Small Black Holes Research Articles

Magnetically charged Euler-Heisenberg black holes with scalar hair

We study the Einstein-Euler-Heisenberg theory in the presence of a self interacting scalar field, minimally coupled to gravity. We solve analytically the field equations for the magnetically charged case and we obtain novel magnetically charged hairy black holes. The scalar field dresses the black hole with a secondary scalar hair. The hairy black hole develops three horizons when Euler-Heisenberg parameter and the magnetic charge are small and the horizon radius is getting large when the scalar charge and the gravitational mass are large. The presence of matter and the magnetic field outside the horizon of the black hole increases the temperature only for small black holes. Calculating the heat capacity we show that the asymptotically AdS Euler-Heisenberg hairy black hole undergoes a second order phase transition and then it is stabilized. Also the weak energy condition is violated for the asymptotically AdS Euler-Heisenberg hairy black hole.

Quantum Explosions of Black Holes and Thermal Coordinates

The Hawking temperature for a Schwarzschild black hole is T=1/8πM, where M is the black hole mass. This formula is derived for a fixed Schwarzschild background metric, where the mass M could be arbitrary small. Note that, for vanishing M→0, the temperature T becomes infinite. However, the Schwarzschild metric itself is regular when the black hole mass M tends to zero; it is reduced to the Minkowski metric, and there are no reasons to believe that the temperature becomes infinite. We point out that this discrepancy may be due to the fact that the Kruskal coordinates are singular in the limit of the vanishing mass of the black hole. To elucidate the situation, new coordinates for the Schwarzschild metric are introduced, called thermal coordinates, which depend on the black hole mass M and the parameter b. The parameter b specifies the motion of the observer along a special trajectory. The thermal coordinates are regular in the limit of vanishing black hole mass M. In this limit, the Schwarzschild metric is reduced to the Minkowski metric, written in coordinates dual to the Rindler coordinates. Using the thermal coordinates, the Schwarzschild black hole radiation is reconsidered, and it is found that the Hawking formula for temperature is valid only for large black holes, while for small black holes, the temperature is T=1/2π(4M+b). The thermal observer in Minkowski space sees radiation with temperature T=1/2πb, similar to the Unruh effect with non-constant acceleration. The thermal coordinates for more general spherically symmetric metrics, including the Reissner–Nordstrom, de Sitter, and anti-de Sitter, are also considered. In these coordinates, one sees a Planck distribution with constant temperature. One obtains that the thermal Planck distribution of massless particles is not restricted to the cases of black holes or constant acceleration, but is valid for any spherically symmetric metric written in thermal coordinates.

Black Hole Solutions as Topological Thermodynamic Defects.

In this Letter, employing the generalized off-shell free energy, we treat black hole solutions as defects in the thermodynamic parameter space. The results show that the positive and negative winding numbers corresponding to the defects indicate the local thermodynamical stable and unstable black hole solutions, respectively. The topological number defined as the sum of the winding numbers for all the black hole branches at an arbitrary given temperature is found to be a universal number independent of the black hole parameters. Moreover, this topological number only depends on the thermodynamic asymptotic behaviors of the black hole temperature at small and large black hole limits. Different black hole systems are characterized by three classes via this topological number. This number could help us in better understanding the black hole thermodynamics and, further, shed new light on the fundamental nature of quantum gravity.

The radial distribution function reveals the underlying mesostructure of the AdS black hole

Based on the equations of state, one can infer the underlying interaction potentials among the black hole molecules in the case of Schwarzschild-AdS and charged AdS black holes. The microscopic molecules with the interaction potential arrange in a specific way to form the mesostructure, whose size is between the macro (black hole system) and the micro (black hole molecules). As a result, the mesostructure leads to the emergence of the macroscopic phase. However, the information about the mesostructure of the AdS black hole are still elusive. In this paper, the radial distribution function is introduced to probe the mesostructure of the AdS black hole. We find that the mesostructure of the Schwarzschild-AdS black hole behaves as the ideal gas when the temperature is high. Furthermore, we find the mesostructure for the liquid-like (gas-like) phase of the small (large) charged AdS black hole. A sudden change of the mesostructure emerges from the liquid-like phase to the gas-like phase when the charged AdS black hole undergoes a phase transition from the small to large black hole, consistent with the viewpoint that the phase transition of the charged AdS black hole is reminiscent of that of the vdW fluid. This study provides a new angle towards understanding the black hole from its mesostructure.

