With a suitable decomposition of its energy-momentum tensor into pressureless matter and a vacuum type term, we investigate the spherical gravitational collapse of a minimally coupled, self-interacting scalar field, showing that it collapses to a singularity. The formed blackhole has a mass $M \sim 1/m$ (in Planck units), where $m$ is the mass of the scalar field. If the latter has the axion mass, $m \sim 10^{-5}$ eV, the former has a mass $M \sim 10^{-5} M_{\odot}$.
We investigate scalarized charged black holes in the Einstein-Maxwell-Scalar theory with two U(1) fields inspired by the $N=4$ supergravity. From the onset of the spontaneous scalarization (tachyonic instability of Reissner-Nordström black hole), these black holes are 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. Adopting radial perturbations, we show that the $n=0$ black hole is stable against the $s(l=0)$-mode scalar perturbation, whereas the $n=1,2$ excited black holes are unstable. This …
We obtain scalar hairy black holes from Einstein-Maxwell-conformally coupled scalar (EMCS) theory with the scalar coupling parameter $α$ to the Maxwell term. In case of $α=0$, the $α=0$ EMCS theory provides constant (charged) scalar hairy black hole and charged BBMB (Bocharova-Bronnikov-Melnikov-Bekenstein) black hole where the former is stable against full perturbations, while the latter remains unstable because it belongs to an extremal black hole. It is noted that for $α\not=0$, the unstable Reissner-Nordström black holes without scalar hair imply infinite branches of $n=0(α\ge 8.019),1(α\g…
We introduce a new microscopic quantity $\varepsilon $ that describes the contribution of a single black hole molecule to black hole entropy and give a key relation that this microscopic quantity is proportional to the macroscopic quantity -- entropy surface density $σ_{S}$, thus connecting a microscopic quantity to a macroscopic quantity of black holes. Such a connection provides a new probe for understanding the black hole microstructure from the macroscopic perspective. We also classify black holes in terms of entropy surface density. When its entropy surface density is larger (smaller) tha…
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-Nordström 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…
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 $α>0$ inspired by the constant scalar hairy black hole as well as infinite branches of $n=0(α\ge 8.019),1(α\ge 40.84),2(α\ge 99.89),\cdots$ scalarized charged black holes found through the spontaneous scalarization on the Reissner-Nordström black hole. It turns out that the black hole in the single branc…
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 Einst…
We study the perturbative behaviour of topological black holes in the presence of a cosmological constant and a scalar field coupled to the Gauss-Bonnet term. We calculate both analytically and numerically the quasi-normal modes of scalar perturbations in the extended scalar-tensor-Gauss-Bonnet gravity. In the case of small black holes we find a phase transition of the topological black hole to a hairy configuration.
The scalarization of Reissner-Nordström black holes was recently proposed in the Einstein-Maxwell-scalar theory. Here, we show that the appearance of the scalarized Reissner-Nordström black hole is closely related to the Gregory-Laflamme instability of the Reissner-Nordström black hole without scalar hair.
In this paper, we study spontaneous scalarization of asymptotically anti-de Sitter charged black holes in the Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In this model, Reissner-Nordström-AdS (RNAdS) black holes are scalar-free black hole solutions, and may induce scalarized black holes due to the presence of a tachyonic instability of the scalar field near the event horizon. For RNAdS and scalarized black hole solutions, we investigate the domain of existence, perturbative stability against spherical perturbations and phase structure. In a …
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-Nordström 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 a…
With certain non-minimal coupling between a massless scalar field and the Gauss-Bonnet curvature invariant in the extended scalar-tensor-Gauss-Bonnet (ESTGB) field theory, tachyonic instability of Kerr-Newman (KN) black hole is promoted. Critical spin and charge for the onset of the spontaneous scalarization phenomenon for the KN black hole are calculated in the infinitely large coupling limit. Then analytical formula for the coupling-strength-dependent critical existence line is obtained for the black-hole-scalar-field configuration in a finite large coupling regime. Moreover, numerical metho…
We extend the recently proposed Black Hole Entropy Distance Conjecture to the case of charged black holes in de Sitter space. By systematically studying distances in the space of black hole geometries with multiple horizons, we find that the distance is generically related to the logarithm of the entropy. From the infinite distance conjecture this predicts the appearance of a massless tower of modes in the limit of infinite entropy. Further, we study the evaporation of these black holes and relate it to the geometric distance. We find that the corresponding distance to the final stage of evapo…
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 $m^2_2<0$, we could not obtain any asymptotically flat black hole solution with scalar hair.
