Scalar Hair Research Articles

Quasistationary hair for binary black hole initial data in scalar Gauss-Bonnet gravity

Recent efforts to numerically simulate compact objects in alternative theories of gravity have largely focused on the time-evolution equations. Another critical aspect is the construction of constraint-satisfying initial data with precise control over the properties of the systems under consideration. Here, we augment the extended conformal thin sandwich framework to construct quasistationary initial data for black hole systems in scalar Gauss-Bonnet theory and numerically implement it in the open-source p code. Despite the resulting elliptic system being singular at black hole horizons, we demonstrate how to construct numerical solutions that extend smoothly across the horizon. We obtain quasistationary scalar hair configurations in the test-field limit for black holes with linear/angular momentum as well as for black hole binaries. For isolated black holes, we explicitly show that the scalar profile obtained is stationary by evolving the system in time and compare against previous formulations of scalar Gauss-Bonnet initial data. In the case of the binary, we find that the scalar hair near the black holes can be markedly altered by the presence of the other black hole. The initial data constructed here enable targeted simulations in scalar Gauss-Bonnet simulations with reduced initial transients. Published by the American Physical Society 2025

Topological classification of critical points for hairy black holes in Lovelock gravity

In various fields of mathematical research, the Brouwer degree is a potent tool for topological analysis. By using the Brouwer degree defined in one-dimensional space, we interpret the equation of state for temperature in black hole thermodynamics, T=T(V,xi), as a spinodal curve, with its derivative defining a new function f. The sign of the slope of f indicates the topological charge of the black hole’s critical points, and the total topological charge can be deduced from the asymptotic behavior of the function f. We analyze a spherical hairy black hole within the framework of Lovelock gravity, paying particular attention to the topological structure of black hole thermodynamics under Gauss–Bonnet gravity. Here, the sign of the scalar hair parameter influences the topological classification of uncharged black holes. When exploring the thermodynamic topological properties of hairy black holes under cubic Lovelock gravity, we find that the spherical hairy black hole reproduces the thermodynamic topological classification results seen under Gauss–Bonnet gravity.

Thermodynamics of black holes featuring primary scalar hair

In this work, we embark on the thermodynamic investigation concerning a family of primary charged black holes within the context of shift and parity symmetric Beyond Horndeski gravity. Employing the Euclidean approach, we derive the functional expression for the free energy and derive the first thermodynamic law, offering a methodology to address the challenge of extracting the thermal quantities in shift-symmetric scalar tensor theories characterized by linear time dependence in the scalar field. Following the formal analysis, we provide some illustrative examples focusing on the thermal evaporation of these objects. Published by the American Physical Society 2024

From low- to high-frequency QPOs around the non-rotating hairy Horndeski black hole: Microquasar GRS 1915+105

Research on the Horndeski black hole, associated with the scalar hairy parameter, offers insights into enigmatic cosmic phenomena such as dark matter. Additionally, the numerical study of the GRS 1915+105 source, which exhibits continuous variability in X-ray observations, along with its physical properties and mechanisms behind Quasi-periodic oscillations (QPOs) frequencies, can contribute to observational studies. Motivated by this, we examine the variations in physical mechanisms around the non-rotating Horndeski black hole with Bondi-Hoyle-Lyttleton (BHL) accretion related to the scalar hair parameter and the resulting QPO frequencies. Numerical simulations have shown the formation of a shock cone around the black hole. With a decrease in the scalar hair parameter, the shock cone opening angle narrows due to the influence of the scalar field potential, and the stagnation point within the cone moves closer to the black hole horizon. With the changing scalar hair parameter, the simultaneous formation of the shock cone and bow shock is observed. Due to the intense increase in scalar potential, both the shock cone and bow shock disappeared, and a cavity surrounding the black hole forms in the area where the shock cone was. Additionally, QPO oscillations induced by the physical mechanisms observed in relation to the hair parameter are revealed through numerical simulations. A broad range of QPO frequencies is observed, from low to high frequencies, with resonance states like 3:2 occurring. The QPO frequencies determined numerically are compared with the observational results of the GRS 1915+105 source, demonstrating a match between the observations and numerical findings. From this, it is concluded that the shock cone, bow shock, and cavity are suitable physical mechanisms for generating QPOs for the GRS 1915+105 source. Lastly, we define the potential range of the spin parameter for the GRS 1915+105 source based on the agreement between observational and numerical results. It has also been found that for most of the QPOs obtained from numerical calculations to be consistent with observations, h/M should be greater than −0.5.

