Nonsingular Black Hole Research Articles

Scalar fields around a rotating loop quantum gravity black hole: waveform, quasi-normal modes and superradiance

Abstract The rotating loop quantum gravity black hole is a newly proposed non-singular black hole, which eliminates spacetime singularities when a regularization parameter is introduced through loop quantum corrections. This parameter is expected to give rise to observable effects. In this paper, the dynamical behavior of a scalar field near a rotating loop quantum gravity black hole is investigated. Given a small initial perturbation, we obtain the waveform of massless scalar fields evolving over time. By analyzing the waveform, we find that the regularization parameter only affects the damping oscillation of waveform, but not the initial outburst and late-time tail stages. This behavior is characterized by quasi-normal modes (QNMs). Under scalar field perturbations, the loop quantum black holes remain stable. Moreover, we calculate the QNMs of massive scalar fields by three numerical methods, which are the Prony, WKB, and shooting methods, respectively. Our results indicate that the real part of QNMs increases when the regularization parameter and angular momentum grow, while the imaginary part depends on the two parameters with a more complex relationship. Finally, we study the amplification effect of rotating black holes, i.e. the superradiance. Our analyses indicate the existence of stronger superradiance around loop quantum gravity black holes compared to Kerr ones.

Observational redshift from general spherically symmetric black holes

In this work, we obtain an expression for the total observational frequency shift of photons emitted by massive geodesic particles circularly orbiting a black hole in a general spherically symmetric background. Our general relations are presented in terms of the metric components and their derivatives that characterize the black hole parameters. As a concrete example of this general relativistic approach, a special case is studied by applying the formalism to a nonsingular black hole conformally related to the Schwarzchild solution that possesses a length scale parameter l and an integer parameter N in addition to the black hole mass. Besides, we express the nonsingular black hole mass in terms of the observational redshift/blueshift. Finally, we investigate the effects of the free parameters of the conformal gravity theory on the observational frequency shift and compare results with those of the standard Schwarzschild black hole.

Images of nonsingular nonrotating black holes in conformal gravity

The accretion disk around a black hole and its emissions play an essential role in theoretical analysis of the black hole image. In the literature, two analytical toy models of accretions are widely adopted: the spherical model and the thin disk model. They are different geometrically but both thin optically. We polish them for free-falling accretions around static spherical black holes. As an application, we investigate the images of a class of nonsingular black holes conformally related to the Schwarzschild black hole. These black holes are vacuum solutions of a family of conformal gravity theories. Results are compared with the Schwarzschild black hole of the same mass. Our results indicate that the conformal factor does not affect the shadow radius seen by distant observers, but it leaves an imprint on the intensity image of black hole.

Remnant loop quantum black holes

Polymer models inspired by Loop Quantum Gravity (LQG) have been used to describe non-singular quantum black holes with spherical symmetry, with the classical singularity replaced by a transition from a black hole to a white hole. A recent model, with a single polymerisation parameter, leads to a symmetric transition with same mass for the black and white phases, and to an asymptotically flat exterior metric. The radius of the transition surface is, however, not fixed, increasing with the mass. Following similar procedures, in a previous paper we have fixed that radius by identifying the minimal area on the transition surface with the area gap of LQG. This allowed to find a dependence of the polimarisation parameter on the black hole mass, with the former increasing as the latter decreases. It also permitted to extend the model to Planck scale black holes, with quantum fluctuations remaining small at the horizon. In the present letter we extend this analysis to charged black holes, showing that the Cauchy horizon lies beyond of the transition surface. We also show the existence of limiting states with zero surface gravity, the lightest one with Q = 0 and m=2/4 , and the heaviest with Q=m=2/2 . Using our solutions to approximate quasi-steady horizons, we show that Hawking evaporation leads asymptotically to these extremal states, leaving remnant black holes of Planck size.

