Symmetric Black Hole Research Articles

Analysis of Dyonic ModMax black hole through accretion disk

In the present study, we probe the geodesic motion and accretion of particles around the spherically symmetric Dyonic ModMax black hole using isothermal fluid. The geodesic motion of the particles around the black hole leads to the formation of disk like structure during the accretion process. We compute the radiant temperature, radioactive efficiency, radiant flux energy, circular orbits and observe the behavior of particles within stable circular orbits in the equatorial plane. We examine how the particles are perturbed during the process by using restoring forces and the oscillatory behavior of the particles surrounding a compact object and also investigate the fluid’s critical flow and maximum accretion rate. Our findings demonstrate how the black hole parameter γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} and charge Q affect the circular geodesic of particles as well as the maximum accretion rate of the Dyonic ModMax black hole.

Exploring antisymmetric tensor effects on black hole shadows and quasinormal frequencies

This study explores the impact of antisymmetric tensor effects on spherically symmetric black holes, investigating photon spheres, shadows, emission rate and quasinormal frequencies in relation to a parameter which triggers the Lorentz symmetry breaking. We examine these configurations without and with the presence of a cosmological constant. In the first scenario, the Lorentz violation parameter, denoted as λ, plays a pivotal role in reducing both the photon sphere and the shadow radius, while also leading to a damping effect on quasinormal frequencies. Conversely, in the second scenario, as the values of the cosmological constant (Λ) increase, we observe an expansion in the shadow radius. Also, we provide the constraints of the shadows based on the analysis observational data obtained from the Event Horizon Telescope (EHT) focusing on Sagittarius A* shadow images. Additionally, with the increasing Λ, the associated gravitational wave frequencies exhibit reduced damping modes.

The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation

In this letter, we will focus on the Klein–Gordon equation with rotating axially symmetric black hole solution of the Einstein–Bumblebee theory, so called the Kerr–Bumblebee black hole, as its 3 + 1 background space-time. We start with constructing the covariant Klein–Gordon equation component by component and with the help of the ansatz of separation of variables, we successfully separate the polar part and found the exact solution in terms of Spheroidal Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that is resulted in a complex-valued energy levels expression for a massive scalar field, where the real part is the scalar particle’s energy while the imaginary part represents the quasibound stats’s decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe the decaying nature of the relativistic scalar field bound in the curved Kerr–Bumblebee space-time. We also investigate the Hawking radiation of the Kerr–Bumblebee black hole’s apparent horizon via the Damour–Ruffini method by making use the obtained exact scalar’s wave functions. The radiation distribution function and the Hawking temperature are successfully obtained.

Analytic Solutions for the Motion of Spinning Particles near Spherically Symmetric Black Holes and Exotic Compact Objects

Analytic Solutions for the Motion of Spinning Particles near Spherically Symmetric Black Holes and Exotic Compact Objects

Love numbers and Love symmetries for p-form and gravitational perturbations of higher-dimensional spherically symmetric black holes

The static Love numbers of four-dimensional asymptotically flat, isolated, general-relativistic black holes are known to be identically vanishing. The Love symmetry proposal suggests that such vanishings are addressed by selection rules following from the emergence of an enhanced \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} (“Love”) symmetry in the near-zone region; more specifically, it is the fact that the black hole perturbations belong to a highest-weight representation of this near-zone \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} symmetry, rather than the existence of the Love symmetry itself, that outputs the vanishings of the corresponding Love numbers. In higher spacetime dimensions, some towers of magic zeroes with regards to the black hole response problem have also been reported for scalar, electromagnetic and gravitational perturbations of the Schwarzschild-Tangherlini black hole. Here, we extend these results by supplementing with p-form perturbations of the Schwarzschild-Tangherlini black hole. We furthermore analytically extract the static Love numbers and the leading order dissipation numbers associated with spin-0 scalar and spin-2 tensor-type tidal perturbations of the higher-dimensional Reissner-Nordström black hole. We find that Love symmetries exist and that the vanishings of the static Love numbers are captured by representation theory arguments even for these higher spin perturbations of the higher-dimensional spherically symmetric black holes of General Relativity. Interestingly, these near-zone \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} structures acquire extensions to Witt algebras. Our setup allows to also study the p-form response problem of a static spherically symmetric black hole in a generic theory of gravity. We perform explicit computations for some black holes in the presence of string-theoretic corrections and investigate under what geometric conditions Love symmetries emerge in the near-zone.