Large and small non-extremal black holes, thermodynamic dualities, and the Swampland

In this paper we discuss black hole solutions parametrized by their entropy mathcal{S} and temperature mathcal{T} in gravitational effective theories. We are especially interested in the analysis of the boundary regions in the mathcal{T} − mathcal{S} diagram, i.e. large/small values of entropy and temperature, and their relation to Swampland constraints. To explore this correlation, we couple the gravitational theories to scalar fields and connect limits of thermodynamic quantities of black holes to scalar field excursions in the corresponding solutions. Whenever the scalar fields traverse an infinite field distance, the Swampland Distance Conjecture allows for a reformulation in terms of entropy- or temperature-distance. The effective theories with scalars we investigate are Einstein-Maxwell-dilaton theory as well as mathcal{N} = 2 supergravity in four dimensions. The relation of the latter to type II string theory compactified on Calabi-Yau 3-folds often allows for a direct identification of the corresponding light tower of states. These setups also point towards various dualities between asymptotic regions of the black hole solution. In the context of mathcal{N} = 2 supergravity black holes, these thermodynamic dualities have an interpretation in terms of T- and S-dualities along the internal directions and their natural action on Kaluza-Klein and winding states.

Corrected Thermodynamics of $$(2+1)D$$ Black Hole Conformally Coupled to a Massless Scalar

We study the corrected entropy due to thermal fluctuation and their effect on the thermodynamics of a conformally dressed black hole in three dimensions. We find that the thermal fluctuation affects the entropy significantly for small black holes. Various corrected thermodynamical variables are also calculated for this black hole. We observe that thermal fluctuation on the thermodynamics of a small conformal black hole has a significant effect. We also analyse the stability of black hole under the effect of thermal fluctuation. Due to thermal fluctuation, instability occurs in the system of small conformal black holes. Isothermal compressibility is also studied for this black hole which diverges for the equilibrium state of the system.

BASS. XXXVI. Constraining the Local Supermassive Black Hole–Halo Connection with BASS DR2 AGNs

We investigate the connection between supermassive black holes (SMBHs) and their host dark matter halos in the local universe using the clustering statistics and luminosity function of active galactic nuclei (AGNs) from the Swift/BAT AGN Spectroscopic Survey (BASS DR2). By forward-modeling AGN activity into snapshot halo catalogs from N-body simulations, we test a scenario in which SMBH mass correlates with dark matter (sub)halo mass for fixed stellar mass. We compare this to a model absent of this correlation, where stellar mass alone determines the SMBH mass. We find that while both simple models are able to largely reproduce the abundance and overall clustering of AGNs, the model in which black hole mass is tightly correlated with halo mass is preferred by the data by 1.8σ. When including an independent measurement on the black hole mass–halo mass correlation, this model is preferred by 4.6σ. We show that the clustering trends with black hole mass can further break the degeneracies between the two scenarios and that our preferred model reproduces the measured clustering differences on one-halo scales between large and small black hole masses. These results indicate that the halo binding energy is fundamentally connected to the growth of SMBHs.

