Black Hole Model Research Articles

The fuzzy BTZ

We introduce a model of a noncommutative BTZ black hole, obtained by quantisation of Poincaré coordinates together with a moving frame. The fuzzy BTZ black hole carries a covariant differential calculus, satisfies Einstein’s equations and has a constant negative curvature. The construction passes through a larger space, the fuzzy anti-de Sitter, and implements discrete BTZ identifications as conjugations by a unitary operator. We derive the spectrum of the suitably regularised radial coordinate: it consists of a continuum of scattering states outside the horizon r+ and an infinite discrete set of bound states inside.

Stable rotating regular black holes

We present a rotating regular black hole whose inner horizon has zero surface gravity for any value of the spin parameter, and is therefore stable against mass inflation. Our metric is built by combining two successful strategies for regularizing singularities, i.e. by replacing the mass parameter with a function of $r$ and by introducing a conformal factor. The mass function controls the properties of the inner horizon, whose displacement away from the Kerr geometry's inner horizon is quantified in terms of a parameter $e$; while the conformal factor regularizes the singularity in a way that is parametrized by the dimensionful quantity $b$. The resulting line element not only avoids the stability issues that are common to regular black hole models endowed with inner horizons, but is also free of problematic properties of the Kerr geometry, such as the existence of closed timelike curves. While the proposed metric has all the phenomenological relevant features of singular rotating black holes -- such as ergospheres, light ring and innermost stable circular orbit -- showing a remarkable similarity to a Kerr black hole in its exterior, it allows nonetheless sizable deviations, especially for large values of the spin parameter $a$. In this sense, the proposed rotating "inner-degenarate" regular black hole solution is not only amenable to further theoretical investigations but most of all can represent a viable geometry to contrast to the Kerr one in future phenomenological tests.

Accretion from Winds of Red Giant Branch Stars May Reveal the Supermassive Black Hole in Leo I

A supermassive black hole (SMBH) of ∼3 × 106 M ⊙ was recently detected via dynamical measurements at the center of the dwarf galaxy Leo I. Standing ∼2 orders of magnitude above standard scaling relations, this SMBH is hosted by a galaxy devoid of gas and with no significant star formation in the last ∼1 Gyr. This detection can profoundly impact the formation models for black holes and their hosts. We propose that winds from a population of ∼100 evolved stars within the Bondi radius of the SMBH produce a sizable accretion rate, with Eddington ratios between 9 × 10−8 and 9 × 10−7, depending on the value of the stellar mass loss. These rates are typical of SMBHs accreting in advection-dominated accretion flow mode. The predicted spectrum peaks in the microwaves at ∼0.1–1 THz (300–3000 μm) and exhibits significant variations at higher energies depending on the accretion rate. We predict a radio flux of ∼0.1 mJy at 6 GHz, mildly dependent on the accretion properties. Deep imaging with Chandra, the Very Large Array, and the Atacama Large Millimeter/submillimeter Array can confirm the presence of this SMBH and constrain its accretion flow.

Quest for realistic non-singular black-hole geometries: regular-center type

We propose seven criteria to single out physically reasonable non-singular black-hole models and adopt them to four different spherically symmetric models with a regular center and their rotating counterparts. In general relativity, all such non-singular black holes are non-generic with a certain matter field including a class of nonlinear electromagnetic fields. According to a criterion that the effective energy-momentum tensor should satisfy all the standard energy conditions in asymptotically flat regions, the well- known Bardeen and Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang black holes respect the dominant energy condition everywhere. Although the rotating Fan-Wang black hole contains a curvature singularity, the rotating Dymnikova black hole is free from scalar polynomial curvature singularities and closed timelike curves. In addition, the dominant energy condition is respected on and outside the event horizons in the latter case. The absence of parallelly propagated curvature singularities remains an open question.

