound for the dark matter state parameter $$\omega \lesssim 10^{-7}$$ ω ≲ 10 - 7 . To this end, we also check the energy conditions of the dark matter fluid outside the black hole/naked singularity, the deflection of light by the galaxy, and the shadow images of the Sgr A$$^\star $$ ⋆ black hole using the rotating and radiating particles. For the black hole case, we find that the effect of dark matter fluid on the shadow radius is small, in particular the angular radius of the black hole is shown to increase by the order $$10^{-4}\, \upmu $$ 10 - 4 μ arcsec compared to the vacuum solution. For the naked singularity we obtain significantly smaller shadow radius compared to the black hole case. Finally, we study the stability of the S2 star orbit around Sgr A$$^\star $$ ⋆ black hole under dark matter effects. It is argued that the motion of S2 star orbit is stable for values $$\omega \lesssim 10^{-7}$$ ω ≲ 10 - 7 , however further increase of $$\omega $$ ω leads to unstable orbits. Using the observational result for the shadow images of the Sgr A$$^\star $$ ⋆ reported by the EHT along with the tightest constraint for $$\omega $$ ω found from the constant flat curve, we show that the black hole model is consistent with the data while the naked singularity in our model can be ruled out.

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Einstein clusters as models of inhomogeneous spacetimes

Cited by 3 publications

References 26 publications

Black holes surrounded by Einstein clusters as models of dark matter fluid

Black holes surrounded by Einstein clusters as models of dark matter fluid

Modelling Einstein cluster using Einasto profile

Black holes surrounded by Einstein clusters as models of dark matter fluid

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