Reissner-Nordstrom Research Articles

Spherical accretion onto higher-dimensional Reissner–Nordström black hole

Abstract We obtain relativistic solutions of spherically symmetric accretion by a dynamical analysis of a generalised Hamiltonian for higher-dimensional Reissner–Nordström (RN) Black Hole (BH). We consider two different fluids namely, an isotropic fluid and a non-linear polytropic fluid to analyse the critical points in a higher-dimensional RN BH. The flow dynamics of the fluids are studied in different spacetime dimensions in the framework of Hamiltonian formalism. The isotropic fluid is found to have both transonic and non-transonic flow behaviour, but in the case of polytropic fluid, the flow behaviour is found to exhibit only non-transonic flow, determined by a critical point that is related to the local sound speed. The critical radius is found to change with the spacetime dimensions. Starting from the usual four dimensions it is noted that as the dimension increases the critical radius decreases, attains a minimum at a specific dimension (D > 4) and thereafter increases again. The mass accretion rate for isotropic fluid is determined using Hamiltonian formalism. The maximum mass accretion rate for RN BH with different equations of state parameters is studied in addition to spacetime dimensions. The flow behaviour and mass accretion rate for a change in BH charge is also studied analytically. It is noted that the maximum mass accretion rate in a higher-dimensional Schwarzschild BH is the lowest, which however, increases with the increase in charge parameter in a higher-dimensional RN BH.

Black Holes with Electroweak Hair.

We construct static and axially symmetric magnetically charged hairy black holes in the gravity-coupled Weinberg-Salam theory. Large black holes merge with the Reissner-Nordström (RN) family, while the small ones are extremal and support a hair in the form of a ring-shaped electroweak condensate carrying superconducting W currents and up to 22% of the total magnetic charge. The extremal solutions are asymptotically RN with a mass below the total charge, M<|Q|, due to the negative Zeeman energy of the condensate interacting with the black hole magnetic field. Therefore, they cannot decay into RN black holes. As their charge increases, they show a phase transition when the horizon symmetry changes from spherical to oblate. At this point they have the mass typical for planetary size black holes of which ≈11% is stored in the hair. Being obtained within a well-tested theory, our solutions are expected to be physically relevant.

Charged gravastar model in noncommutative geometry under [formula omitted] gravity

In this article, we study the properties of charged gravastars in torsion-based f(T) gravity in the presence of noncommutative geometry. We have taken the interior from noncommutative motivated space–time, noting that why, from a physical point of view, such a choice is justified, then we have taken the thin shell as stiff matter and taken three different exterior metrics (Reissner–Nordstrom (R–N), Bardeen and Ayon-Beato–Garcia (ABG) metric) to construct the gravastar model. We have studied the physical properties like proper length, entropy, energy, and EoS for these models, and we have also used Israel junction conditions to study the effective pressure, energy density, and potential of the thin shell. Finally, we comment on the stability of such a thin shell and the deflection angle caused by such a thin shell, which could, in principle, be tested by future radio telescopes like the Event Horizon Telescope (EHT).

Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy

We consider the dimensional reduction to two dimensions of certain gravitational theories in D ≥ 4 dimensions at the two-derivative level. It is known that the resulting field equations describe an integrable system in two dimensions which can also be obtained by a dimensional reduction of the self-dual Yang-Mills equations in four dimensions. We use this relation to construct a single copy prescription for classes of gravitational solutions in Weyl-Lewis-Papapetrou coordinates. In contrast with previous proposals, we find that the gauge group of the Yang-Mills single copy carries non-trivial information about the gravitational solution. We illustrate our single copy prescription with various examples that include the extremal Reissner-Nordstrom solution, the Kaluza-Klein rotating attractor solution, the Einstein-Rosen wave solution and the self-dual Kleinian Taub-NUT solution.

