Investigating the interplay of the braneworld gravity and the plasma environment on the black hole shadow

TL;DR

This work analyzes the shadow of a rotating braneworld black hole in dispersive plasma, modeled by a Kerr–Newman–like metric with mass $M$, spin $a$, and tidal charge $q$, to test higher-dimensional gravity using EHT observations of M87* and Sgr A*. Light propagation is treated via a Hamiltonian formalism in non-magnetized plasma, yielding separable geodesics and spherical photon orbits that define the shadow boundary projected onto the observer’s sky; three plasma profiles parameterized by $\alpha_i$ are used to assess how plasma dispersion competes with background geometry. The authors constrain $(q,\alpha_i)$ by comparing theoretical shadow diameters $\Delta\Theta_{th}$ and Schwarzschild deviation parameters $\delta_{sh}$ to EHT measurements, finding that low-density plasmas favor negative $q$ while high-density plasmas allow compensating effects from the plasma environment; M87* and Sgr A* generally exhibit geometry-dominated shadows under current observational constraints, though plasma effects become non-negligible in denser environments. Overall, the study demonstrates the necessity of incorporating realistic plasma environments when testing braneworld gravity with black hole shadows and highlights the potential of future multi-band EHT data and polarimetric modelling to tighten constraints on higher-dimensional gravity.

Abstract

We investigate the shadow of a rotating braneworld black hole in dispersive plasma environments and assess the potential of the Event Horizon Telescope (EHT) observations to constrain braneworld gravity. The spacetime around a rotating braneworld black hole is modelled by a Kerr-Newman-like metric determined by its mass $M$, spin $a$, and tidal charge $q$, which encodes the gravitational effects of the bulk spacetime. We consider both inhomogeneous and homogeneous plasma environments characterized by plasma parameters $α_i$ ($i=1,2\text{ and }3$) to study light propagation and the interplay of the background spacetime and the plasma environment in influencing the shadow size and shape. We find that as the plasma density increases, inhomogeneous plasma environments decrease the shadow size, however homogeneous plasma enlarges it. On studying the effect due to background spacetime we find that $q<0$ (negative tidal charge) increases the shadow diameter, while $q>0$ decreases it. Using the EHT measurements of M87* and Sgr A*, we constrain the $(q,α_i)$ parameter space. The EHT data constrains the tidal charge in the range $-1.15 \lesssim q \lesssim 0.45$ for M87* and $-0.65 \lesssim q \lesssim 0.8$ for Sgr A* in the low density plasma limit. As the plasma density increases, the data exhibits a preference towards negative tidal charge for inhomogeneous plasma environments and positive tidal charge for homogeneous plasma environments. Our study reveals that the size of the shadow is primarily governed by the background geometry in presence of low density plasma environments such as that observed in M87* and Sgr A*. However, if supermassive blackholes are surrounded by high density plasma then the shadow size is dictated by both the background metric and the plasma environment.

Figures (12)

• Figure 1: Variation of $F_r(r,\theta)$ with distance for different values of $a$ and $\theta$ for profile 1.
• Figure 2: Plots showing effect of plasma profile 1 on shadow of braneworld black hole for different combinations of $q$ and $a$ at $\theta=90^\circ$.
• Figure 3: Variation of $F_\theta(r,\theta)$ with distance for different values of $a$ and $\theta$ for profile 2.
• Figure 4: Plots showing effect of plasma profile 2 on shadow of braneworld black hole for different combinations of $q$ and $a$ at $\theta=90^\circ$.
• Figure 5: Variation of $F_h(r,\theta)$ with distance for different values of $a$ and $\theta$ for homogeneous plasma.