Quasinormal modes, and different aspects of Hawking radiation within the metric-affine bumblebee gravity framework

We consider a static and spherically symmetric black hole metric that emerges from the vacuum solution of the traceless metric-affine bumblebee model. Our study focuses on the possible implications of the modifications induced by the model on various astrophysical observables that include quasinormal modes, ringdown waveforms, Hawking radiation spectrum, sparsity of that radiation, and the lifetime of a black hole. We explore the impact of the Lorentz symmetry-breaking (LSB) parameter α on the quasinormal modes with the help of the 6th-order WKB method. Our inquisition reveals that the emission frequency and decay rate initially decreases with α and then grows up. As a result, the LSB becomes critically important for maintaining the stability of the system after being exposed to perturbation. The convergence of the WKB method for various orders is also studied here. We then analyze the Hawking temperature, radiation spectrum, and sparsity in this modified gravity framework that provides valuable insights into the thermal radiation emitted by black holes. It points out that the Hawking temperature, the peak of the power spectrum, and the total power emitted initially decreases and then increases with α. However, The variation of the sparsity with α follows a reverse trend. Finally, we obtain the analytical expression of the ‘lifetime’ of black holes and scrutinize the effect of α on it.

Dynamical de Sitter black holes in a quasi-stationary expansion

We revisit and improve the analytic study (Gregory et al 2018 Class. Quantum. Grav. 35 155008) of spherically symmetric but dynamical black holes in Einstein’s gravity coupled to a real scalar field. We introduce a series expansion in a small parameter ε that implements slow time dependence. At the leading order (LO), the generic solution is a quasi-stationary Schwarzschild–de Sitter (SdS) metric, i.e. one where time-dependence enters only through the mass and cosmological constant parameters of SdS. The two coupled ODEs describing the LO time dependence are solved up to quadrature for an arbitrary scalar potential. Higher order corrections can be consistently computed, as we show by explicitly solving the Einstein equations at the next to LO as well. We comment on how the quasi-stationary expansion we introduce here is equivalent to the non-relativistic 1/c expansion.

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

We study the optical properties of spacetime around a novel black hole (BH) in general relativity (GR) coupled to nonlinear electrodynamics (NED), which is asymptotically flat. First, we study the angular velocity and Lyapunov exponent in unstable photon circular orbits in the novel spherically symmetric BH spacetime. Later, we obtain the rotating BH solution using the Newmann-Janis algorithm and determine the event horizon properties of the BH. We analyze the effective potential for the circular motion of photons in the spacetime of the novel rotating BH. Also, we analyze the photon sphere around the novel BH and its shadow using celestial coordinates. We obtain that an increase of the BH spin and charge as well as NED field nonlinearity parameters causes an increase in the distortion parameter of the BH shadow, while, the area of the shadow and its oblateness decrease. Moreover, we also obtain the constraint values for the BH charge and the non-linearity parameters using Event Horizon Telescope data from shadow sizes of super-massive BHs Sgr A* and M87*. Finally, the emission rate of BH evaporation through Hawking radiation is also studied.

Generic spherically symmetric thin-shell wormholes with equilibrium throat at the innermost photonsphere are unstable

In this research, we prove analytically that a generic spherically symmetric thin-shell wormhole (TSW) with its throat located at the innermost photonsphere of the bulk asymptotically flat black hole and supported by a generic surface barotropic perfect fluid is unstable against a radial linear perturbation. This is the generalization of the instability of the Schwarzschild TSW (STSW) with the throat’s radius located at a0=3M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0}=3M$$\\end{document} that was revealed by Poisson and Visser in their seminal work (Poisson and Visser in Phys Rev D 52, 7318, 1995). where they studied the mechanical stability of STSW. Our proof provides a link between the instability of the null circular geodesics on the innermost photonsphere of a generic static spherically symmetric asymptotically black hole and the TSW constructed in the same bulk with a0=rc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{0}=r_{c}$$\\end{document} where a0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ a_{0} $$\\end{document} and rc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{c}$$\\end{document} are the radius of the TSW and the innermost photonsphere, respectively. For asymptotically flat spherically symmetric black holes possessing more than one photonspheres, the number of the photonspheres is odd and at least one photonsphere is stable which implies the corresponding TSW with its throat identical with the stable photonsphere is also stable.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

Abstract We obtain an exact solution of spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter (PFDM). Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable, we analyse the thermodynamics of our black holes in the extended phase space. Owing to the background clouds of strings parameter ($a$) and the parameter endowed with PFDM ($\beta$), we analyse the Hawking temperature, entropy and specific heat. We also investigate the relationship between the photon sphere radius and the phase transition for the Letelier AdS black holes immersed in PFDM. Through the analysis, we find with a particular condition, there are non-monotonic behaviours between the photon sphere radius, the impact parameter, the PFDM parameter, temperature, and pressure. We can regard both the changes of photon sphere radius and impact parameter before and after phase transition as the order parameter; their critical exponents near the critical point are equal to the same value 1/2, just like ordinary thermal systems. These indicate that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