Geometric Analysis of Black Hole with Primary Scalar Hair

Within the novel context of primary scalar hair black holes, this article explores the fascinating subject of black hole thermal stability. Thermodynamic stability is the main subject of our investigation, which involves measuring the bound points, divergence points, black hole mass, thermal temperature, and specific heat capacity. In addition, we determine the scalar curvatures of thermodynamic geometries like Ruppeiner, Weinhold, Hendi-Panahiyah-Eslam-Momennia, and geometrothermodynamics formulations inside the framework of primary scalar hair black holes and delve into their complexities. Improving our knowledge of fundamental scalar hair black holes, this study sheds light on the intricate thermal geometric properties of these objects.

Nonlinear studies of modifications to general relativity: Comparing different approaches

Studying the dynamical, nonlinear regime of modified theories of gravity remains a theoretical challenge that limits our ability to test general relativity. Here we consider two generally applicable, but approximate, methods for treating modifications to full general relativity that have been used to study binary black hole mergers and other phenomena in this regime, and compare solutions obtained by them to those from solving the full equations of motion. The first method evolves corrections to general relativity order by order in a perturbative expansion, while the second method introduces extra dynamical fields in such a way that strong hyperbolicity is recovered. We use shift-symmetric Einstein-scalar-Gauss-Bonnet gravity as a benchmark theory to illustrate the differences between these methods for several spacetimes of physical interest. We study the formation of scalar hair about initially nonspinning black holes, the collision of black holes with scalar charge, and the inspiral and merger of binary black holes. By directly comparing predictions, we assess the extent to which those from the approximate treatments can be meaningfully confronted with gravitational wave observations. We find that the order-by-order approach cannot faithfully track the solutions when the corrections to general relativity are non-negligible. The second approach, however, can provide consistent solutions, provided the timescale over which the dynamical fields are driven to their target values is made short compared to the physical timescales. Published by the American Physical Society 2024

Nonminimal coupling holographic superconductors

We explore a holographic superconductor model in which a real scalar field is nonminimally coupled to a gauge field. We consider several types of the nonminimal coupling function h(ψ) including exponential, hyperbolic (cosh), power-law, and fractional forms. We investigate the influences of the nonminimal coupling parameter α on condensation, critical temperature, and conductivity. We can categorize our results in two groups. In the first group, conductor/superconductor phase transition is easier to occur for larger values of α, while in the second group stronger effects of the nonminimal coupling makes the formation of scalar hair harder. Although the real and imaginary parts of conductivity are impressed by different forms of h(ψ), they follow some universal behaviors such as connecting with each other through Kramers–Kronig relation in ω → 0 limit or the appearance of gap frequency at low temperatures around ωg ∼ 8 Tc, which shifts to larger values by increasing the strength of α. Among all forms of h(ψ) we observe that h(ψ) = 1 + αψ2 gives us better information in wide range of nonminimal coupling constant and temperature. Choosing the best form of h(ψ), we construct a family of solutions for holographic conductor/superconductor phase transitions to discover the effect of the hyperscaling violation when the gauge and scalar fields are nonminimally coupled. we find that the critical temperature increases for higher effects of hyperscaling violation θ and nonminimal coupling constant α. By increasing these two parameters, we obtain lower values of condensation which means that conductor/superconductor phase transition will acquire easier. Furthermore, we understand that the hyperscaling violation affects the conductivity σ of the holographic superconductors and changes the expected relation in the gap frequency. Some universal behaviors like infinite DC conductivity are observed. In addition, we consider a five-dimensional Gauss–Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant, λ, or smaller values of nonminimal coupling constant, α, which means that the condensation is harder to form. Moreover, we study the electrical conductivity in the holographic setup. We observe that the gap frequency shifts to larger values for stronger λ, and becomes flat by increasing α.

Extended holographic Rényi entropy and hyperbolic black hole with scalar hair

Extended holographic Rényi entropy and hyperbolic black hole with scalar hair

Stability of charged scalar hair on Reissner–Nordström black holes

Stability of charged scalar hair on Reissner–Nordström black holes

Orbital motion, epicyclic oscillations, and collision of particles around conformally coupled charged black hole

The orbital and oscillatory motion of test particles around a non-rotating, conformally coupled charged black hole with scalar hair is studied in this work. The impact of the black hole parameters on particle motion is investigated. The stable circular orbits, specific angular momentum, and radial profiles with specific energy are computed using an analytical approach. We discuss the stability of circular orbits using the effective potential technique. We also compute the effective force and innermost stable circular orbits around a conformally connected charged black hole with scalar hair. In addition, we display the trajectories of particles around a conformally connected charged black hole with scalar hair and numerically integrate the equations of motion for the test particle. Additionally, we determine the formulae for the frequencies of latitudinal and radial harmonic oscillations about the mass of the black hole and the model’s parameters. The main characteristics of quasi-periodic oscillations close to stable circular orbits in the black hole’s equatorial plane are examined for test particles. Furthermore, the Periastron precession process is explored. We show particle motion around black holes strongly depends on the model parameters. It is important to note that the graphical behavior describing our findings is viable.

