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We investigate the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with a positive coupling parameter $\alpha$. This corresponds to exploring the onset of spontaneous scalarization for KN black holes. For this purpose, we use the hyperboloidal foliation method (HFM) to solve the linearized scalar equation numerically. We obtain a 3D graph [$\log_{10}\alpha(a,Q)$] which indicates the onset surface for spontaneous scalarization of KN black holes in the EMS theory. We find that there is no lower bound on the rotational parameter $a$, but its upper bound is given by $M^2-Q^2 \ge a^2$. Also, we confirm that the high rotation enhances spontaneous scalarization of KN black holes in the EMS theory., Comment: 21 pages, 6 figures, Version accepted for publication in PRD. arXiv admin note: text overlap with arXiv:2206.11587

In this paper, we consider the tachyonic instability of Kerr-Newman (KN) black holes in the Einstein-Maxwell-scalar (EMS) theory with nonminimal negative scalar coupling to Maxwell term, and then obtain a bound $(\frac{a}{r_+}\geq0.4142)$ for spin parameter $a$ of KN black hole in the limit of coupling constant $\alpha\rightarrow-\infty$ by using analytical method. In addition, we perform a $(2+1)$-dimensional time evolution of linearized scalar field perturbation on the KN black hole background by implementing the hyperboloidal foliation method numerically in the EMS theory. It recovers the \textit{spontaneous scalarization} phenomenon for KN black hole in some certain regions of the parameter spaces. We further plot corresponding threshold curves $\alpha(a)$ which describe a boundary between bald KN black holes and scalarized spinning black holes in the EMS theory., Comment: 23 pages, 6 figures

In this paper, the Joule–Thomson expansion of Born–Infeld AdS black holes in the consistent Aoki–Gorji–Mukohyama theory of 4D Einstein–Gauss–Bonnet gravity is studied in the extended phase space. We further analyze the effect of parameters [Formula: see text] and [Formula: see text] on the inversion curves and plot the inversion and isenthalpic curves in the [Formula: see text]–[Formula: see text] plane, which can determine the cooling–heating regions.

In this paper, the $P-V$ criticality and Joule-Thomson Expansion of Hayward-AdS black holes in 4D Einstein-Gauss-Bonnet gravity are studied in the extended phase space. We find the black hole always exhibits a phase transition similar to that of the Van der Waals system for any arbitrary positive parameters $\alpha$ and $g$. We also study the dependence of $\alpha$ and $g$ on the inversion curves and plot the inversion and isenthalpic curves in the $T-P$ plane, which can determine the cooling-heating regions., Comment: arXiv admin note: text overlap with arXiv:2009.03096

We perform the stability analysis on scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory by computing quasinormal mode spectrum. It is noted that the appearance of these black holes with scalar hair is closely related to the instability of Reissner-Nordstr\"om black holes without scalar hair in the EMS theory. The scalarized black hole solutions are classified by the node number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental branch and $n=1,2,\cdots$ denote the $n$ excited branches. Here, we show that the $n=1,2$ excited black holes are unstable against against the $s(l=0)$-mode scalar perturbation, while the $n=0$ fundamental black hole is stable against all scalar-vector-tensor perturbations. This is consistent with other scalarized black holes without charge found in the Einstein-Scalar-Gauss-Bonnet theory., Comment: 19 pages, 12 figures, version to appear in PLB

We perform the stability analysis of the Kerr black hole in the Einstein-Chern-Simons-Scalar theory with quadratic scalar coupling. For positive coupling parameter ($\alpha>0$), we introduce the (2+1)-dimensional hyperboloidal foliation method to show that the Kerr black hole is unstable against scalar-mode perturbation. In case of $\alpha, Comment: 12 pages, 3 figures

It is interesting to note that most black holes are born very slowly rotating. We investigate scalarization of slowly rotating black holes in the Einstein-scalar-Chern-Simons (EsCS) theory. In the slow rotation approximation, the CS term takes a linear form of rotation parameter $a$ which determines the tachyonic instability. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. It is shown that the slowly rotating black holes are unstable against a spherically symmetric scalar-mode perturbation for positive coupling $\alpha$, whereas these black holes are unstable for negative coupling without any $a$-bound., Comment: 12 pages, 3 figures