Black hole evaporation process and Tangherlini–Reissner–Nordström black holes shadow

In this article, we study the black hole evaporation process and shadow property of the Tangherlini-Reissner-Nordström (TRN) black holes. The TRN black holes are the higher-dimensional extension of the Reissner-Nordström (RN) black holes and are characterized by their mass M, charge q, and spacetime dimensions D. In higher-dimensional spacetime, the black hole evaporation occurs rapidly, causing the black hole’s horizon to shrink. We derive the rate of mass loss for the higher-dimensional charged black hole and investigate the effect of higher-dimensional spacetime on charged black hole shadow. We derive the complete geodesic equations of motion with the effect of spacetime dimensions D. We determine impact parameters by maximizing the black hole’s effective potential and estimate the critical radius of photon orbits. The photon orbits around the black hole shrink with the effect of the increasing number of spacetime dimensions. To visualize the shadows of the black hole, we derive the celestial coordinates in terms of the black hole parameters. We use the observed results of M87 and Sgr A∗ black hole from the Event Horizon Telescope and estimate the angular diameter of the charge black hole shadow in the higher-dimensional spacetime. We also estimate the energy emission rate of the black hole. Our finding shows that the angular diameter of the black hole shadow decreases with the increasing number of spacetime dimensions D.

Stability Analysis of Stable Circular Orbit in Multi-Static Black Hole Spacetime

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits.

Nonlinear Maxwell’s theory mimics dark energy

In a recent study (Sadeghi and Noori Gashti, 2024) the so-called Reissner–Nordström (RN) black hole surrounded by perfect fluid dark matter (PFDM) has been investigated. Here in this Letter, we prove that technically such a black hole does not exist in the context of Maxwell’s linear theory coupled minimally to a PFDM. Furthermore, it is shown that this black hole is the result of nonlinear corrections to the linear Maxwell’s Lagrangian in the Einstein–Maxwell theory. The energy–momentum tensor is split into Maxwell’s linear theory and a correction term. The latter i.e., the correction part of the energy–momentum tensor represents an anisotropic dark energy. This result brings the question if nonlinear electrodynamics can be the source of dark matter/energy.

Topology of black hole thermodynamics via Rényi statistics

In this paper, we investigate the topological numbers of the four-dimensional Schwarzschild black hole, d-dimensional Reissner–Nordström (RN) black hole, d-dimensional singly rotating Kerr black hole and five-dimensional Gauss–Bonnet black hole via the Rényi statistics. We find that the topological number calculated via the Rényi statistics is different from that obtained from the Gibbs–Boltzmann (GB) statistics. However, what is interesting is that the topological classifications of different black holes are consistent in both the Rényi and GB statistics: the four-dimensional RN black hole, four-dimensional and five-dimensional singly rotating Kerr black holes, five-dimensional charged and uncharged Gauss–Bonnet black holes belong to the same kind of topological class, and the four-dimensional Schwarzschild black hole and d(>5)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d(>5)$$\\end{document}-dimensional singly rotating Kerr black holes belong to another kind of topological class. In addition, our results suggest that the topological numbers calculated via the Rényi statistics in asymptotically flat spacetime background are equal to those calculated from the standard GB statistics in asymptotically AdS spacetime background, which provides more evidence for the connection between the nonextensivity of the Rényi parameter λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} and the cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}.

Thermodynamic stability versus chaos bound violation in D-dimensional RN black holes: Angular momentum effects and phase transitions

We compute the Lyapunov exponents for test particles orbiting in unstable circular trajectories around D-dimensional Reissner-Nordström (RN) black holes, scrutinizing instances of the chaos bound violation. Notably, we discover that an increase in particle angular momentum exacerbates the breach of the chaos bound. Our research centrally investigates the correlation between black hole thermodynamic phase transitions and the breaking of the chaos limit. Findings suggest that the chaos bound can only be transgressed within thermodynamically stable phases of black holes. Specifically, in the four-dimensional scenario, the critical point of the thermodynamic phase transition aligns with the threshold condition that delineates the onset of chaos bound violation. These outcomes underscore a deep-rooted link between the thermodynamic stability of black holes and the constraints imposed by the chaos bound on particle dynamics.

Circular motion and collisions of charged spinning particles near Kerr Newman black holes

We investigate the dynamics of spinning particles with an electric charge orbiting electrically charged Kerr–Newman black holes. First, we derive the equations of motion for the test particles using the Mathisson-Papapetrou-Dixon (MPD) equations, taking into account electromagnetic interaction and the interaction between the particle spin and the spacetime curvature known as the Lorentz coupling term in the MPD equation. We analyze the related effective potential in various scenarios of particle spin, angular momentum, and black hole spin orientation. In addition, we provide graphical analyses of the radius of innermost stable circular orbits (ISCOs) of the particles, their angular momentum, and energy at ISCOs and superluminal bounds. The ISCOs for positive and negatively charged particles are almost the same. The combined effects of the black hole and particle spins enhance the Coulomb interaction effect on the ISCO radius. The ISCO energy and angular momentum decrease with the increase in particle spin. In the Reissner–Nordström (RN) black hole limit, the decreasing rate is faster at positive values of the particle spin, and the spin limit changes in the Kerr–Newman black hole case. Finally, we study collisions between spinning charged particles near Kerr–Newman black holes. The critical values of the angular momentum of spinning charged particles are explored, and the particles can collide in various cases of particle and black hole spin, as well as the particle angular momentum. We also analyze electromagnetic and spin effects on the center-of-mass energy of the colliding particles.

