Loop Quantum Black Hole Research Articles

Quasi-normal modes of loop quantum black holes formed from gravitational collapse

In this paper, we study the quasi-normal modes (QNMs) of a scalar field in the background of a large class of quantum black holes that can be formed from gravitational collapse of a dust fluid in the framework of effective loop quantum gravity. The loop quantum black holes (LQBHs) are characterized by three free parameters, one of which is the mass parameter, while the other two are purely due to quantum geometric effects. Among these two quantum parameters, one is completely fixed by black hole thermodynamics and its effects are negligible for macroscopic black holes, while the second parameter is completely free (in principle). In the studies of the QNMs of such LQBHs, we pay particular attention to the difference of the QNMs between LQBHs and classical ones, so that they can be observed for the current and forthcoming gravitational wave observations, whereby place the LQBH theory directly under the test of observations.

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.

Effective four-dimensional loop quantum black hole with a cosmological constant

Effective four-dimensional loop quantum black hole with a cosmological constant

Enhanced Blandford Znajek jet in loop quantum black hole

The Blandford-Znajek (BZ) process powers energetic jets by extracting the rotating energy of a Kerr black hole. It is important to understand this process in non-Kerr black hole spacetimes. In this study, we conduct two-dimensional and three-dimensional two-temperature General Relativistic Magnetohydrodynamic (GRMHD) simulations of magnetized accretion flows onto a rotating Loop-Quantum black hole (LQBH). Our investigation focuses on the accretion flow structure and jet launching dynamics from our simulations.We observe that the loop quantum effects increase the black hole angular frequency for spinning black holes.This phenomenon intensifies the frame-dragging effect, leading to an amplification of the toroidal magnetic field within the funnel region and enhancement of the launching jet power.It is possible to fit the jet power following a similar fitting formula of the black hole angular frequency as seen in the Kerr black hole.Based on the General Relativistic Radiation Transfer (GRRT) calculation, we find that the jet image from LQBH has a wider opening angle and an extended structure than the Kerr BH.

On the improved dynamics approach in loop quantum black holes

In this paper, we consider the Böhmer–Vandersloot (BV) model of loop quantum black holes obtained from the improved dynamics approach. We adopt the Saini–Singh gauge, in which it was found analytically that the BV spacetime is geodesically complete. We show that black/white hole horizons do not exist in this geodesically complete spacetime. Instead, there exists only an infinite number of transition surfaces, which always separate trapped regions from anti-trapped ones. Comments on the improved dynamics approach adopted in other models of loop quantum black holes are also given.

Constraints from Solar System tests on a covariant loop quantum black hole

Constraints from Solar System tests on a covariant loop quantum black hole

Shadows of loop quantum black holes: semi-analytical simulations of loop quantum gravity effects on Sagittarius A* and M87*

In this study, we delve into the observational implications of rotating Loop Quantum Black Holes (LQBHs) within an astrophysical framework. We employ semi-analytical General Relativistic Radiative Transfer (GRRT) computations to study the emission from the accretion flow around LQBHs. Our findings indicate that the increase of Loop Quantum Gravity (LQG) effects results in an enlargement of the rings from LQBHs, thereby causing a more circular polarization pattern in the shadow images. We make comparisons with the Event Horizon Telescope (EHT) observations of Sgr A* and M87*, which enable us to determine an upper limit for the polymetric function P in LQG. The upper limit for Sgr A* is 0.2, while for M87* it is 0.07. Both black holes exhibit a preference for a relatively high spin (a ≳ 0.5 for Sgr A* and 0.5 ≲ a ≲ 0.7 for M87*). The constraints for Sgr A* are based on black hole spin and ring diameter, whereas for M87*, the constraints are further tightened by the polarimetric pattern. In essence, our simulations provide observational constraints on the effect of LQG in supermassive black holes (SMBH), providing the most consistent comparison with observation.

