Rotating Charged Black Holes with Scalar Hair Constructed via the Newman-Janis Algorithm: Accretion Disk Structure and Shadow Characteristics

TL;DR

We construct a rotating charged black hole with scalar hair in Einstein-Maxwell-Conformally coupled Scalar (EMCS) theory by applying the Newman–Janis algorithm to a static seed with line element and $f(r)=1-\frac{2M}{r}+\frac{Q^{2}+s}{r^{2}}$. The rotating solution features horizon structure governed by $\Delta$ and ergosurface properties that depend on $a$, $Q$, and $s$, while accretion-disk emissions are modeled with the Novikov–Thorne framework and the shadow is analyzed from null geodesics using celestial coordinates $(X,Y)$ and shadow observables $R_{s}$ and $\delta_{s}$. The results show that increasing $Q$ or $s$ shrinks the shadow and enhances non-circular distortions (cusps appear at high $a$), and that $F(r)$ and $T(r)$ rise with $Q$ or $s$ for fixed $a$, indicating higher radiative efficiency in hairy, charged spacetimes. When confronted with EHT observations of Sgr A$^*$, the model yields bounds $0<Q<0.522745$ (at $s=0.1$) and $0<s<0.283373$ (at $Q=0.3$), demonstrating compatibility with current BH-imaging data and providing concrete observational signatures to test strong-field gravity beyond general relativity.

Abstract

In this paper, we generate a rotating charged black hole (BH) with scalar hair via the Newman--Janis algorithm (NJA) and study its thin accretion disk and shadow. The structure of the event horizon and ergosurface is analyzed in detail, revealing how the charge parameter $Q$ and scalar hair parameter $s$ influence the spacetime geometry. We analyze the energy flux and temperature distribution of the accretion disk, finding that increasing either $Q$ or $s$ leads to higher energy flux and peak temperature. The BH shadow is also examined, showing that its apparent size decreases monotonically with increasing $Q$ or $s$. Notably, in the near-extremal regime, the shadow develops a distinctive cuspy edge, indicative of strong light bending in the scalarized and charged spacetime. By comparing the theoretically predicted shadow diameter with Event Horizon Telescope (EHT) observations of Sgr A$^*$, we derive observational constraints on the model parameters. For inclination angles of $17^\circ$ and $90^\circ$, a joint analysis constrains the charge parameter to $0<Q<0.522745$ (at fixed $s=0.1$) and the scalar hair parameter to $0<s<0.283373$ (at fixed $Q=0.3$). Our results demonstrate how scalar hair and electric charge leave imprints on accretion disk emissions and black hole shadows, offering new observational signatures for testing gravity theories beyond general relativity.

Figures (9)

• Figure 1: Regions of BH horizon existence in the $(a, Q, s)$ parameter space.
• Figure 2: The shapes of the outer horizon (black solid line) and outer ergosphere (red solid line) are compared to the outer event horizon in the static case (blue solid line).
• Figure 3: The energy flux $F(r)$ from an accretion disk around a rotating charged black hole with scalar hair is plotted for different values of $Q$ and $s$. The top row shows results for fixed $Q = 0.3$, while the bottom row corresponds to fixed $s = 0.1$.
• Figure 4: The temperature $T(r)$ from an accretion disk around a rotating charged black hole with scalar hair is shown for various values of $Q$ and $s$. The top row presents results for a fixed value of $Q=0.3$, whereas the bottom row corresponds to a fixed value of $s=0.1$.
• Figure 5: Shadows of a rotating charged black hole with scalar hair are presented for varying spin parameter $a$ and scalar hair parameter $s$, with $Q = 0.3$ fixed.