We study scalarization of slowly rotating black holes in the Einstein-scalar-Gauss-Bonnet (GB)-Chern-Simons (CS) theory. In the slow rotation approximation of $a\ll1$ with rotation parameter $a$, the GB term is given by a term for Schwarzschild black hole, whereas the CS term takes a linear term of $a$. The tachyonic instability for slowly rotating black holes represents the onset of spontaneous scalarization. We use the (2+1)-dimensional hyperboloidal foliation method to show the tachyonic instability for slowly rotating black holes by considering the time evolution of a spherically symmetric scalar mode. A threshold (existence) curve is obtained from the constant scalar modes under time evolution, which means the boundary between stable and unstable black holes. It is found that the slowly rotating black holes turn out to be unstable against a spherically symmetric scalar-mode propagation for positive coupling $\alpha$. However, we could not find tachyonic instability and any $a$-bound for scalarization for negative coupling $\alpha$., Comment: 16 pages, 4 figures. version to appear in PRD

We perform the stability analysis for the scalarized charged black holes obtained from Einstein-Maxwell-conformally coupled scalar (EMCS) theory by employing the radial perturbations. The targeting black holes include a single branch of scalarized charged black hole with the coupling parameter $\alpha>0$ inspired by the constant scalar hairy black hole as well as infinite branches of $n=0(\alpha \ge 8.019),1(\alpha \ge 40.84),2(\alpha \ge 99.89),\cdots$ scalarized charged black holes found through the spontaneous scalarization on the Reissner-Nordstr\"om black hole. It turns out that the black hole in the single branch and the $n = 0$ black hole are stable against radial perturbations, while the $n = 1, 2$ excited black holes are unstable in the EMCS theory with both quadratic and exponential couplings., Comment: 1+25 pages, 11 figures, stablity analysis corrected, version to appear in PRD

We discuss the P−V criticality and phase transition in the extended phase space of anti-de Sitter(AdS) black holes in four-dimensional Rastall theory and recover the Van der Waals (VdW) analogy of small/large black hole (SBH/LBH) phase transition when the parameters ωs and ψ satisfy some certain conditions. Later, we further explore the quasinormal modes (QNMs) of massless scalar perturbations to probe the SBH/LBH phase transition. It is found that it can be detected near the critical point, where the slopes of the QNM frequencies change drastically in small and large black holes.

We obtain a newly charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole solution from the Einstein-Weyl-Maxwell-conformal (conformally coupled) scalar theory with a positive Weyl coupling parameter $m^2_2$ numerically. This solution has a primary scalar hair, compared to a secondary scalar hair in the charged BBMB black hole solution. The limiting case of $m_2^2\to\infty$ leads to the series form of the charged BBMB black hole solution. However, for $m^2_2, 1+14 pages, 3 figures, version to appear in PRD

We investigate the Einstein-Maxwell-scalar theory with a quasi-topological term. Considering exponential couplings to Maxwell term, quasi-topological term, and both terms, we obtain three sets of infinite scalarized charged black holes by taking into account tachyonic instability of dyonic Reissner-Nordstr\"{o}m black hole. Each set of infinite scalarized charged black holes is classified by the number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental black hole and $n=1,2,\cdots$ denote the $n$-excited black holes. All $n=0$ black holes are stable against the radial perturbation, while all $n=1,2$ black holes are unstable., Comment: 20 pages, 11 Figures, version to appear in PRD. arXiv admin note: text overlap with arXiv:2009.05193

In four-dimensional Einstein-Gauss-Bonnet (EGB) gravity, we consider the thermodynamic and phase transitions of (charged) AdS black holes. For the negative GB coefficient , the system allows two physical critical points, corresponding to the reentrant phase transition, when the charge . For arbitrary , the system always leads to a van der Waals phase transition. We then study the quasinormal modes (QNMs) of massless scalar perturbations to probe the van der Waals-like phase transition between small and large black holes (SBH/LBH) for (charged) AdS black holes. We find that the signature of this SBH/LBH phase transition in the isobaric process can be detected since the slopes of the QNM frequencies change dramatically in small and large black holes near the critical point. The obtained results further support that QNMs can be a dynamic probe of thermodynamic properties in black holes.