Enhanced Approaches to Gravitational Lensing: A Regular Charged Black Hole in Weak Field Limit

Gravitational lensing, an integral aspect of general relativity, profoundly impacts our understanding of black holes (BH’s). The presence of a centered singularity resulting from gravitational collapse is a fundamental characteristic of a BH Nonetheless, the exploitation of non-linear electrodynamics (NLED) divulges the emphatic concept of non-singularity. Our analysis primarily focuses on calculating the deflection angle in the weak field approximation, deliberately excluding the original spacetime configuration. The photon’s effective geometry is typically linked to NLED. Instead, a photon traverses an effective null geodesic that aligns with the geometry of a regular metric. The findings reveal an additional term in the deflection angle compared to the Reissner-Nordström (RN) metric, evidenced by a shifted positional displacement of the tertiary image associated with a regular BH This study succinctly encapsulates these findings, positioning them within the extensive terminology ambient to BH’s singularity and GL, thus edifying the scientific memoir with precise astrophysical insights.

Exploring Weak Gravitational Lensing Effects by a Regular Black Hole

Gravitational lensing is one of the physical consequences of Einstein’s general theory of relativity, which has been observationally confirmed. This work aims to study the weak gravitational lensing scenario where the lens is a spherically symmetric, charged-nonsingular black hole that asymptotically behaves as the Reissner-Nordström (RN). The difference exists in the higher-order expansion. Therefore, the metric function of the regular charged black hole is expanded up to the fourth order, and the deflection angle is calculated. The thin lens equation is used, leading to five images: two imaginary and three real images. The exact positions of the images and magnification properties are calculated by providing the physical parameters such as mass, charge, and distances. Our calculation shows that the third image position shifted away from the optical axis. The formalism is applied to the case of a supermassive black hole located at the center of our galaxy with the assumption that it has an electric charge.

Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS

In the Einstein-Maxwell-charged scalar system with a negative cosmological constant in arbitrary dimensions higher than three, there exists a horizonless charged soliton solution, which we construct explicitly for an arbitrary mass of the scalar in perturbative series in small charge. We find that the stability of the soliton is determined by the validity of the AdS weak gravity conjecture. The existence of a stable soliton might endanger the convexity of the (free) energy as a function of the charge because the phase transition between the soliton and the extremal Reissner-Nordstrom black hole would be discontinuous. We, however, argue that the existence of the hairy black hole solution circumvents the violation of convexity. The thermodynamic properties of the hairy black hole show that the phase transition becomes continuous irrespective of whether the AdS weak gravity conjecture holds. When it holds, the phase transition occurs between the soliton and the hairy black hole, and when it is violated, the phase transition occurs between the extremal Reissner-Nordstrom black hole and the hairy black hole.

The effect of scalar hair on the charged black hole with the images from accretions disk

In this paper, we investigate the optical properties of a charged black hole with scalar hair (CSH) within the context of four-dimensional Einstein–Maxwell–Dilaton gravity. To achieve this, we consider three distinct toy models of thin accretion disks. The presence of dilaton coupling allows us to express both the solutions of CSH and the Reissner–Nordström (RN) black hole in terms of their mass (M) and charge (Q). Our findings reveal differences in the effective potentials Veff\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V_{eff}$$\\end{document}, photon sphere radii rph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ph}$$\\end{document}, and innermost stable circular orbit risco\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{isco}$$\\end{document} between the CSH and RN black hole cases, which become increasingly pronounced as the charge parameter Q increases. However, no noticeable distinctions are observed concerning the critical impact parameter bph\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_{ph}$$\\end{document}. When the ratio of the photon ring band and the lensed ring band exceeds 0.1, it may suggest the presence of a charged black hole with scalar hair. Furthermore, our results underscore the significant influence of the charge parameter Q on the brightness distributions of the direct, lensed ring, and photon ring for three standard emission functions. These findings emphasize the potential for distinguishing between CSH and RN black holes through an analysis of direct intensity and peak brightness in specific accretion disk models.