Effects of a global monopole on the thermodynamic phase transition of a charged AdS black hole* *Supported by the National Natural Science Foundation of China (11873001, 12047564), the Fundamental Research Funds for the Central Universities (2021CDJZYJH-003) and the Postdoctoral Science Foundation of Chongqing (cstc2021jcyj-bsh0124)

We study the dynamical properties of the thermodynamic phase transition (PT) of a charged AdS black hole (BH) with a global monopole via the Gibbs free energy landscape and reveal the effects of the global monopole on the kinetics of thermodynamic PTs. First, we briefly review the thermodynamics of a charged AdS BH with a global monopole. Then, we introduce the Gibbs free energy landscape to investigate the thermodynamic stability of the BH states. Because of thermal fluctuations, the small black hole (SBH) state can transit to a large black hole (LBH) state, and vice versa. Further, we use the Fokker-Planck equation with the reflecting boundary condition to study the probability evolution of the BH state with and without a global monopole separately. It is found that for both the SBH and LBH states, the global monopole could slow down the evolution of the BH state. In addition, we obtain the relationship between the first passage time and the monopole parameter η. The result shows that as the monopole parameter η increases, the mean first passage time becomes longer for both the SBH and LBH states.

Black holes surrounded by modified Chaplygin gas in Lovelock theory of gravity

The Lovelock theory of gravity is a natural extension of the Einstein’s theory of general relativity to higher dimensions, which presents the criteria of general covariance and is free of ghosts. In this work, we consider a model that static spherically-symmetric black hole is surrounded by the modified Chaplygin gas with equation of state p=Aρ−B/ρα. We find that the energy density of the modified Chaplygin gas can be characterized by four parameters. The black hole thermodynamical quantities, consisting of gravitational mass, temperature, entropy and heat capacity, as functions of horizon radius, are calculated. Concerning the thermodynamical stability of the black holes, we consider the third-order Lovelock gravity as a specific case and show in figures the heat capacity versus the horizon radius, observing that there exist a phase of thermodynamically stable small black hole and a phase of thermodynamically unstable large black hole for D=7, while an additional intermediate local unstable phase as well as an intermediate local stable phase appear for D=8 with configuring properly the model parameters. The effects of the modified Chaplygin gas and Lovelock gravity on thermodynamical stability of the black holes are discussed.

Shadow thermodynamics of non-linear charged Anti-de Sitter black holes* *Supported by the National Natural Science Foundation of China (12075143)

It is well known that when vacuum polarization emerges in quantum electrodynamics, the non-linear interaction between electromagnetic fields should be considered. Moreover, the corresponding field of non-linear electrodynamics can have important effects on black hole physics. In this work, we focus on the relationship between an observable quantity, that is, the shadow radius, and the first-order phase transition of non-linear charged AdS black holes in the framework of Einstein-power-Yang-Mills gravity. The results show that, under a certain condition, there exists a first-order phase transition from the viewpoint of both the shadow radius and horizon radius, which depend on temperature (or pressure). From the viewpoint of the shadow radius, the phase transition temperature is higher than that from the viewpoint of the horizon radius under the same condition. This may be due to the non-linear Yang Mills charge and the gravitational effect. This indicates that the shadow radius can be regarded as a probe to reveal the thermodynamic phase transition information of black holes. The thermal profiles of coexistent large and small black hole phases when the system is undergoing the phase transition are presented for two different values of the non-linear Yang Mills charge parameter: . Furthermore, the effects of the non-linear Yang Mills charge parameter on the shadow radius and thermal profile are investigated.

Black holes entangled by radiation

We construct three models to describe the scenario where two eternal black holes are separated by a flat space, and can eventually be entangled by exchanging radiation. In the doubly holographic setup, we compute the entanglement entropy and mutual information among subsystems and obtain the dynamic phase structure of the entanglement. The formation of entanglement between these two black holes is delayed by the space which the radiation must travel through. If the black holes exchange sufficient Hawking modes, the final state is characterized by a connected entanglement wedge; otherwise, the final entanglement wedge contains two separate islands. In the former case, the entanglement wedge of the black holes forms at the time scale proportional to the size of the flat space between them. While in both cases, the unitarity of the evolution is preserved. When the sizes of the black holes are not equal, we observe a loss of entanglement between the smaller black hole and the radiation at late times. On the field theory side, we consider two Sachdev-Ye-Kitaev (SYK) clusters coupled to a Majorana chain, which resemble two black holes connected by a radiation region. We numerically compute the same entanglement measures and obtain similar phase structures as the bulk results. In general, a time delay of the entanglement between the SYK clusters is found in cases with a long Majorana chain. In particular, when the SYK clusters are different in size, similar entanglement loss between the smaller SYK cluster and the Majorana chain is observed. Finally, we investigate a chain model composed of EPR clusters with particles exchanging between neighboring clusters and reproduce the features of entanglement observed in the previous models.

