Constraining Black Hole Shadows in Dunkl Spacetime using CUDA Numerical Computations

TL;DR

The paper addresses how Dunkl spacetime deformations modify black hole shadows and how to constrain these effects with Event Horizon Telescope data. It derives the Dunkl-deformed metric function $f(r)$ for charged rotating black holes, constructs rotating solutions via the Newman-Janis algorithm, computes shadow boundaries from null geodesics using the Hamilton–Jacobi formalism, and uses CUDA-based simulations to map the deformation parameters $( ilde{\tau},\text{delta})$ against EHT measurements. Key contributions include an explicit charged Dunkl metric form incorporating $Q$, $a$, $\delta$, and $\zeta$, analysis of horizon structure, and quantitative bounds on the deformation parameters that are compatible with M87$^*$ and Sgr A$^*$ shadows, together with energy-emission implications tied to the shadow size via $T_H$. The work demonstrates how optical observables can constrain fundamental spacetime deformations and showcases CUDA-driven approaches for rapid exploration of parameter spaces in modified gravity models.

Abstract

With the help of CUDA high-performance numerical codes exploited in machine learning, we investigate the shadow aspect of new rotating and charged black holes using the Dunkl derivative formalism. Precisely, we first establish the corresponding metric function encoding the involved physical properties including the optical character. Exploiting such accelerated simulations, we approach the horizon radius behaviors in order to determine the regions of the module space providing physical solutions. Applying the Hamilton-Jacobi mechanism, we assess the shadow aspect for non-rotating and rotating solutions. Using such an aspect, we evaluate the energy rate of emission. Developing a high-performance CUDA numerical code, we derive strict constraints on the Dunkl deformation parameters in order to establish a link with the shadow observations provided by the Event Horizon Telescope collaboration.

Figures (8)

• Figure 1: Left: Black hole horizons in terms of $\zeta$ and $\delta$ for $Q=0.5$ . Right: Black hole horizons in terms of $\zeta$ and $\delta$ for $Q=0.01$.
• Figure 2: Parameter region of the moduli space ensuring the existence of a real event horizon for the charged Dunkl black hole by taking $M\epsilon_M =1$.
• Figure 3: Metric function behaviors for $M\epsilon_M=1$, $Q=0.2$, and $\zeta = 0.5$.
• Figure 4: Regions in the $(\delta, a)$--plane, where the metric admits at least one real event horizon radius for $M\epsilon_M=1$.
• Figure 5: Non-rotating shadow behaviors in the celestial coordinates $(x,y)$ by varying $\delta$ and $\zeta$ and taking $M\epsilon_M=1$.