GRRMHD simulations of MAD accretion discs declining from super-Eddington to sub-Eddington accretion rates

ABSTRACT We present two general relativistic radiation magnetohydrodynamics (GRRMHD) simulations of magnetically arrested discs (MADs) around non-spinning (a* = 0) and spinning (a* = 0.9) supermassive black holes (BHs). In each simulation, the mass accretion rate is decreased with time such that we sample Eddington-scaled rates over the range $3 \gtrsim \dot{M}/\dot{M}_{\rm {Edd}}\gtrsim 0.3$. For the non-spinning BH model, the total and radiative efficiencies increase as the accretion rate decreases, varying over the range $\eta _{\rm {tot}}\sim 9\!-\!16{{\ \rm per\ cent}}$ and $\eta _{\rm {rad}}\sim 6{-}12{{\ \rm per\ cent}}$, respectively. This model shows very little jet activity. In contrast, the spinning BH model has a strong relativistic jet powered by spin energy extracted from the BH. The jet power declines with accretion rate such that $\eta _{\rm {jet}}\sim 18{-}39{{\ \rm per\ cent}}$ while the total and radiative efficiencies are $\eta _{\rm {tot}}\sim 64{-}100{{\ \rm per\ cent}}$ and $\eta _{\rm {rad}}\sim 45{-}79{{\ \rm per\ cent}}$, respectively. We confirm that mildly sub-Eddington discs can extract substantial power from a spinning BH, provided they are in the MAD state. The jet profile out to $100\, GM/c^2$ is roughly parabolic with a power-law index of k ≈ 0.43−0.53 during the sub-Eddington evolution. Both models show significant variability in the outgoing radiation which is likely associated with episodes of magnetic flux eruptions. The a* = 0.9 model shows semiregular variations with a period of $\sim 2000\, GM/c^3$ over the final $\sim 10\, 000\, GM/c^3$ of the simulation, which suggests that magnetic flux eruptions may be an important source of quasi-periodic variability. For the simulated accretion rates, the a* = 0 model is spinning up while the a* = 0.9 model is spinning down. Spinup–spindown equilibrium of the BH will likely be achieved at 0.5 < a*, eq < 0.6, assuming continuous accretion in the MAD state.

Loop Quantum Gravity motivated multihorizon rotating black holes

With a semiclassical polymerization in the loop quantum gravity (LQG), the interior of the Schwarzschild black holes provides a captivating single-horizon regular black hole spacetime. The shortage of rotating black hole models in loop quantum gravity (LQG) substantially restrains the progress of testing LQG from observations. Motivated by this, starting with a spherical LQG black hole as a seed metric, we construct a rotating spacetime using the revised Newman-Janis algorithm, namely, the LQG-motivated rotating black holes (LMRBH), which encompasses Kerr (l = 0) black holes as an exceptional case. We discover that for any random l > 0, unlike Kerr black hole, an extremal LMRBH refers to a black hole with angular momentum a > M. The rotating metric, in parameter space, describes (1) black holes with an event and Cauchy horizon, (2) black holes with three horizons, (3) black holes with only one horizon or (4) no horizon spacetime. We also discuss the horizon and global structure of the LMRBH spacetimes and its dependence on l/M that exhibits rich spacetime structures in the (M, a, l) parameter space.

Signatures of extra dimensions in black hole jets

One of the leading mechanisms powering relativistic black hole jets is the Blandford-Znajek (BZ) process. Inspired by its success we construct energy extracting models for black holes in five space-time dimensions. Here, we find solutions to the force-free electrodynamic equations representing plasma-magnetospheres for slowly rotating Myers-Perry black holes. Both, energy and angular momentum fluxes are computed for these solutions realizing power extraction from black holes in higher dimensions. Comparisons of the main features of the five-dimensional BZ models with lower four-dimensional counterparts are discussed.

Page curve and symmetries

Motivated by the quantum process of black hole evaporation and its implications for symmetries, we consider a qubit system with a random dynamics as a toy model of black hole. We compute its symmetry-resolved entropies and discuss its implications. We first consider the case where charges are conserved and compute the symmetry-resolved entropies. We derive a symmetry-resolved analogue of the Page curve. We then consider the case where symmetry is explicitly broken and charges are no longer conserved. It serves as a toy model for global symmetry breaking in black hole evaporation. Despite the simple framework, the symmetry-resolved entropies capture various interesting features during the analogous process of black hole evaporation in our qubit model.