Ruppeiner geometry, P–V criticality and interacting microstructures of black holes in dRGT massive gravity

We probe the microstructure of the dRGT massive black hole in an anti-de Sitter background. The calculations are performed in an extended phase space with pressure and volume taken as fluctuation variables. We analyze the microstructure by exploiting the Ruppeiner geometry, where the thermodynamic curvature scalar is constructed via adiabatic compressibility. The nature of the curvature scalar along the coexistence line of small black hole (SBH) and large black hole (LBH) is investigated. In the microscopic interaction, we observe that the SBH phase behaves as an anyonic gas and the LBH phase is analogous to a boson gas. Further, we study the effect of graviton mass on the underlying microstructure of the black hole.

Intermediate mass-ratio inspirals with dark matter minispikes

The dark matter (DM) distributed around an intermediate massive black hole (IMBH) forms an overdensity region called DM minispike. We consider the binary system which consists of an IMBH with DM minispike and a small black hole inspiralling around the IMBH in eccentric orbits. The factors which affect the evolution of the orbit include the gravity of the system, the dynamical friction and accretion of the small black hole caused by the DM minispike, and the radiation reaction of gravitational waves (GWs). Using the method of osculating orbit, we find that when the semi-latus rectum $p\ensuremath{\ll}{10}^{5}{R}_{s}$ (${R}_{s}$ is the Schwarzschild radius of the IMBH) the dominated factors are the dynamical friction and accretion from the DM minispike, and the radiation reaction. When $p\ensuremath{\gg}{10}^{5}{R}_{s}$, the gravity from the DM minispike dominates the orbital evolution. The existence of DM minispike leads to the deviation from the Keplerian orbit, such as extra orbital precession, henceforth extra phase shift in the GW waveform. By calculating the signal-to-noise ratio for GWs with and without DM minispikes and the mismatch between them, we show that the effect of the DM minispike in GW waveforms can potentially be detected by future space-based GW detectors such as LISA, Taiji, and Tianqin.

Godzilla, a monster lurks in the Sunburst galaxy

We model the strong lensing effect in the galaxy cluster PSZ1 G311.65-18.48 (z = 0.443) with an improved version of the hybrid method WSLAP+. We extend the number of constraints by including the position of critical points, which are combined with the classic positional constraints of the lensed galaxies. We pay special attention to a transient candidate source (Tr) previously discovered in the giant Sunburst arc (z = 2.37). Our lens model predicts Tr to be within a fraction of an arcsecond from the critical curve, which has a larger magnification factor than previously found, but still not large enough to explain the observed flux and lack of counterimages. Possible candidate counterimages are discussed that would lower the magnification required to explain Tr, but extreme magnification factors (μ > 600) are still required, even in that case. The presence of a small mass perturber with a mass comparable to a dwarf galaxy (M ∼ 108 M⊙) near the position of Tr is needed in order to explain the required magnification and morphology of the lensed galaxy. We discuss how the existence of this perturber could potentially be used to constrain models of dark matter. The large apparent brightness and unresolved nature of the magnified object implies a combination of extreme magnification and a very luminous and compact source (r < 0.4 pc). Possible candidates are discussed, including an hyperluminous star, a small group of stars, or an accretion disk around a relatively small supermassive black hole (SMBH). Based on spectral information and flux requirements, we argue that a luminous blue variable (LBV) star caught during an outburst is the most likely candidate. Owing to the extreme magnification and luminosity of this source, we dub it Godzilla.