Bondi-Hoyle-Lyttleton accretion around the rotating hairy Horndeski black hole

Modeling of the shock cone formed around a stationary, hairy Horndeski black hole with Bondi-Hoyle-Lyttleton (BHL) accretion has been conducted. We model the dynamical changes of the shock cone resulting from the interaction of matter with the Horndeski black hole, where the scalar field and spacetime have a strong interaction. The effects of the scalar hair, the black hole rotation parameter, and the impacts of the asymptotic speed have been examined, revealing the influence of these parameters on the shock cone and the trapped QPO modes within the cone. Numerical calculations have shown that the hair parameter significantly affects the formation of the shock cone. As the absolute value of the hair parameter increases, the matter in the region of the shock cone is observed to move away from the black hole horizon. The rate of matter expulsion increases as h/M changes. After h/M < -0.6, a visible change in the physical structure of the shock cone occurs, ultimately leading to the complete removal out of the shock cone. On the other hand, it has been revealed that the asymptotic speed significantly affects the formation of the shock cone. As h/M increases in the negative direction and the asymptotic speed increases, the stagnation point moves closer to the black hole horizon. When the value of the hair parameter changes, the rest-mass density of the matter inside the cone decreases, whereas the opposite is observed with the asymptotic speed. Additionally, the formed shock cone has excited QPO modes. The deformation of the cone due to the hair parameter has led to a change or complete disappearance of the QPOs. Meanwhile, at asymptotic speeds of V ∞/c < 0.4, all fundamental frequency modes are formed, while at V ∞/c = 0.4, only the azimuthal mode is excited, and 1:2:3:4:… resonance conditions occur. No QPOs have formed at V ∞/c = 0.6. The results obtained from numerical calculations have been compared with theoretical studies for M87*, and it has been observed that the possible values of h/M found in the numerical simulations are consistent with the theory. Additionally, the results have been compared with those for the GRS 1915+105 black hole, and the hair parameters corresponding to the observed frequencies have been determined.

A thermodynamic study of (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf {(2+1)}}$$\\end{document}-dimensional analytic charged hairy black holes with Born–Infeld electrodynamics

This work presents analytical black hole solutions for a coupled Einstein–Born–Infeld–Scalar gravity system in AdS spacetime with two different non-minimal coupling functions f(z). For both solutions, we establish the regularity of the scalar field and curvature scalars outside the horizon. For one of the considered coupling cases, thermodynamic analysis in the canonical ensemble reveals stability across all temperatures, while the other case exhibits the Hawking/Page phase transition between the stable large phase of the black hole and thermal-AdS. We investigate the effect of the scalar hair parameter and black hole charge on the phase transition temperature and observe that the critical values of the scalar hair and the charge parameters constrain the feasibility of Hawking/Page phase transition.

New look at AdS black holes with conformal scalar hair

New look at AdS black holes with conformal scalar hair

Reissner-Nordström dyonic black holes with gauged scalar hair

For gauged scalar fields minimally coupled to Einstein-Maxwell theory, the Mayo-Bekenstein no-hair theorem can be circumvented when including appropriate scalar self-interactions, allowing static, electrically charged black holes to be endowed with (Abelian) gauged scalar hair. Here we show these spherically symmetric solutions can be extended to include a magnetic charge in a model with scalar multiplets. The resulting dyonic configurations share most of the properties of the electrically charged solutions, in particular satisfying the same resonance condition, with the existence of a mass gap with respect to the bald Reissner-Nordström dyonic black holes. A distinctive feature, however, is that no solitonic limit exists for a non-zero magnetic charge.

Stability of lower dimensional counter-rotating thin-shell wormholes with scalar hair

The motivation for constructing a thin-shell wormhole from a (2+1)-dimensional rotating black hole arises from the desire to study the effects of a nonminimally coupled scalar field in this particular spacetime. By investigating the behavior of such a field in the presence of rotation, we can gain insights into the interplay between gravity and scalar fields in lower-dimensional systems. Additionally, this construction allows us to explore potential connections between black hole physics and exotic phenomena like traversable wormholes. The radial perturbation around the equilibrium throat radius is considered to explore the stable configuration for specific values of physical parameters. Then, the equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter is used to conduct an extensive investigation into the stability of the counter-rotating thin-shell wormholes. Our results show that the presence of a scalar field enhances the stability of the counter-rotating thin-shell wormholes.

