Symmetric Black Hole Solutions Research Articles

Electrically charged black holes in [formula omitted]-Euler–Heisenberg theory

Drawing on the concept of the non-linear dynamics of electromagnetic fields in vacuum in terms of the Euler–Heisenberg system, a static and spherically symmetric black hole solution is derived by coupling the Euler–Heisenberg term and F(R) gravity. In applying the curvature singularity tools, the black hole solution induces a singular behaviour at the centre r=0 while exhibiting a regular shape at high distances. Using the heat capacity (CQ) and the Helmholtz free energy (F), we analyse the thermodynamic stability locally and globally. Furthermore, an investigation is conducted using class tools of Geometrothermodynamics (GTs) features such as Weinhold, Ruppeiner, Hendi–Panahiyan–Eslam–Momennia (HPEM), and Quevedo to identify phase transition points associated with heat capacity, including both physical boundary points (root of the heat capacity) and second critical phase transition points (divergent points of the heat capacity). We have even examined the relevant sparsity of Hawking radiation, showing how the black hole solution behaves as a black body at specific limits. Overall, this study enhances our knowledge of the mergers of a class of non-linear dynamics of electromagnetic fields in a vacuum within F(R) gravity by modelling black hole solutions.

Scrutinizing black hole stability in cubic vector Galileon theories

In a subclass of generalized Proca theories where a cubic vector Galileon term breaks the U(1) gauge invariance, it is known that there are static and spherically symmetric black hole (BH) solutions endowed with nonvanishing temporal and longitudinal vector components. Such hairy BHs are present for a vanishing vector-field mass (m=0) with a non-zero cubic Galileon coupling β 3. We study the linear stability of those hairy BHs by considering even-parity perturbations in the eikonal limit. In the angular direction, we show that one of the three dynamical perturbations has a nontrivial squared propagation speed c Ω,1 2, while the other two dynamical modes are luminal.We could detect two different unstable behaviors of perturbations in all the parameter spaces of hairy asymptotically flat BH solutions we searched for. In the first case, an angular Laplacian instability on the horizon is induced by negative c Ω,1 2. For the second case, it is possible to avoid this horizon instability, but in such cases, the positivity of c Ω,1 2 is violated at large distances. Hence these hairy BHs are generally prone to Laplacian instabilities along the angular direction in some regions outside the horizon. Moreover, we also encounter a pathological behavior of the radial propagation speeds c r possessing two different values of c r 2 for one of the dynamical perturbations. Introducing the vector-field mass m to cubic vector Galileons, however, we show that the resulting no-hair Schwarzschild BH solution satisfies all the linear stability conditions in the small-scale limit, with luminal propagation speeds of three dynamical even-parity perturbations.

Quasinormal modes of the Mannheim–Kazanas black holes

Abstract A spherically symmetric black hole solution in the conformal Weyl gravity was found by Mannheim and Kazanas in 1988. While the quasinormal modes (QNMs) of these black holes have been considered in a few works, here we complement these studies by considering in detail the regime of vanishing cosmological constant and negative values of the Weyl parameter for which we find quasinormal frequencies for scalar, Dirac and electromagnetic perturbations with the time-domain integration and WKB methods. In particular, we derive the compact and remarkably accurate analytic formula for the frequencies in the form of expansion in terms of the inverse multipole number. Comparison with the time-domain integration shows that the 6th order WKB method with the Padé approximants is quite accurate, unless the black hole is in the near extreme state.

Holographic Einstein rings of a black hole with a global monopole

The global monopole solutions which give rise to quite unusual physical phenomena have captured considerable attention. In this paper, we study the Einstein ring of the spherically symmetric AdS black hole solution with a global monopole based on the AdS/CFT correspondence. With the help of the given response function of the QFT on the boundary, we construct the holographic images of the black hole in the bulk. Our results exhibit the absolute amplitude of total response function |⟨O⟩|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\langle \\mathcal {O}\\rangle |$$\\end{document} increases with the decrease of the monopole parameter b and the temperature T. And the frequency ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} of the Gaussian source will also increase the absolute amplitude. These parameters also affects the Einstein ring. With the change of the observation position, this ring will change from the concentric stripe to a luminosity-deformed ring, or light points. And the monopole parameter has an effect on the brightness and the position of Einstein ring. All these results imply that the holographic images can be used as an effective tool to distinguish different types of black holes for fixed wave source and optical system. These theoretical proposal opens a door to gravitational phenomena on strongly correlated material. Therefore, the holographic Einstein ring is of great theoretical and experimental significance for our research. In theory, it provides us a new way to find a necessary condition for the existence of the dual black hole. And experimentally speaking, if we can realize suitable targets for observing AdS black holes successfully, we would be able to observe Einstein rings by tabletop experiments when we apply localized sources on such materials and measure their responses.