The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box

We revisit the stability of black hole saddles for the Euclidean path integral describing the canonical partition function Z(β) for gravity inside a spherical reflecting cavity. The boundary condition at the cavity wall couples the transverse-traceless (TT) and pure-trace modes that are traditionally used to describe fluctuations about Euclidean Schwarzschild black holes in infinite-volume asymptotically flat and asymototically AdS spacetimes. This coupling obstructs the familiar Gibbons-Hawking-Perry treatment of the conformal factor problem, as Wick rotation of the pure-trace modes would require that the TT modes be rotated as well. The coupling also leads to complex eigenvalues for the Lichnerowicz operator. We nevertheless find that the Lichnerowicz operator can be diagonalized in the space of coupled modes. This observation allows the eigenmodes to define a natural generalization of the pure-trace Wick-rotation recipe used in infinite volume, with the result that a mode with eigenvalue λ is stable when Re λ > 0. In any cavity, and with any cosmological constant Λ ≤ 0, we show this recipe to reproduce the expectation from black hole thermodynamics that large Euclidean black holes define stable saddles while the saddles defined by small Euclidean black holes are unstable.

The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss–Bonnet gravity: from the critical point to the triple point

Ruppeiner geometry has been successfully applied in the study of the black hole microstructure by combining with the small–large black hole phase transition, and the potential interactions among the molecular-like constituent degrees of freedom are uncovered. In this paper, we will extend the study to the triple point, where three black hole phases coexist acting as a typical feature of black hole systems quite different from the small–large black hole phase transition. For the six-dimensional charged Gauss–Bonnet anti-de Sitter black hole, we thoroughly investigate the swallow tail behaviors of the Gibbs free energy and the equal area laws. After obtaining the black hole triple point in a complete parameter space, we exhibit its phase structures both in the pressure–temperature and temperature–horizon radius diagrams. Quite different from the liquid–vapor phase transition, a double peak behavior is present in the temperature–horizon radius phase diagram. Then we construct the Ruppeiner geometry and calculate the corresponding normalized curvature scalar. Near the triple point, we observe multiple negatively divergent behaviors. Positive curvature scalar is observed for the small black hole with high temperature, which indicates that the repulsive interaction dominates among the microstructure. Furthermore, we consider the variation of the curvature scalar along the coexisting intermediate and large black hole curves. Combining with the observation for different fluids, the result suggests that this black hole system behaves more like the argon or methane. Our study provides a first and preliminary step towards understanding black hole microstructure near the triple point, as well as uncovering the particular properties of the Gauss–Bonnet gravity.

Piercing of a boson star by a black hole

New light fundamental fields are natural candidates for all or a fraction of dark matter. Self-gravitating structures of such fields might be common objects in the universe, and could comprise even galactic halos. These structures would interact gravitationally with black holes, a process of the utmost importance since it dictates their lifetime, the black hole motion, and possible gravitational radiation emission. Here, we study the dynamics of a black hole piercing through a much larger fully relativistic boson star, made of a complex minimally coupled massive scalar without self-interactions. As the black hole pierces through the bosonic structure, it is slowed down by accretion and dynamical friction, giving rise to gravitational-wave emission. Since we are interested in studying the interaction with large and heavy scalar structures, we consider mass ratios up to $q\ensuremath{\sim}10$ and length ratios $\mathcal{L}\ensuremath{\sim}62$. Somewhat surprisingly, for all our simulations, the black hole accretes more than 95% of the boson star material, even if an initially small black hole collides with large velocity. This is a consequence of an extreme ``tidal capture'' process, which binds the black hole and the boson star together, for these mass ratios. We find evidence of a ``gravitational atom'' left behind as a product of the process.