We study some physical properties of black holes in Null Aether Theory (NAT)--a vector-tensor theory of gravity. We first review the black hole solutions in NAT and then derive the first law of black hole thermodynamics. The temperature of the black holes depends on both the mass and the NAT \textquotedblleft charge" of the black holes. The extreme cases where the temperature vanishes resemble the extreme Reissner-Nordström black holes. We also discuss the contribution of the NAT charge to the geodesics of massive and massless particles around the NAT black holes.
The thermodynamic geometry has been proved to be quite useful in understanding the microscopic structure of black holes. We investigate the phase structure, thermodynamic geometry and critical behavior of a Reissner-Nordstrom-AdS black hole and a Reissner-Nordstrom black hole in a cavity, which can reach equilibrium in a canonical ensemble. Although the phase structure and critical behavior of both cases show striking resemblance, we find that there exist significant differences between the thermodynamic geometry of these two cases. Our results imply that there may be a connection between the …
We consider f(R) gravity theories in the presence of a scalar field minimally coupled to gravity with a self-interacting potential. When the scalar field backreacts to the metric we find at large distances scalarized Schwarzschild-AdS and Schwarzschild-AdS-like black hole solutions. At small distances due to strong curvature effects and the scalar dynamis we find a rich structure of scalarized black hole solutions. When the scalar field is conformally coupled to gravity we also find scalarized black hole solutions at small distances.
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 ($α>0$), 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 $α<0$, it is shown that the Kerr black hole is unstable without any $α$-independent bound on the rotation parameter $a$ when using the the hyperboloidal foliation method. The disappearance of the $a$-bound is confirmed analytically by implementing the (1+1)-dimensional l…
We construct spontaneously vectorized black holes where a real vector field is coupled to the Gauss-Bonnet invariant. We employ three coupling functions for the vector field, and determine the respective domains of existence of the vectorized black holes. These domains of existence are bounded by the marginally stable Schwarzschild black holes and the critical vectorized black holes. We also address the effects of a mass term. For a given black hole mass the horizon radius is smaller for the vectorized black holes than for the Schwarzschild black holes. Since the vector field vanishes at the h…
We introduce a new set of chemical variables for the accelerating black hole. We show how these expressions suggest that conical defects emerging from a black hole can be considered as true hair -- a new charge that the black hole can carry -- and discuss the impact of conical deficits on black hole thermodynamics from this `chemical' perspective. We conclude by proving a new {\it Reverse Isoperimetric Inequality} for black holes with conical defects.
We study the dynamics of black holes in Einstein-scalar-Gauss-Bonnet theories that exhibit spontaneous black hole scalarization using recently introduced methods for solving the full, non-perturbative equations of motion. For one sign of the coupling parameter, non-spinning vacuum black holes are unstable to developing scalar hair, while for the other, instability only sets in for black holes with sufficiently large spin. We study scalarization in both cases, demonstrating that there is a range of parameter space where the theory maintains hyperbolic evolution and for which the instability sat…
Based on the gedanken experiment for black hole complementarity in the Schwarzschild black hole, we calculate the energy required to duplicate information in the BTZ black hole under the assumption of absorbing boundary condition and its dual solution of the black string, respectively, in order to justify the validity of the no-cloning theorem in quantum mechanics. For the BTZ black hole, the required energy for the duplication of information can be made fairly small, whereas for the black string it exceeds the total mass of the black string, although they are related to each other under the d…
Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the …
Spontaneous scalarization is a gravitational phenomenon in which deviations from general relativity arise once a certain threshold in curvature is exceeded, while being entirely absent below that threshold. For black holes, scalarization is known to be triggered by a coupling between a scalar and the Gauss-Bonnet invariant. A coupling with the Ricci scalar, which can trigger scalarization in neutron stars, is instead known to not contribute to the onset of black hole scalarization, and has so far been largely ignored in the literature when studying scalarized black holes. In this paper, we stu…
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 $m^2_ϕ=α/β$, where $α$ is a coupling parameter and $β$ is a mass-like parameter. It turns out that any scalarized charged black holes are not allowed for the case of $β\le 4.4$ with $q=0.7(M=0.5,Q=0.35)$ because this case implies the stable Reissner-Nodström (RN) black holes. In the massless limit of $β\to \infty$, one recovers the case of the EMS theory. We note that the unstable RN black hole implies the appearance of scalarized cha…
It was confirmed that the negative modes of the Euclidean section for asymptotically flat black holes reveal the thermodynamic instability of these black holes in the grand canonical ensemble (GCE). These include Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes. In this work, we develop the relation between thermodynamic instability in the GCE and tachyonic instability for asymptotically flat black holes, where the latter is the onset for obtaining black holes with scalar hair. This implies that the tachyonic instability of black holes when introducing scalar coupling to th…
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 $α$, whereas these bla…