Optical appearance of a nonsingular de Sitter core black hole geometry under several thin disk emissions

Optical appearance of a nonsingular de Sitter core black hole geometry under several thin disk emissions

Regular black hole from a confined spin connection in Poincaré gauge gravity

Within the asymptotic safety program, it is possible to construct renormalization group (RG) improved spacetimes by replacing the gravitational coupling G by its running counterpart G(k), and subsequently identifying the RG scale k with a physical distance scale. This procedure has been used to construct a regular Schwarzschild geometry, but it fails in the presence of a cosmological constant. This can only be avoided if the dimensionless cosmological constant has a trivial ultraviolet fixed point, but so far no such scenario has been encountered in quantum general relativity (with or without matter). In this Letter we provide a possible solution to this problem. In Poincaré gauge gravity an effective cosmological constant arises naturally, and if the non-Abelian Lorentz spin connection is asymptotically free, it generates a trivial ultraviolet fixed point for this cosmological constant. We thereby tentatively propose a nonsingular black hole consistent with the principles of asymptotic safety, embedded in Poincaré gauge gravity.

A comment on “Singular and nonsingular black holes using the Gaussian distribution”

In this work, we join the controversial discussion on singular and nonsingular black holes using the Gaussian distribution. Our result which uses correct boundary conditions shifts the debate in favor of regular black holes at the center. The present findings add new insights into the ongoing discussions surrounding singularities in black hole solutions of the Einstein equations.

Cosmological coupling of nonsingular black holes

We show that — in the framework of general relativity (GR) — if black holes (BHs) are singularity-free objects, they couple to the large-scale cosmological dynamics. We find that the leading contribution to the resulting growth of the BH mass (M BH) as a function of the scale factor a stems from the curvature term, yielding M BH ∝ ak , with k = 1. We demonstrate that such a linear scaling is universal for spherically-symmetric objects, and it is the only contribution in the case of regular BHs. For nonsingular horizonless compact objects we instead obtain an additional subleading model-dependent term. We conclude that GR nonsingular BHs/horizonless compact objects, although cosmologically coupled, are unlikely to be the source of dark energy. We test our prediction with astrophysical data by analysing the redshift dependence of the mass growth of supermassive BHs in a sample of elliptical galaxies at redshift z = 0.8–0.9. We also compare our theoretical prediction with higher redshift BH mass measurements obtained with the James Webb Space Telescope (JWST). We find that, while k = 1 is compatible within 1σ with JWST results, the data from elliptical galaxies at z = 0.8–0.9 favour values of k > 1. New samples of BHs covering larger mass and redshift ranges and more precise BH mass measurements are required to settle the issue.

Shadow and deflection angle of asymptotic, magnetically-charged, non-singular black hole

In this paper, we investigate a solution for an asymptotic, magnetically-charged, non-singular (AMCNS) black hole. By utilizing the Gauss–Bonnet theorems, we aim to unravel the intricate astrophysics associated with this unique black hole. The study explored various aspects including the black hole’s gravitational field, intrinsic properties, light bending, the shadow and greybody bounding of the black hole. Through rigorous calculations and simulations, we derive the weak deflection angle of the optical metric of AMCNS black hole. Additionally, we investigate the impact of the dark matter medium on the deflection angle, examined the distinctive features of the black hole’s shadow, and bound its greybody factors. Our findings not only deepen our understanding of gravitational lensing but also pave the way for future improvements in black hole theories by minimizing restrictive assumptions and incorporating a more realistic representation of these cosmic phenomena.

Evaporation and information puzzle for 2D nonsingular asymptotically flat black holes

We investigate the thermodynamics and the classical and semiclassical dynamics of two-dimensional (2D), asymptotically flat, nonsingular dilatonic black holes. They are characterized by a de Sitter core, allowing for the smearing of the classical singularity, and by the presence of two horizons with a related extremal configuration. For concreteness, we focus on a 2D version of the Hayward black hole. We find a second order thermodynamic phase transition, separating large unstable black holes from stable configurations close to extremality. We first describe the black-hole evaporation process using a quasistatic approximation and we show that it ends in the extremal configuration in an infinite amount of time. We go beyond the quasistatic approximation by numerically integrating the field equations for 2D dilaton gravity coupled to N massless scalar fields, describing the radiation. We find that the inclusion of large backreaction effects (N ≫ 1) allows for an end-point extremal configuration after a finite evaporation time. Finally, we evaluate the entanglement entropy (EE) of the radiation in the quasistatic approximation and construct the relative Page curve. We find that the EE initially grows, reaches a maximum and then goes down towards zero, in agreement with previous results in the literature. Despite the breakdown of the semiclassical approximation prevents the description of the evaporation process near extremality, we have a clear indication that the end point of the evaporation is a regular, extremal state with vanishing EE of the radiation. This suggests that the nonunitary evolution, which commonly characterizes the evaporation of singular black holes, could be traced back to the presence of the singularity.