Thermodynamic geometry of pure Lovelock black holes

In this paper, we study thermodynamic geometry for pure Lovelock black holes. The thermodynamics scalar curvature contains information about the interaction of microstates that might be repulsive or attractive. We obtain critical exponents and critical amplitudes of scalar and extrinsic curvatures for small and large black holes for various dimensions. We demonstrate that this model’s thermodynamic Ricci scalar scaling behavior has a universal behavior for different dimensions. Moreover, we determine the order of phase transition by using Ehrenfest’s equations and the Prigogine–Defay ratio. We also consider the extended phase space and investigate the critical behavior of the pure Lovelock black holes for various dimensions.

BASS. XXVI. DR2 Host Galaxy Stellar Velocity Dispersions

We present new central stellar velocity dispersions for 484 Sy 1.9 and Sy 2 from the second data release of the Swift/BAT AGN Spectroscopic Survey (BASS DR2). This constitutes the largest study of velocity dispersion measurements in X-ray-selected obscured active galactic nuclei (AGN) with 956 independent measurements of the Ca ii H and K λ3969, 3934 and Mg I λ5175 region (3880–5550 Å) and the calcium triplet region (8350–8730 Å) from 642 spectra mainly from VLT/X-Shooter or Palomar/DoubleSpec. Our sample spans velocity dispersions of 40–360 km s1, corresponding to 4–5 orders of magnitude in black hole mass (M BH = 105.5−9.6 M ⊙), bolometric luminosity (L bol ∼ 1042–46 erg s−1), and Eddington ratio (L/L Edd ∼ 10−5 to 2). For 281 AGN, our data and analysis provide the first published central velocity dispersions, including six AGN with low-mass black holes (M BH = 105.5−6.5 M ⊙), discovered thanks to high spectral resolution observations (σ inst ∼ 25 km s−1). The survey represents a significant advance with a nearly complete census of velocity dispersions of hard X-ray–selected obscured AGN with measurements for 99% of nearby AGN (z < 0.1) outside the Galactic plane (∣b∣ > 10°). The BASS AGN have much higher velocity dispersions than the more numerous optically selected narrow-line AGN (i.e., ∼150 versus ∼100 km s−1) but are not biased toward the highest velocity dispersions of massive ellipticals (i.e., >250 km s−1). Despite sufficient spectral resolution to resolve the velocity dispersions associated with the bulges of small black holes (∼104–5 M ⊙), we do not find a significant population of super-Eddington AGN. Using estimates of the black hole sphere of influence from velocity dispersion, direct stellar and gas black hole mass measurements could be obtained with existing facilities for more than ∼100 BASS AGN.

Neutron star quantum death by small black holes

Neutron stars can be destroyed by black holes at their center accreting material and eventually by swallowing the entire star. Here we note that the accretion model adopted in the literature, based on Bondi accretion or variations thereof, is inadequate for small black holes---black holes whose Schwarzschild radius is comparable to, or smaller than, the neutron's de Broglie wavelength. In this case, quantum mechanical aspects of the accretion process cannot be neglected, and give rise to a completely different accretion rate. We show that for the case of black holes seeded by the collapse of bosonic dark matter, this is the case for electroweak-scale dark matter particles. In the case of fermionic dark matter, typically the black holes that would form at the center of a neutron star are more massive, unless the dark matter particle mass is very large, larger than about ${10}^{10}\text{ }\text{ }\mathrm{GeV}$. We calculate the lifetime of neutron stars harboring a ``small'' black hole, and find that black holes lighter than $\ensuremath{\sim}{10}^{11}\text{ }\text{ }\mathrm{kg}$ quickly evaporate, leaving no trace. More massive black holes destroy neutron stars via quantum accretion on timescales much shorter than the age of observed neutron stars. We find that the range where seed black holes inside neutron stars are massive enough that they do not quickly evaporate away, but not so massive that a fluid accretion picture is warranted is limited to between $\ensuremath{\sim}{10}^{11}$ and ${10}^{12}\text{ }\text{ }\mathrm{kg}$, but our results are key to accurately determine the actual critical black hole mass corresponding to the onset of neutron star destruction.