Observational redshift from general spherically symmetric black holes

In this work, we obtain an expression for the total observational frequency shift of photons emitted by massive geodesic particles circularly orbiting a black hole in a general spherically symmetric background. Our general relations are presented in terms of the metric components and their derivatives that characterize the black hole parameters. As a concrete example of this general relativistic approach, a special case is studied by applying the formalism to a nonsingular black hole conformally related to the Schwarzchild solution that possesses a length scale parameter l and an integer parameter N in addition to the black hole mass. Besides, we express the nonsingular black hole mass in terms of the observational redshift/blueshift. Finally, we investigate the effects of the free parameters of the conformal gravity theory on the observational frequency shift and compare results with those of the standard Schwarzschild black hole.

Observational appearance of the spherically symmetric black hole in PFDM

We investigate the observational appearance of spherically symmetric black holes in perfect fluid dark matter (PFDM), with the celestial sphere and an accretion disk being light sources. For the celestial sphere model, we show the variations in black holes’ appearance from different angles. And for an optically thin accretion disk, the intensity observed can be characterized by the redshift factor and the transfer functions. Then we investigate the angular dependencies for a resting and rotating accretion disk, respectively. It is found that as the observation angle increases, the blue-shift effect of black holes in rotating accretion disks becomes more pronounced. Our study may provide new insights into the physical characteristics of PFDM black holes and their surrounding environment.

Erratum — Static spherically symmetric black holes of Brans–Dicke theory of gravity

Erratum — Static spherically symmetric black holes of Brans–Dicke theory of gravity

ЭФФЕКТ САНЬЯКА В ПРОСТРАНСТВЕ-ВРЕМЕНИ ВРАЩАЮЩЕЙСЯ ЧЕРНОЙ ДЫРЫ В ЧЕТЫРЕХМЕРНОЙ ТЕОРИИ ЭЙНШТЕЙНА–ГАУССА–БОННЕ

Recently, Glavan and Lin proposed a new four-dimensional theory of Einstein-Gauss-Bonnet (EGB) gravity by rescaling the Gauss-Bonnet (GB) coupling constant ߙ→ ܦ(/ߙ− 4) and adopting the ܦ→ 4 constraint at the level of the equations of motion. The GB coupling constant contributes to the field equations and thus bypasses Lovelock's theorem. This theory preserves the number of degrees of freedom and avoids Ostrogradsky instability. Glavan and Lin obtained an exact solution for nonsingular static and spherically symmetric black holes in the four-dimensional EGB theory of gravity. Later, Kumar and Ghosh applied the Newman-Janis algorithm to the static solution and constructed a solution for a rotating black hole in the 4-dimensional EGB theory of gravity. Since the theory solves many observational problems in astrophysics and is promising for research, the influence of the GB coupling parameter on astrophysical effects is actively studied in the literature. However, this theory has not been tested previously using time effects. The work examines one of the most interesting time effects – the Sagnac effect. Thus, the goal of the work is to study the Sagnac effect in the space-time of a rotating black hole in the four-dimensional EGB theory and obtain a constraint on the GB coupling parameter using observational data of the Sagnac effect. In the most general case, the Sagnac effect is understood as the difference in the time it takes light beams moving in opposite directions to pass through a closed circle. The effect has many applications, is observable on Earth and is taken into account in satellite navigation systems (GPS, GLONASS) when synchronizing time signals.

Exact massive and massless scalar quasibound states solutions of the Einstein–Maxwell-dilaton (EMD) black hole

In this letter, we will focus on the Klein–Gordon equation with static spherically symmetric black hole solution of the Einstein–Maxwell-dilaton (EMD) theory as its 3+1 background space-time. The Klein–Gordon equation represents quasibound states of both massive and massless scalar fields which are localized in the black hole potential well. By using the covariant Klein–Gordon equation, we investigate the behaviour of both massive and massless scalars in the EMD black hole space-time. We successfully exactly solved the relativistic wave equation and are going to present the novel exact results in this letter. The exact solutions, the wave functions and the energy levels, describe the decaying nature of the relativistic scalar field bound in the curved space-time. The massive scalar quasibound state has complex-valued energy levels where the real part is the massive scalar’s energy while the imaginary part represents the decay. For the massless scalar quasibound state, pure imaginary energy levels are discovered. In this letter, by using the obtained exact scalar particle’s wave functions, we also consider the Hawking radiation of the apparent horizon of the EMD black hole that is calculated via Damour–Ruffini method. In principle, the investigation of black hole quasibound states could provide possibility for laboratory testing of effects whose nature are absolutely related with quantum effects in gravity.