Reissner-Nordström black holes surrounded by perfect fluid dark matter: Testing the viability of weak gravity conjecture and weak cosmic censorship conjecture simultaneously

A possible violation of the weak gravity conjecture (WGC) by cosmic censorship is one of the major challenges in the field of general relativity. The cosmic censorship is a fundamental principle that ensures the consistency of the theory of gravity. According to this principle, a charged black hole in four dimensions cannot violate the weak cosmic censorship conjecture (WCCC) under normal conditions. However, in this paper, we explore the possibility of reconciling the WGC and the WCCC by considering Reissner-Nordström (R-N) black holes embedded in perfect fluid dark matter (PFDM) in asymptotically flat spacetimes. These two conjectures are seemingly unrelated, but a recent proposal suggested that they are connected surprisingly. In particular, We argue a promising class of valid counterexamples to the WCCC in the four-dimensional Einstein-Maxwell theory, considering a charged black hole when WGC is present. We demonstrate that by imposing certain constraints on the parameters of the metric, the WGC and the WCCC can be compatible. Furthermore, we investigate the properties of the charged black hole in the presence of PFDM for Q>M and present some intriguing figures to test the validity of the WGC and the WCCC simultaneously. When PFDM is absent (γ=0), the RN black hole either has two event horizons if Q2/M2≤1 or none if Q2/M2>1. The second scenario results in a naked singularity, which contradicts the WCCC. But when PFDM is present (γ≠0), the RN black hole has event horizons with regard to Q and M. This implies that the singularity is always covered, and the WGC and the WCCC are fulfilled. Furthermore, we demonstrate that there is a critical value of γ, called γext, that makes the RN black hole extremal when γ=γext. In this situation, the black hole has an event horizon, and the WGC and the WCCC are still fulfilled. We infer that PFDM can make the WGC and the WCCC compatible with the RN black hole and that the WGC and the WCCC agree with each other when PFDM is present.

Distinguishing the observational signatures of hot spots orbiting Reissner-Nordström spacetime*

Abstract This paper investigates observable signatures of hot spots orbiting Reissner-Nordström (RN) black holes and naked singularities. For an RN black hole, we find two discernible lensing image tracks in time integrated images, capturing a complete orbit of hot spots and a image shadow within the critical curve where photons with a small impact parameter fall into the event horizon. Conversely, in RN singularities, additional image tracks can be found within the critical curve, originating from photons reflected by the infinitely high effective potential well. Moreover, we find incomplete and converging tracks from the time integrated images of hot spot orbiting RN singularities that have no photon sphere. The presence of these additional image tracks significantly influences temporal magnitudes at their local maxima, enabling us to differentiate between RN black holes and RN naked singularities.

Testing gravitational lensing effects by supermassive massive black holes with superstring theory metric: Astrophysical implications and EHT constraints

We investigate gravitational lensing, both strong and weak, induced by charged black holes within heterotic superstring theory – α′-corrected Reissner–Nordström (RN) black holes characterized by an additional parameter, denoted as α, in addition to mass M and charge Q. Our findings reveal that as the parameter α increases, various crucial parameters such as the unstable photon orbit radius rph, critical impact parameter uph, deflection angle αD(θ), and angular position θ∞ also increase. Concurrently, the angular separation s decreases, while the relative magnitude rmag increases with the growing value of α. Utilizing supermassive black holes (SMBH) Sgr A* and M87* as gravitational lenses, the deflection angle resulting from the α′-corrected RN black hole, in both strong and weak field limits, surpasses that of the RN black holes (α=0) and falls below that of Schwarzschild black holes (α=0, Q=0). For Sgr A*, the angular position θ∞ lies within (24.08, 26.38) μas, while for M87* it ranges from (18.23, 19.96) μas. Estimating the time delay between the first and second relativistic images using twenty supermassive galactic center black holes as lenses, we find, for instance, that the time delay for Sgr A* and M87*, with Q=0.5 and α=5, can reach approximately 9.81 min and 14835.6 min, respectively. Remarkably, the EHT results for Sgr A* impose more stringent limits on the parameter space of α′-corrected RN black holes compared to those established by the EHT results for M87*. Our analysis deduces that, within the 1σ region, a substantial portion of the parameter space for α′-corrected RN black holes aligns with the Event Horizon Telescope (EHT) results for M87* and Sgr A*, and that and one cannot rule out the possibility of that heterotic superstring theory’s α′-corrected RN black holes being strong candidates for astrophysical black holes.