We analyze the stability of scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory with quadratic coupling. These black holes are labelled by the number of $n=0,1,2,\cdots$, where $n=0$ is called the fundamental black hole and $n=1,2,\cdots$ denote the $n$-excited black holes. We show that the $n=0$ black hole is stable against full perturbations, whereas the $n=1,2$ excited black holes are unstable against the $s(l=0)$-mode scalar perturbation. This is consistent with the EMS theory with exponential coupling, but it contrasts to the $n=0$ scalarized black hole in the Einstein-Gauss-Bonnet-Scalar theory with quadratic coupling. This implies that the endpoint of unstable Reissner-Nordstr\"{o}m black holes with $\alpha>8.019$ is the $n=0$ black hole with the same $q$. Furthermore, we study the scalarized charged black holes in the EMS theory with scalar mass $m^2_\phi=\alpha/\beta$., Comment: 23 pages, 11 figures. arXiv admin note: text overlap with arXiv:1812.03604

We investigate the black holes in the new massive conformal gravity which is not invariant under conformal transformations because of the presence of the Einstein-Hilbert term. First, we show that the small Schwarzschild black hole is unstable against the $s$-mode of linearized Ricci tensor by solving the Lichnerowicz-Ricci tensor equation. This instability induces the appearance of the non-BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole that has both Ricci tensor and conformal scalar hair., 17 pages, 3 figures, title changed, version to appear in PRD

We construct charged asymptotically flat black hole solutions in Einstein-Maxwell-Weyl(EMW) gravity. These solutions can be interpreted as generalizations of two different groups: Schwarzschild black hole (SBH) and non-Schwarzschild black hole (NSBH) solutions. In addition, we discuss the thermodynamic properties of two groups of numerical solutions in detail, and show that they obey the first law of thermodynamics., new charged black hole solutions in EW gravity

We carry out the stability analysis of the Schwarzschild black hole in Gauss-Bonnet and Chern-Simons-scalar theory. Here, we introduce two quadratic scalar couplings ($\phi_1^2,\phi_2^2$) to Gauss-Bonnet and Chern-Simons terms, where the former term is parity-even, while the latter one is parity-odd. The perturbation equation for the scalar $\phi_1$ is the Klein-Gordon equation with an effective mass, while the perturbation equation for $\phi_2$ is coupled to the parity-odd metric perturbation, providing a system of two coupled equations. It turns out that the Schwarzschild black hole is unstable against $\phi_1$ perturbation, leading to scalarized black holes, while the black hole is stable against $\phi_2$ and metric perturbations, implying no scalarized black holes., Comment: 18 pages, 2 figures, version to appear in IJMPD

We study the scalarized charged black holes in the Einstein-Maxwell-Scalar (EMS) theory with scalar mass term. In this work, the scalar mass term is chosen to be $m^2_\phi=\alpha/\beta$, where $\alpha$ is a coupling parameter and $\beta$ is a mass-like parameter. It turns out that any scalarized charged black holes are not allowed for the case of $\beta \le 4.4$ with $q=0.7(M=0.5,Q=0.35)$ because this case implies the stable Reissner-Nodstr\"{o}m (RN) black holes. In the massless limit of $\beta\to \infty$, one recovers the case of the EMS theory. We note that the unstable RN black hole implies the appearance of scalarized charged black holes. The other unstable case of $\beta>4.4$ with $q=0.7$ allows us to obtain the $n=0,1,2,\cdots$ scalarized charged black holes for $\alpha(\beta)\ge \alpha_{\rm th}(\beta)$ where $\alpha_{\rm th}(\beta)$ represents the threshold of instability for the RN black hole. Furthermore, it is shown that the $n=0$ black hole is stable against radial perturbations, while the $n=1$ black hole is unstable. This stability result is independent of the mass parameter $\beta$., Comment: 18 pages, 8 figures, version to appear in PRD