Solutions with a Flat Horizon in D Dimensions within the Cubic Form of f(Q) Gravity

Given the AdS/CFT relationship, the study of higher-dimensional AdS black holes is extremely important. Furthermore, since the restriction derived from f(Q)’s field equations prevents it from deriving spherically symmetric black hole solutions, the result is either Q′=0 or fQQ=0. Utilizing the cylindrical coordinate system within the context the cubic form of f(Q) theory while imposing the condition of a coincident gauge, we establish the existence of static solutions in D-dimensions. The power-law ansatz, which is the most practical based on observations, will be used in this study, where f(Q)=Q+12γQ2+13γQ3−2Λ and the condition D≥4 are met. These solutions belong to a new solution class, the properties of which are derived only from the non-metricity Q modification, since they do not have a general relativity limit. We examine the singularities present in the solutions by calculating the non-metricity and curvature invariant values. In conclusion, we compute thermodynamic parameters such as Gibbs free energy, Hawking temperature, and entropy. These thermodynamic calculations confirm that our model is stable.

Black hole shadows in Einstein-Bel-Robinson gravity* *Supported by the Internal Project (2023/2211) of Excellent Research of the Faculty of Science of Hradec Králové University

Gravity models given by higher-order scalar curvature corrections are believed to bear important consequences. Einstein-Bel-Robinson (EBR) gravity with quartic curvature modification motivated Sajadi et al. to explore static spherically symmetric black hole solutions using perturbative methods. In this study, inspired by their work, we investigate AdS black hole shadows in EBR gravity and demonstrate how the gravity parameter alters the energy emission rate. Finally, we address the same problem in the presence of plasma, because the black holes are thought to be surrounded by a medium that changes the geodesic of photons.

Modeling the black holes surrounded by a dark matter halo in the galactic center of M87

In this paper, the structure of a dark matter halo can be well described by the mass model of M87 and the Einasto profile for the cold dark matter model, i.e., ρeina(r)=ρeexp(-2α-1((r/re)α-1))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho _{\ ext {eina}} (r)=\\rho _\ ext {e} \\exp ( -2 \\alpha ^{-1} ((r/r_\ ext {e})^\\alpha -1 ) )$$\\end{document}(Wang et al. in Nature 585:39–42, 2020). Under these conditions, we construct a solution of a static spherically symmetric black hole in a dark matter halo. Then, using the Newman–Janis algorithm, we extend this static solution to the case of rotation, and obtain a solution for the Kerr-like black hole. We prove that this solution of the Kerr-like black hole is indeed a solution to the Einstein field equations. Finally, taking M87 as an example, we study and analyze some physical properties of this Kerr-like black hole, and then compare them with the Kerr black hole. Particularly, from the perspective of the black hole shadow and the fact that the Kerr-like black hole and the Kerr black hole is distinguishable, we give the upper limit of the shape parameter of the Einasto density profile, that is approximately α<0.22\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha <0.22$$\\end{document}, which may provide a new method to further improve and perfect the density profile of dark matter model. These research results for the black hole in a dark matter halo may indirectly provide an effective method for detecting the existence of dark matter.

Geometrically thick equilibrium tori around a dyonic black hole with quasi-topological electromagnetism

We study geometrically thick and non-self gravitating equilibrium tori orbiting a static spherically symmetric dyonic black hole with quasi-topological electromagnetism. Our results show that the electric and magnetic charges together with the coupling parameter in the quasi-topological electromagnetism lead to a much richer class of equilibrium tori. There are a range of parameters which allow for the existence of double tori. The properties of double equilibrium tori become far richer. There exist transitions between single torus and double tori solutions as we change the specific angular momentum of the fluid. These properties of equilibrium tori could help to understand the dyonic black hole and its thick accretion disk.

Kaluza-Klein monopole with scalar hair

We construct a new family of rotating black holes with scalar hair and a regular horizon of spherical topology, within five dimensional (d = 5) Einstein’s gravity minimally coupled to a complex, massive scalar field doublet. These solutions represent generalizations of the Kaluza-Klein monopole found by Gross, Perry and Sorkin, with a twisted S1 bundle over a four dimensional Minkowski spacetime being approached in the far field. The black holes are described by their mass, angular momentum, tension and a conserved Noether charge measuring the hairiness of the configurations. They are supported by rotation and have no static limit, while for vanishing horizon size, they reduce to boson stars. When performing a Kaluza-Klein reduction, the d = 5 solutions yield a family of d = 4 spherically symmetric dyonic black holes with gauged scalar hair. This provides a link between two seemingly unrelated mechanisms to endow a black hole with scalar hair: the d = 5 synchronization condition between the scalar field frequency and the event horizon angular velocity results in the d = 4 resonance condition between the scalar field frequency and the electrostatic chemical potential.