General upper limit on the electric charge of Sgr A* in the Reissner–Nordström metric

ABSTRACT In general relativity, the gravitational field of an electrically charged, non-rotating, spherically symmetric body is described by the Reissner–Nordström (RN) metric. Depending on the charge to mass ratio, the solution describes a black hole or a naked singularity. In the naked-singularity regime, a general property of this metric is the existence of a radius, known as the zero-gravity radius, where a test particle would remain at rest. As a consequence of repulsive gravity there is no circular orbit inside this radius, and at least a part of any quasi-stable structure must necessarily lie outside of it. Assuming the iconic torus in the compact source Sgr A* at the Galactic centre observed by the Event Horizon Telescope (EHT) to be the image of a quasi-stationary fluid structure, we provide rigorous constraints in the RN metric on the electric charge-to-mass ratio Q/M of Sgr A*. A comparison between the EHT observations and the space–time zero-gravity radius provides the most conservative limit on the charge of Sgr A* to be |Q/M| &amp;lt; 2.32 in geometrized units. A charged naked singularity respecting this charge-to-mass constraint is consistent with the current EHT observations, if the image is not interpreted as a photon ring.

Stability analysis of anisotropic stellar structures in Rastall theory of gravity utilizing cracking technique

In this manuscript, we employ the cracking technique in the Rastall gravity framework to assess how local density perturbations affect the stability of anisotropic stellar structures. To achieve this, we developed field equations for spherically symmetric spacetime with the charge inclusion in the context of Rastall gravity and then employed the krori Barua approach and barotropic equation of state while considering Reissner–Nordstrom metric as exterior spacetime, to develop the solution of the field equations. Further, we formulated the Tolman–Oppenheimer–Volkoff (TOV) equation by considering the non-conservation of energy–momentum tensor in the context of Rastall gravity. The stability of configuration is then disrupted by incorporating local density perturbations. Subsequently, our proposed approach is employed on the following compact stars: Her X-1, SAX J1808.4-3658, 4U 1820-30, PSR J1614-2230, Vela X-1, Cen X-3, and RXJ1856-37 to demonstrate its viability. The findings demonstrate that all stars under consideration experience cracking. This work particularly emphasizes the crucial role of cracking method in offering insightful information on the stability analysis of anisotropic stellar structures.

Images of hairy Reissner–Nordström black hole illuminated by static accretions

In this paper, we investigate the shadow and optical appearance of the hairy Reissner–Nordström (RN) black hole illuminated by two toy models of static accretion. The hairy RN black hole was constructed in the gravitation decoupling approach to describe the deformation of a Schwarzschild black hole due to the inclusion of additional arbitrary source (scalar field, tensor field, fluidlike dark matter, etc.). So it is characterized by the parameters: mass (M), deformation factor (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}), electric charge (Q) and the additional hairy charge (lo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_o$$\\end{document})., differentiating from the case in RN black hole. Though the specific background theory that results in this hairy RN black hole is still tricky, here we shall focus on the novel observable features introduced by the hair of this black hole. First, we find that for the hairy RN black hole, the event horizon, radius of photon sphere and critical impact parameter all increase as the increasings of Q and lo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_o$$\\end{document}, but decrease as α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} grows. Furthermore, the three characterized parameters are found to have significant effects on the photon trajectories, and shadows as well as images of the hairy RN black hole surrounded by the static accretion disk and spherical accretion, respectively. In particular, both Q and lo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l_o$$\\end{document} have mutually reinforcing effects on the optical appearance and shadows of the hairy RN black hole, which implies that we may not distinguish the electric charge and hairy charge from the shadow and image of black hole in this scenario. Additionally, because of the competing effects of the charge parameters (Q,lo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q, l_o$$\\end{document}) and the deviation parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} on the observed intensities of brightness, the optical appearance between the hairy RN black hole and RN black hole could have degeneracies, indicating the indistinguishability. Our current results contribute more to the phenomenal aspects which could be helpful to build the background theory of this hairy RN black hole.