Timelike bound orbits and pericenter precession around black hole with conformally coupled scalar hair

We investigate the geodesic motions of timelike particles around a static hairy black hole with conformally coupled scalar field. We mainly focus on the effects of the scalar charge and electric charge on the marginally bound orbits (MBO), innermost stable circular orbits (ISCO) and on the precessing orbits around this black hole. Our results show that both the scalar and electric charges suppress the energy as well as the angular momentum of the particles in the bound orbits. Then, we study the relativistic periastron precessions of the particles and constrain the charge parameters by employing the observational result of the S2 star’s precession in SgrA*. It is found that the constraints on the charge parameters from S2 star’s motion are tighter than those from black hole shadow. Finally, we analyze the periodic motions of the particles and figure out samples of periodic orbits’ configurations around the hairy black hole.

Thermodynamic analysis of Magnetically charged Euler–Heisenberg black holes with scalar hair via Renyi-entropy using logarithmic correction

In this article, we investigate the thermodynamic properties of the Euler–Heisenberg black hole solution with magnetic charge and scalar hair. We also examine the evaluation of thermal fluctuations, Gibbs free energy, and energy emission. The Hawking temperature, geometric mass, and heat capacity are among the numerous factors that are computed to evaluate local and global thermodynamic stability. The first law of thermodynamics is applied to determine the temperature of the black hole, and the energy emission rate is also calculated. We investigate the phase transition behavior of the Euler–Heisenberg black hole with scalar hair by computing the Gibbs free energy, with particular attention to characteristics like eating tails. We also obtain the corrected entropy to investigate the impact of thermal fluctuations on massive and small black holes. Notably, we contrast the outcomes for large and small black holes in order to examine the effects of correction terms on the thermodynamic system.

Superradiant instability of a charged regular black hole

We show that a charged, massive scalar field in the vicinity of an electrically charged Ayón-Beato–García (ABG) regular black hole has a spectrum of quasibound states that (in a certain parameter regime) grow exponentially with time, due to black hole superradiance. Superradiant quasibound states are made possible by the enhancement of the electrostatic potential at the horizon in nonlinear electrodynamics; in contrast, the Reissner-Nordström black hole does not appear to possess such superradiant quasibound states. Here we compute the spectrum for a range of multipoles ℓ across the parameter space, and we find the fastest growth rate in the monopole mode. We find that a regular black hole with a small charge can still trigger a significant superradiant instability if the charge-to-mass ratio of the field is compensatingly large. We estimate the amount of black hole mass that can be deposited in the scalar field, finding an upper bound of circa 20% in the extreme charge scenario. Finally, we consider the stationary bound states at the superradiant threshold, and we conjecture that, due to this instability, the ABG black hole will evolve toward a configuration with charged scalar hair. Published by the American Physical Society 2024

Holographic supersymmetric Rényi entropies from hyperbolic black holes with scalar hair

We study holographic supersymmetric Rényi entropies from a family of hyperbolic black holes in an Einstein-Maxwell-dilaton (EMD) system under the BPS condition. We calculate the thermodynamic quantities of these hyperbolic black holes. We find a remarkably simple formula of the supersymmetric Rényi entropy that unifies (interpolates) 11 cases embeddable to 10 or 11 dimensional supergravity. It reproduces many known results in the literature, and gives new results with distinctive features. We show that the supersymmetric version of the modular entropy and the capacity of entanglement cannot be mapped to thermal quantities, due to the dependence of the temperature and the chemical potential by the BPS condition. We also calculate the entanglement spectrum. We derive the potential of the EMD system from a V = 0 solution and obtain two neutral solutions with scalar hair as a byproduct.

Motion of particles around a magnetically charged Euler–Heisenberg black hole with scalar hair and the Event Horizon Telescope

We study the motion of uncharged particles and photons in the background of a magnetically charged Euler–Heisenberg (EH) black hole (BH) with scalar hair. The spacetime can be asymptotically (A)dS or flat. After investigating particle motions around the BH and the behavior of the effective potential of the particle radial motion, we determine the contribution of the BH parameters to the geodesics. Photons follow null geodesics of an effective geometry induced by the corrections of the EH non-linear electrodynamics. Thus, after determining the effective geometry, we calculate the shadow of the BH. We also analyze in detail the case of extremal BH spacetimes and we find that the radius of both the event horizon and shadow exhibits discontinuities when varying with respect to either the magnetic charge or the scalar charge. These extremal scenarios exist for sufficiently small values of the EH parameter, and imply the formation of a second photon ring around the BH shadow. Upon comparing the theoretically calculated BH shadow to the images of the shadows of M87* and Sgr A* observed by the Event Horizon Telescope collaboration, we impose constraints on the BH parameters, namely the scalar hair (ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u $$\\end{document}), the magnetic charge (Qm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_{m}$$\\end{document}) and the EH 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}). For sufficiently large values of the EH parameter, our model is in agreement with the EHT observations for approximately every value for the BH magnetic charge.