Compact extra dimensions as the source of primordial black holes

This article discusses a model of primordial black hole (PBH) formation at the reheating stage. These small/massive black holes appear due to the specific properties of the compact extra dimensions. The latter gives rise to the low energy model, containing an effective scalar field potential capable of domain wall production. Formed during inflation, these walls are quite dense, meaning they collapse soon after inflation ends. Discussion of the model is framed by the scope of multidimensional f(R)-gravity. We study the possibility of the pure gravitational formation of primordial black holes (PBHs). Interpreting the scalar curvature of compact extra space Rn as an effective scalar field in an Einstein framework and consider effective scalar-field theory that might potentially be capable of producing domain walls with a certain choice of parameters. Hence, we demonstrate that f(R)-gravity contains a mechanism for PBH formation. The study assumed that cosmological inflation is an external process, which satisfied all the cosmological constraints on our mechanism.

Conformally Schwarzschild cosmological black holes

We thoroughly investigate conformally Schwarzschild spacetimes in different coordinate systems to seek for physically reasonable models of a cosmological black hole. We assume that a conformal factor depends only on the time coordinate and that the spacetime is asymptotically flat Friedmann–Lemaître–Robertson–Walker Universe filled by a perfect fluid obeying a linear equation state p = wρ with w > −1/3. In this class of spacetimes, the McClure–Dyer spacetime, constructed in terms of the isotropic coordinates, and the Thakurta spacetime, constructed in terms of the standard Schwarzschild coordinates, are identical and do not describe a cosmological black hole. In contrast, the Sultana–Dyer and Culetu classes of spacetimes, constructed in terms of the Kerr–Schild and Painlevé–Gullstrand coordinates, respectively, describe a cosmological black hole. In the Sultana–Dyer case, the corresponding matter field in general relativity can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous null fluid, which is valid everywhere in the spacetime unlike Sultana and Dyer’s interpretation. In the Culetu case, the matter field can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous anisotropic fluid. However, in both cases, the total energy–momentum tensor violates all the standard energy conditions at a finite value of the radial coordinate in late times. As a consequence, the Sultana–Dyer and Culetu black holes for −1/3 < w ⩽ 1 cannot describe the evolution of a primordial black hole after its horizon entry.

Regular black holes without mass inflation instability

Generic models of regular black holes have separate outer and inner horizons, both with nonzero surface gravity. It has been shown that a nonzero inner horizon surface gravity results in exponential instability at the inner horizon controlled by this parameter. This phenomenon takes the name of “mass inflation instability”, and its presence has put in question the physical viability of regular black holes as alternatives to their (singular) general relativity counterparts. In this paper, we show that it is possible to make the inner horizon surface gravity vanish, while maintaining the separation between horizons, and a non-zero outer horizon surface gravity. We construct specific geometries satisfying these requirements, and analyze their behavior under different kinds of perturbations, showing that the exponential growth characteristic of mass inflation instability is not present for these geometries. These “inner-extremal” regular black holes are thereby better behaved than singular black holes and generic regular black holes, thus providing a well-motivated alternative of interest for fundamental and phenomenological studies.

Space of solutions of the Ashtekar-Olmedo-Singh effective black hole model

We consider a general choice of integration constants in the resolution of the dynamical equations derived from a recently proposed effective model that describes black hole spacetimes in the context of loop quantum cosmology. The interest of our analysis is twofold. On the one hand, it allows for a study of the entire space of solutions of the model, which is absent in the literature and is fundamental for understanding the relation with any underlying quantum theory. On the other hand, choices of integration constants that generalize the type of solutions considered so far may lead to exotic behaviors in the effective black hole geometry, as well as modified thermodynamical properties. With these motivations in mind, we discuss the interior and exterior geometries, and present the conditions that a satisfactory matching at the horizons imposes. Then, we turn our attention to the Hawking temperature associated with the black horizon of the model, which we find to be affected by the freedom of choice of integration constants. Finally, we briefly comment on the asymptotic structure of the general solution and compare different notions of mass.

Holes in the atmosphere of the universe: An empirical qualitative study on mental models of students regarding black holes

Black holes are both interesting to many students and are part of several school and university curricula. However, it has not yet been documented in detail what kind of mental models of black holes students have. As such, this study qualitatively reports on the mental models of 53 university students, most of them with a non-physics major. The gestalts of the mental models found were mostly disc shaped holes or black spheres, though some funnels or ellipsoids were also described by the students. As for the functionality, students associated attractive functions with a black hole, though more elaborate descriptions such as time dilation or gravitational lensing and Hawking radiation were also named. All university students described a kind of black hole creation, though not all knew about their change in time and only described growth or could not give founded reasons for the change. Several participants showed potential problems by seeing their mental model as a direct replica of reality and assumed that black holes were literally holes. Conceptual problems regarding things “behind” the holes were raised. The results show that many rudimentary properties of black holes are known to university students without explicit education in that field, and a surprising amount of physics quantities were associated with them, although things like density or mass were described inadequately in several cases. Though mental models of black holes were not documented this extensively before, parallels in thinking with mental models in other areas of physics could be observed, making the findings consistent with literature.