We study quasinormal modes (QNMs) of charged black holes in the Einstein-Maxwell-Weyl (EMW) gravity by adopting the test scalar field perturbation. We find that the imaginary part of QNM frequencies is consistently negative for different angular parameters l, indicating that these modes always decay and are therefore stable. We do not observe a linear relationship between the QNM frequency ω and parameter p for these black holes, as their charge Q causes a nonlinear effect. We evaluate the massive scalar field perturbation in charged black holes and find that random long lived modes (i.e., quasiresonances) could exist in this spectrum.

The scalarization of Reissner-Nordstr\"{o}m black holes was recently proposed in the Einstein-Maxwell-scalar theory. Here, we show that the appearance of the scalarized Reissner-Nordstr\"{o}m black hole is closely related to the Gregory-Laflamme instability of the Reissner-Nordstr\"{o}m black hole without scalar hair., Comment: 22 pages, 10 figures, version to appear in EPJC

We investigate the stability analysis of Schwarzschild black hole in Einstein-scalar-Gauss-Bonnet (ESGB) theory because the instability of Schwarzschild black hole without scalar hair implies the Gauss-Bonnet black hole with scalar hair. The linearized scalar equation is compared to the Lichnerowicz-Ricci tensor equation in the Einstein-Weyl gravity. It turns out that the instability of Schwarzschild black hole in ESGB theory is interpreted as not the tachyonic instability, but the Gregory-Laflamme instability of black string. In the small mass regime of $1/\lambda, Comment: 14 pages, 4 figures, version to appear in Physical Review D

In this work, we utilize the quasinormal modes (QNMs) of a massless scalar perturbation to probe the Van der Waals-like small and large black holes (SBH/LBH) phase transition of charged topological Anti-de Sitter (AdS) black holes in four-dimensional massive gravity. We find that the signature of this SBH/LBH phase transition is detected in the isobaric as well as in the isothermal process.This further supports the idea that the QNMs can be an efficient tool to investigate the thermodynamical phase transition., Comment: 18 pages, V3: minor corrections

In $$(2+1)$$ -dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter $$k=1$$ and $$k\ne 1$$ ), in the Einstein–Power–Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with $$k\ne 1$$ , we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.

We study the $P-V$ criticality and phase transition in the extended phase space of anti-de Sitter (AdS) black holes in higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity, treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Besides the usual small/large black hole phase transitions, the interesting thermodynamic phenomena of reentrant phase transitions (RPTs) are observed for black holes in all $d\geq6$-dimensional spacetime when the coupling coefficients $c_i m^2$ of massive potential satisfy some certain conditions., Comment: 14 pages, several references are added, v2: published in EPJC

Motivated by recent developments of black hole thermodynamics in de Rham, Gabadadze and Tolley(dRGT) massive gravity, we study the critical behaviors of four-dimensional topological Anti-de Sitter(AdS) black holes in the presence of Born-Infeld nonlinear electrodynamics by treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. It shows that besides the Van der Waals-like SBH/LBH phase transitions appears, the so-called reentrant phase transitions (RPTs) are also observed when the coupling coefficients $c_i m^2$ of massive potential and Born-Infeld parameter $b$ satisfy some certain conditions., Comment: arXiv admin note: text overlap with arXiv:1612.08056; text overlap with arXiv:1402.2837, arXiv:1306.5756 by other author

In this paper, the ratio of shear viscosity to entropy density in the context of dRGT massive gravity is studied. The massive graviton breaks the diffeomorphism invariance in the bulk geometry so that the momentum dissipates in the boundary theory. The ratio is calculated numerically and analytically by using Kubo formula. It is shown that exhibits a non-trivial temperature dependence. We find that approaches to a constant value at high temperature, while it tends to zero with a scaling law at low temperature.

We compute the mass and the temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient $\alpha_2, Comment: 15 pages, 22 figures