Relativistic structure of a supermassive black hole embedded in the dark matter halo of NGC 4649 (M60)

TL;DR

This paper develops a model of a supermassive black hole within a dark matter halo based on observations of galaxy NGC 4649, analyzing how the halo affects black hole properties and potential observational signatures.

Contribution

It introduces a non-vacuum, spherically symmetric black hole solution embedded in a dark matter halo calibrated to real galaxy data, extending Schwarzschild spacetime.

Findings

Halo influences event horizon and photon sphere sizes

Kretschmann scalar shows increased sensitivity to halo effects

Thermodynamics of the black hole are modified in the extremal limit

Abstract

We construct a static, spherically symmetric black hole (BH) solution embedded within a dark matter (DM) halo, formulated as a non-vacuum extension of the Schwarzschild spacetime. The DM distribution is modeled via an empirical density profile calibrated to observations of the elliptical galaxy NGC 4649 (M60), incorporating Hubble Space Telescope (HST) imaging, stellar velocity dispersion data, and globular cluster dynamics. The resultant spacetime metric depends on three independent parameters: the black hole mass $M$, the asymptotic circular velocity $V_c$, and the halo scale radius $a$, and smoothly reduces to the Schwarzschild limit as $V_c \to 0$ and $a \to 0$. We analyze the influence of the halo on key geometric and physical quantities, including the event horizon radius, photon sphere, shadow size, and curvature invariants. The Kretschmann scalar exhibits an enhanced sensitivity to halo-induced modifications, particularly in the near-horizon regime. Thermodynamic properties of the solution are also examined. In the extremal limit, characterized by a vanishing surface gravity, the model supports a finite tangential pressure, implying a non-trivial extension of standard black hole thermodynamics. These results highlight the relevance of incorporating astrophysical environments into BH modeling and offer new avenues for testing strong-field gravity through precision observational data.