Internal structure and its connection with thermodynamics and dynamics in black holes

In general, a finite metric function at the center of a black hole describes a non-singular spacetime but an infinite metric at the center gives a singular spacetime, where the former is associated with convergent Ricci and Kretschmann scalars together with complete radial geodesics, while the latter is related to divergent Ricci and Kretschmann scalars together with incomplete radial geodesics. For the charged black hole in the four-dimensional Einstein-Gauss-Bonnet theory, we find that its metric function is finite at its center in one region of parameters but complex in the other region of parameters. The finite case describes a strange spacetime which presents the Ricci and Kretschmann scalars of a singular spacetime and the radial geodesics of a non-singular spacetime, while the complex case gives rise to the similar situation. We verify that the cosmic censorship conjecture is maintained for the black hole model. Further, we investigate the second-order phase transition, quasinormal modes of perturbation of a test scalar field in the eikonal limit, and shadow radius for the black hole and find that the thermodynamic and dynamic properties depend on the metrics. In this way, we connect the internal structure with the thermodynamics and dynamics for this black hole. Moreover, we compare such a black hole of modified gravity with the Reissner-Nordström black hole of Einstein's general relativity in these thermodynamic and dynamic properties.

Annihilation-to-nothing: DeWitt boundary condition inside a black hole

In canonical quantum gravity, the wave function for a hypersurface inside a Schwarzschild black hole can be obtained by solving the Wheeler–DeWitt equation. What is of prime importance is the behavior of the wave function for the future boundary near the singularity, and the DeWitt boundary condition implies that it should vanish here. In this paper, we provide several generalizations, and new interpretations, of the DeWitt boundary condition. First, we summarize existing works on the wave function inside the black hole to justify the DeWitt boundary condition. Next, we investigate the wave function for the collapsing null shell to show that due to the reflection symmetry in space and time, there exists a destructive interference near the singularity and hence a vanishing boundary condition can be natural. If we extend this point of view to the black hole spacetime itself, then the DeWitt boundary condition is equivalent to saying that there exists a symmetric anti-black hole contribution, such that eventually these two geometries are annihilated-to-nothing near the quantum transition surface. This symmetric model can be realized within black hole models of loop quantum gravity with a novel interpretation for the arrow(s) of time.

The black hole of traffic

Car pileups due to low visibility on the road offer an analog model for black holes that may help prevent accidents.

Cosmic Explorer: A Next-Generation Ground-Based Gravitational-Wave Observatory

Cosmic Explorer is a concept for a new laser interferometric observatory in the United States to extend ground-based gravitational-wave astrophysics into the coming decades. Aiming to begin operation in the 2030s, Cosmic Explorer will extend current and future detector technologies to a 40 km interferometric baseline—ten times larger than the LIGO observatories. Operating as part of a global gravitational-wave observatory network, Cosmic Explorer will have a cosmological reach, detecting black holes and neutron stars back to the times of earliest star formation. It will observe nearby binary collisions with enough precision to reveal details of the dynamics of the ultradense matter in neutron stars and to test the general-relativistic model of black holes.