Nonsingular black holes from conformal symmetries

We derive the form of the metric for static, nonsingular black holes with a de Sitter core, representing a deformation of the Schwarzschild solution, by assuming that the gravitational sources describe a flow between two conformal points, at small and great distances. The resulting black-hole metric turns out to be a particular case of the Fan & Wang metric, whose parameters have been recently constrained by using the data of the S2 star orbits around the galactic center SgrA.

Quantum vacuum effects on the formation of black holes

We study the backreaction of quantum fields induced through the vacuum polarization and the conformal anomaly on the collapse of a thin shell of dust. It is shown that the final fate of the collapse process depends on the physical properties of the shell, including its rest and gravitational masses. Investigating the conditions for the formation of black holes, we notice that quantum effects modify the geometry and structure of Schwarzschild space-time in such a way that black holes have two horizons, an inner and an outer horizon. If the gravitational mass of the shell is about that of an ordinary star, then in most cases, the semi-classical collapse will terminate in a singularity, and in general, quantum fluctuations are not strong enough to prevent the creation of the singularity. Although under certain conditions, it is possible to form a non-singular black hole, i.e., a regular black hole. In this way, the collapse stops at a radius much larger than the Planck length below the inner horizon, and the shell bounces and starts an expansion.

Strong lensing and shadow of Ayon-Beato–Garcia (ABG) nonsingular black hole

We study nonsingular black holes viewed from the point of view of Ayon-Beato–Garcia (ABG) nonlinear electrodynamics (NLED) and present a complete study of their corresponding strong gravitational lensing. The NLED modifies the the photon’s geodesic, and our calculations show that such effect increases the corresponding photon sphere radius and image separation, but decreases the magnification. We also show that the ABG’s shadow radius is not compatible with bound estimates of Sgr A* from Keck and VLTI (Very Large Telescope Interferometer). Thus, the possibility of Sgr A* being a nonsingular ABG black hole is ruled out.

Generic features of a polymer quantum black hole

Non-singular black holes models can be described by modified classical equations motivated by loop quantum gravity. We investigate what happens when the sine function typically used in the modification is replaced by an arbitrary bounded function, a generalization meant to study the effect of ambiguities such as the choice of representation of the holonomy. A number of features can be determined without committing to a specific choice of functions. We find generic singularity resolution. The presence and number of horizons is determined by global features of the function regularizing the angular components of the connection, and the presence and number of bounces by global features of the function regularizing the time component. The trapping or anti-trapping nature of regions inside horizons depends on the relative location with respect to eventual bounces. We use these results to comment on some of the ambiguities of polymer black hole models.

Black holes without Cauchy horizons and integrable singularities

In general relativity, nonsingular black holes contain (at least) a Cauchy horizon, a null hypersurface beyond which determinism breaks down. Even though the strong cosmic censorship conjecture establishes the impossibility of extending spacetime beyond this region, in this paper we investigate how far we can go, without invoking this conjecture, in the building of a physically reasonable black hole without a Cauchy hypersurface. Following this reasoning, we find a black hole lacking of Cauchy horizon, asymptotically flat and satisfying either the strong or dominant energy condition. The above is possible by demanding integrable singularity for the Ricci scalar, whose direct consequence is the appearance of finite tidal forces. We show that the spacetime inside the event horizon represents a warped anti-de Sitter spacetime, which might be interpreted in terms of a finite superposition of configurations.