Linear stability of vector Horndeski black holes

Horndeski's vector-tensor (HVT) gravity is described bya Lagrangian in which the field strength fμν = ∂μAν-∂νAμ of a vector field Aμ interacts with a double dualRiemann tensor Lμναβ in the form βLμναβ Fμν Fαβ ,where β is a constant.In Einstein-Maxwell-HVT theory, there are static andspherically symmetric black hole (BH) solutions withelectric or magnetic charges, whose metric componentsare modified from those in the Reissner-Nordström geometry. The electric-magnetic duality of solutions is broken even at the background level by the nonvanishing coupling constant β.We compute a second-order action of BH perturbationscontaining both the odd- and even-parity modes andshow that there are four dynamical perturbationsarising from the gravitational and vector-field sectors.We derive all the linear stability conditions associatedwith the absence of ghosts and radial/angular Laplacianinstabilities for both the electric and magnetic BHs.These conditions exhibit the difference between theelectrically and magnetically charged casesby reflecting the breaking of electric-magnetic dualityat the level of perturbations.In particular, the four angular propagation speedsin the large-multipole limit are different from eachother for both the electric and magnetic BHs.This suggests the breaking of eikonal correspondencebetween the peak position of at least one of the potentials of dynamical perturbations and the radiusof photon sphere.For the electrically and magnetically charged cases,we elucidate parameter spaces of the HVT coupling and the BH charge in which the BHs without naked singularities arelinearly stable.

Quasinormal modes and greybody factor of a Lorentz-violating black hole

Recently, a static spherically symmetric black hole solution was found in gravity nonminimally coupled a background Kalb-Ramond field. The Lorentz symmetry is spontaneously broken when the Kalb-Ramond field has a nonvanishing vacuum expectation value. In this work, we focus on the quasinormal modes and greybody factor of this black hole. The master equations for the perturbed scalar field, electromagnetic field, and gravitational field can be written into a Schrödinger equation. We use three methods to solve the quasinormal frequencies in the frequency domain. The results agree well with each other. The time evolution of a Gaussian wave packet is studied. The quasinormal frequencies fitted from the time evolution data agree well with that of frequency domain. The greybody factor is calculated by Wentzel-Kramers-Brillouin (WKB) method. The effect of the Lorentz-violating parameter on the quasinormal modes and greybody factor are also studied.

Relativistic massive and massless scalar fields bound to the Bumblebee gravity's black hole

In this letter, we examine massive and massless scalar quasibound states bound in the static spherically symmetric black hole solution of the Einstein-Bumblebee space-time. We start with constructing the governing relativistic fields' dynamical equation, i.e. the Klein-Gordon equation, component by component. With the help of the ansatz of separation of variables, we find the exact solution of the angular part in terms of Spherical 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 reveals a complex-valued energy levels expression for the case of massive scalar, where the real part is the scalar particle's energy and the imaginary part represents the quasibound state's decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe decaying relativistic states bound in the black hole's gravitational potential well. At the end, we investigate the Hawking radiation of the static Bumblebee black hole's horizon by deriving and investigating the radiation distribution function.

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.

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.

Static black hole in minimal Horndeski gravity with Maxwell and Yang-Mills fields and some aspects of its thermodynamics

In this work we obtain a static spherically symmetric charged black hole solution in the framework of minimal Horndeski gravity with additional Maxwell and Yang-Mills fields. The obtained solution is examined; in particular, its asymptotics are studied. Thermodynamics of the black hole is investigated, namely, we use an effective surface gravity to derive black hole temperature. To obtain the first law of black hole thermodynamics, the Wald method is applied. We also use the extended thermodynamics approach, namely, it allows us to derive the Smarr relation, Gibbs free energy, and the thermal equation of state. The study of thermal values in the extended space shows rich phase behavior, in particular, the domain where the first-order phase transition takes place and the critical point with the second-order phase transition. We also study thermal behavior near the critical point, obtain critical exponents, and analyze the Ehrenfest equations at the critical point. Finally, we calculate the Prigogine-Defay ratio confirming the conclusion about the second-order phase transition at the critical point. Published by the American Physical Society 2024

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.

Exact scalar quasibound states solutions of f(R) theory's static spherically symmetric black hole

Following the recent developments in black holes' quasibound states exact solutions by Senjaya (2023b,c), in this letter, we present a novel exact solution of quasibound states of a scalar around a static spherically symmetric black hole solution of f(R) theory of gravity. We start with the relativistic scalar field wave equation, i.e. the Klein-Gordon equation, isolating the radial equation and finally successfully obtain the exact radial wave solutions in terms of General Heun functions. Having the exact solutions in hand, the energy levels expression is obtained from the radial wave polynomial conditions. In the last part of this letter, the Hawking radiation is investigated via the Damour-Ruffini method and the Hawking temperature is obtained from radiation distribution function.

Analytical quasibound states of black holes emerging from modified theories of gravity

The Rayleigh–Schrodinger method or more commonly called time independent perturbation theory is a powerful method to solve a Hamiltonian system with a relatively small perturbation [W. Nolting, Theoretical Physics 7: Quantum Mechanics–Methods and Applications (Springer International, 2017); F. Schwabl, Quantum Mechanics, 4th edn. (Springer, 2007)]. In this work, we make use of the Rayleigh–Schrodinger method to formulate a general method to calculate quasibound states of static spherically symmetric black hole solutions arising from modified theories of gravity. We discover that the Schwarzschild-like term corresponds to the main Hamiltonian while the modified theory of gravity’s contribution of the spacetime metric corresponds to the perturbation terms. At the end, formula to calculate main Hamiltonian and perturbed Hamiltonian are discovered and presented.