The discovery of the oldest supermassive black hole

<p indent="0mm">On December 20, 2021, the website of <italic>Science News</italic> summarized “6 surprising records science set in 2021”, including the oldest black hole discovered by astronomers. These new findings extend the limits of scientific research and the imagination of human beings. Here we present a brief introduction to the discovery of the oldest black hole in the early Universe and its importance in science, and give some prospects of the related studies in the future. Quasars are luminous active galactic nuclei with supermassive black holes (SMBHs) in their centers, accreting the surrounding gas and emitting huge power. Distant quasars are unique tracers to study the formation of the earliest SMBHs and the history of cosmic reionization. On January 14, 2021, in a paper appeared in the <italic>Astrophysical Journal Letters</italic>, an international team led by Dr. Feige Wang, Dr. Jinyi Yang and Prof. Xiaohui Fan at University of Arizona reported the discovery of a luminous quasar J0313-1806 at redshift 7.64. This discovery breaks the former redshift record, 7.54 for the quasar J1342+0928, making J0313-1806 the most distant quasar discovered so far, with a distance of about 13 billion light years from us. The near-infrared spectra taken with several largest ground based telescopes reveal the existence of a black hole of 1.6 billion solar masses in the center of J0313-1806. It becomes the oldest black hole in the early Universe, with the age of only 670 million years after the Big Bang. How can a black hole grow to 1.6 billion solar masses within 670 million years (only about 5% of the universe’s current age)? The discovery of the oldest black hole provides the most serious challenge to the current understanding of the black hole formation and growth. SMBHs are thought to grow from smaller seed black holes that accrete the surrounding matter. The popular idea is that the seed black holes formed through the collapse of the first generation massive stars (or population III stars), but this can only make the seed black holes up to a few hundred solar masses in most cases, or up to a few thousand solar masses for the extreme cases in the dense stellar clusters. However, even if we assume that J0313-1806’s seed black hole grew as fast as possible, it would have needed a starting mass of at least 10000 solar masses at redshift 30. Among the theoretical models currently known, only the direct collapse black hole (DCBH) model involving the vast amounts of primordial cold hydrogen gas can provide a possible explanation. In addition, J0313-1806 also shows many important features. The rest-frame UV spectrum exhibits broad absorption troughs, which are thought to be produced by the extremely high-velocity outflows launched from the accretion disk around the central black hole. These outflows have a maximum velocity up to 20% of the speed of light, and can provide strong feedbacks to affect the star formation in the quasar host galaxy due to the extremely high kinetic power. J0313-1806’s host galaxy has a very rapid star formation process, with the star formation rate 200 times higher than the Milky Way. Together with its huge luminosity of 36 trillion times higher than the Sun, J0313-1806 has become one of the most important targets to study the formation and growth of the supermassive black holes, as well as their influences on the host galaxies in the early Universe. There will be more observations on the oldest black hole in the near future. The James Webb Space Telescope (JWST) was successfully launched on December 25, 2021. The team who discovered the oldest black hole has been awarded the JWST time of more than two hundred hours. More surprising discoveries are expected to be revealed by the future JWST observations on the most distant black holes, galaxies and quasars in the epoch of cosmic reionization.

Black Hole–Black Hole Total Merger Mass and the Origin of LIGO/Virgo Sources

The LIGO–Virgo–KAGRA (LVK) Collaboration has reported nearly 100 black hole (BH)–BH mergers. LVK provides estimates of rates, masses, effective spins, and redshifts for these mergers. Yet the formation channel(s) of the mergers remains uncertain. One way to search for a formation site is to contrast the properties of detected BH–BH mergers with different models of BH–BH merger formation. Our study is designed to investigate the usefulness of the total BH–BH merger mass and its evolution with redshift in establishing the origin of gravitational-wave sources. We find that the average intrinsic BH–BH total merger mass shows exceptionally different behaviors for the models that we adopt for our analysis. In the local universe (z = 0), the average merger mass changes from for the common envelope binary evolution and open cluster formation channels, to for the stable Roche lobe overflow binary channel, to for the globular cluster channel. These differences are even more pronounced at larger redshifts. However, these differences are diminished when considering the LVK O3 detector sensitivity. A comparison with the LVK O3 data shows that none of our adopted models can match the data, despite the large errors on BH–BH masses and redshifts. We emphasize that our conclusions are derived from a small set of six models that are subject to numerous known uncertainties. We also note that BH–BH mergers may originate from a mix of several channels, and that other (than those adopted here) BH–BH formation channels may exist.

Black Holes as the Source of All Matter and Radiation in the Universe

An in-depth study of general relativity has led to the development of a theory, CBU for the continuously breeding universe, in which the universe emerges from a quantum fluctuation and continues to expand due to the inflow of new matter, foremostly electrons and positrons. According to a novel model for black holes, a continuous inflow of matter prevents the black holes from becoming singularities, the contraction pressure is counteracted by the expansion pressure. The study shows that the gravitational energy gap between the event horizon and the inner photon sphere of a black hole is the source of incoming real matter from a QED vacuum foam of virtual particles. The calculated CBU results are in good agreement with current observations.