Vacuum-dual static perfect fluid obeying in dimensions

We obtain the general -dimensional static solution with an -dimensional Einstein base manifold for a perfect fluid obeying a linear equation of state . It is a generalization of Semiz’s four-dimensional general solution with spherical symmetry and consists of two different classes. Through the Buchdahl transformation, the class-I and class-II solutions are dual to the topological Schwarzschild–Tangherlini-(A)dS solution and one of the Λ-vacuum direct-product solutions, respectively. While the metric of the spherically symmetric class-I solution is at the Killing horizon for n = 4 and 5, it is C 1 for and then the Killing horizon turns to be a parallelly propagated curvature singularity. For n = 4 and 5, the spherically symmetric class-I solution can be attached to the Schwarzschild–Tangherlini vacuum black hole with the same value of the mass parameter at the Killing horizon in a regular manner, namely without a lightlike massive thin-shell. This construction allows new configurations of an asymptotically (locally) flat black hole to emerge. If a static perfect fluid hovers outside a vacuum black hole, its energy density is negative. In contrast, if the dynamical region inside the event horizon of a vacuum black hole is replaced by the class-I solution, the corresponding matter field is an anisotropic fluid and may satisfy the null and strong energy conditions. While the latter configuration always involves a spacelike singularity inside the horizon for n = 4, it becomes a non-singular black hole of the big-bounce type for n = 5 if the ADM mass is larger than a critical value.

Are nonsingular black holes with super-Planckian hair ruled out by S2 star data?

We investigate a nonsingular black hole spacetime representing a strong deformation of the Schwarzschild solution with mass $M$ by an additional hair $\ensuremath{\ell}$, which may be hierarchically larger than the Planck scale. The spacetime is an exact solution of Einstein's equations sourced by an anisotropic fluid. The model presents a de Sitter core and $\mathcal{O}({\ensuremath{\ell}}^{2}/{r}^{2})$ slow-decaying corrections to the Schwarzschild solution. These solutions are thermodynamically preferred when $0.2\ensuremath{\lesssim}\ensuremath{\ell}/GM\ensuremath{\lesssim}0.3$ and are characterized by strong deviations in the orbits of test particles from the Schwarzschild case. In particular, we find corrections to the perihelion precession angle scaling linearly with $\ensuremath{\ell}$. We test our model using the available data for the orbits of the S2 star around ${\text{SgrA}}^{*}$. These data strongly constrain the value of the hair $\ensuremath{\ell}$, casting an upper bound on it of $\ensuremath{\sim}0.47GM$ but do not rule out the possible existence of regular black holes with super-Planckian hair.

Nonsingular black hole chemistry in 4D Einstein-Gauss-Bonnet gravity

The EGB is an outcome of quadratic curvature corrections to the Einstein-Hilbert gravity action in the form of a Gauss-Bonnet (GB) term in D>4 dimensions, and EGB gravity is topologically invariant in 4D. Several ways have been proposed for regularizing the D→4 limit of EGB for non-trivial gravitational dynamics in 4D. Motivated by the importance of AdS/CFT, we obtain an exact static spherically symmetric nonsingular black hole in 4D EGB gravity coupled to the nonlinear electrodynamics (NED) in an AdS spacetime. We interpret the negative cosmological constant Λ as the positive pressure, via P=−Λ/8π, of the system's thermodynamic properties of the nonsingular black hole with an AdS background. We find that for P<Pc, the black holes with CP>0 are stable to thermal fluctuations and unstable otherwise. We also analyzed the Gibbs free energy to find that the small globally unstable black holes undergo a phase transition to the large globally stable black holes. Further, we study the P−V criticality of the system and then calculate the critical exponents to find that our system behaves like Van der Walls fluid.

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.

Dynamics and stability of Bardeen-de Sitter thin shell wormholes

A dynamical equation of thin-shell wormhole joining two identical copies of non-singular Bardeen-de Sitter black hole spacetime through the cut and paste techniques is constructed. The stability of the Bardeen-de Sitter wormhole, as the static solution of linear perturbation at the wormhole throat and a variable modified generalized Chaplygin gas equation of state, is analyzed.The existence of stability configurations depends on the particular values of different parameters involved in the equation of state as well as the space-time metric performed. The existence of Bardeen-de Sitter parameters and the equation of state parameters to enlarge the stability regions may be obtained.