Thin accretion disk around Schwarzschild-like black hole in bumblebee gravity

TL;DR

This work examines how Lorentz symmetry breaking in bumblebee gravity, parameterized by $l$, modifies the thin accretion disk around a Schwarzschild-like black hole compared with GR. It combines the Novikov–Thorne thin-disk model with ray-tracing to compute the energy flux $F(r)$, temperature $T(r)$, emission spectrum $L( u)$, and direct/secondary disk images for varying $l$ and observer inclination, using the photon geodesic structure including the photon sphere and ISCO. Key results show that decreasing $l$ enhances $F(r)$, $T(r)$, and $ u L( u)$, while the direct image expands outward and the secondary image contracts; the redshift factor $(1+z)$ grows as $l$ decreases, affecting observed flux and color. These findings offer potential observational tests to distinguish bumblebee gravity from GR via BH accretion-disk imaging and spectral signatures, though degeneracies with accretion physics must be carefully addressed.

Abstract

The physical properties and optical appearance of a thin accretion disk surrounding a Schwarzschild-like black hole (BH) are investigated within the framework of bumblebee gravity. To understand how the Lorentz symmetry breaking (LSB) parameter $l$ affects the disk's behavior, we analyze main characteristics such as energy flux, temperature distribution, and emission spectrum. In addition, direct and secondary images of the accretion disk are generated and examined to explore how both the observational inclination angle and the LSB parameter $l$ shape the visual profile. Furthermore, we compute the redshift and observed flux distributions of the disk from the perspective of distant observers at various inclination angles. Our results indicate that the redshift factor grows as $l$ decreases. When the parameter $l$ assumes negative values, the BH exhibits enhanced luminosity with decreasing $l$. These findings highlight the crucial influence of the LSB parameter $l$ on the observable features of BHs.

Figures (12)

• Figure 1: The functions $G(u)$ for different values of $l$, as a function of $u$. Left panel: $l=-0.5$. Right panel: $l=-0.1$. $u_{ph}=1/r_{ph}$, $u_{min}$ is the minimum positive root of $G(u)$ when $b>b_{c}$.
• Figure 2: The azimuthal angle $\varphi(b)$ for different values of $l$, as a function of $b$.
• Figure 3: The behavior of photon trajectories around a Schwarzschild-like BH in bumblebee gravity as a function of the impact parameter $b$ for different values of the parameter $l$. The upper panel displays the total number of orbits $(n = \phi/2\pi)$, classifying trajectories into three categories based on $n$: direct emission $(n<3/4)$ depicted in black, lensed trajectories $(3/4 < n < 5/4)$ shown in orange, and photon ring trajectories $(n > 5/4)$ colored in red. In the lower panel, selected photon paths are visualized using Euclidean polar coordinates $(r, \phi)$. The impact parameter spacing is adjusted to $1/10$, $1/100$, and $1/1000$ for direct emissions, lensed paths, and photon rings, respectively. Three scenarios are analyzed: setting $l=-0.5$ in the first column; $l=-0.3$ in the second column; and $l=0$ in the third column.
• Figure 4: The energy flux $F(r)$ from a disk around a Schwarzschild-like BH in bumblebee gravity for different values of $l$.
• Figure 5: Variety of the disk temperature $T(r)$ with different parameters $l$ for the thin disk around a Schwarzschild-like BH in bumblebee gravity.