Quasiperiodic Oscillations and Dynamics of Test Particles around Regular-Kiselev Black Holes

Testing gravity theories combining (massive and massless) scalar & electrodynamic fields become the most important issue in relativistic astrophysics using data from, black hole observations. In the present work, we first show a spherically symmetric black hole solution in general relativity coupling to generic-type nonlinear electrodynamics (NED) together with the quintessential field. We also obtain possible values for the parameters of the quintessential field and NED charge in the black hole environment for different values of degree of nonlinearity. Also, event horizon properties and scalar invariants of the black hole spacetime are studied. We investigate the equatorial motion of test particles around the regular-Kiselev black holes and study the combined effects of quintessential field and the NED charge of the black hole on particle angular momentum together with its energy at their circular orbits as well as their innermost circular stable orbits (ISCOs) and compared the obtained results with Reissner-Nordström black hole (RN BH) case. Moreover, we study particle oscillations along the orbits above than ISCO and applications to quasiperiodic oscillations (QPOs) where we obtain constrain values for the quintessential parameter and black hole mass charge parameters using observational QPO data from microquasars.

Gauss-Bonnet solution with a cloud of strings in de Sitter and anti-de Sitter space* *Supported by the National Natural Science Foundation of China (12275087) and the Fundamental Research Funds for the Central Universities.

In this study, we investigate exact spherically symmetric Gauss-Bonnet black hole solutions surrounded by a cloud of string fluid with the cosmological constant in dimensions. Both charged and uncharged cases are considered. We focus on the de Sitter solutions in the main text and provide the anti-de Sitter solutions in the appendix. We analyze the features of event horizons and thermodynamic properties of the black hole solutions. The mass, Hawking temperature, thermal stability, and phase transitions are discussed. Moreover, the equation of state and critical phenomena associated with these solutions are explored.

Noether Gauge Symmetry Approach Applying for the Non‐Minimally Coupled Gravity to the Maxwell Field

AbstractTaking the Noether gauge symmetry approach into account, spherically symmetric static black hole solutions of the non‐minimal gauge‐gravity Lagrangian of the model is found. At first, a system of differential equations for the general non‐minimal couplings of type is considered, and then, it is regarded as a particular non‐minimal model to find the exact black hole solution and analyze its symmetries. As the next step, the thermodynamical quantities of the black hole and its interesting behavior is calculated. Besides, thermal stability and examining the possibility of the van der Waals‐like phase transition is addressed.

Gravitationally decoupled non-Schwarzschild black holes and wormhole space–times

In this article, using gravitational decoupling by means of minimal geometric deformation approach, we obtain a new spherically symmetric and static black hole solution. To progress, we close the system by assuming that the average pressure of the theta -sector is vanishing. Also, we tackle the problem regarding how, for a given minimally deformed black hole solution, one can connect it to a wormhole space–time.

Charged solution with equal metric ansatz in Gauss–Bonnet theory coupled to scalar field

In this study, we apply the Gauss–Bonnet equation of motions coupled with the scalar field and potential and derive a new charged spherically symmetric black hole (BH) solution. In this study, we derive this BH using an equal metric potential, i.e., gtt=grr. Among many things, we succeed in determining the form of the scalar field, the function of the scalar, and the Gauss–Bonnet term. We investigate the physics of this BH solution and show that we have additional terms than the Riessner Nordström BH solution, i.e., O(1r6) and O(1r9). The existence of these additional terms is due to the contribution of the scalar field ξ. These additional terms are responsible for reproducing the multi-horizon BH solution. Due to the existence of these additional terms, the modified first law of thermodynamics and the corresponding Smarr relation are derived.

Black Hole Solutions with Dark Matter Halos in the Four‐Dimensional Einstein‐Gauss‐Bonnet Gravity

AbstractBlack holes (BHs) convey information about different matter‐energy distributions in their immediate environment, as they bear the imprints of the intrinsic spacetime geometry and exotic surrounding matter. In this regard, exact spherically symmetric regular black hole (BH) solutions supported by two phenomenological distributions of dark matter galactic halos in Eintein‐Gauss‐Bonnet gravity are explored. Analytical solutions for the metric and the corresponding thermodynamic properties, including heat capacity (), Gibbs' free energy (), and Hawking temperature () associated with the BH's horizon radius and quasinormal modes (QNMs) are found. The specific heat is investigated, and it is discovered that a Hawking‐Page phase transition with divergent occurred at a critical radius, . Consequently, the authors have regular BHs with Cauchy and event horizons, and evaporation results in thermodynamically stable double‐horizon BH remnants with zero temperatures. The QNMs of the scalar field perturbations on the regular background of the BHs are then discussed comprehensively.