Estimation of Correction of Ground State Energy of Hydrogen Atom in Presence of Quadratic GUP

Abstract: String Theory, Quantum Geometry, Loop Quantum Gravity and Black Hole physic all predict the existence of a observable minimal length at Planck scale. For example, in case of string theory it is conjectured that a particle described as a string does not interact at distances smaller than its size. As a consequence, the HUP has to be generalized to take into account this aspect. The models which are designed to implement the minimal length scale and/or the maximum momentum in different physical systems entered into the literature as the Generalized Uncertainty Principle (GUP). Here, quadratic GUP model has been used to estimate the quantum-gravitational correction of ground state energy of hydrogen atom (H-atom).

Loop Quantum Black Hole

In recent decades, there has been growing interest in the quantization of black holes using techniques developed in loop quantum cosmology. Due to the quantum geometry effect, the resulting quantum-corrected black hole provides non-singular models. The quantization scheme can be roughly divided into four types: (1) the μ0 scheme, (2) the μ¯ scheme, (3) the generalized μ0 scheme, and (4) the quantum collapsing model. This paper provides an introduction of the loop quantum black hole model, a summary of the progress made in this field, as well as the quantum effective dynamics and physical applications of these models.

On the horizon area of effective loop quantum black holes

Effective models of quantum black holes inspired by loop quantum gravity (LQG) have had success in resolving the classical singularity with polymerisation procedures and by imposing the LQG area gap as a minimum area. The singularity is replaced by a hypersurface of transition from black to white holes, and a recent example is the Ashtekar, Olmedo and Singh (AOS) model for a Schwarzschild black hole. More recently, a one-parameter model, with equal masses for the black and white solutions, was suggested by Alonso-Bardaji, Brizuela and Vera (ABBV). An interesting feature of their quantisation is that the angular part of the metric retains its classical form and the horizon area is therefore the same as in the classical theory. In the present contribution we solve the dynamical equations derived from the ABBV effective Hamiltonian and, by applying the AOS minimal area condition, we obtain the scaling of the polymerisation parameter with the black hole mass. We then show that this effective model can also describe Planck scale black holes, and that the curvature and quantum corrections at the horizon are small even at this scale. By generating the exterior metric through a phase rotation in the dynamical variables, we also show that, for an asymptotic observer, the Kretschmann scalar is the same as in the classical Schwarzschild solution, but with a central mass screened by the quantum fluctuations.

Shadow of quantum extended Kruskal black hole and its super-radiance property

We perform the shadow calculation of the loop quantum gravity motivated regular black hole recently proposed by Ashtekar, Olmedo and Singh (will be termed AOS black hole hereafter). In the process, we also construct the rotating loop quantum gravity inspired solution of the originally proposed static spherically symmetric AOS black hole by applying the modified Newman-Janis algorithm. We study the quantum effects on the shadows of both the non-rotating and rotating loop quantum black hole solutions. It is observed that the general shape of the shadow for non-rotating AOS black hole is circular in shape as is expected for its classical counter part too, but the presence of loop quantum gravity inspired modification contracts the shadow radius and the effect reduces with the increase in the mass of the black hole. On a similar note, in the rotating situation, we find contraction in shadow radius due to quantum effects and the tapered nature of the shadow as expected from the classical Kerr case. However, instead of the symmetrical contraction, like non-rotating one, we found more contraction on one side relative to the other when we compare our result with the shadow of the Kerr black hole. We finally studied super-radiance in rotating AOS background and observed that the super-radiance condition for massless scalar field is identical to that of the Kerr case with the rotation of the BH being more compared to Kerr in the low mass regime. With an increase in mass of the rotating AOS black hole, the difference from Kerr starts to become insignificant.

Understanding quantum black holes from quantum reduced loop gravity

We systematically study the top-down model of loop quantum black holes (LQBHs), recently derived by Alesci, Bahrami and Pranzetti (ABP). To understand the structure of the model, we first derive several well-known LQBH solutions by taking proper limits. These include the B\"ohmer-Vandersloot and Ashtekar-Olmedo-Singh models, which were all obtained by the so-called bottom-up polymerizations within the framework of the minisuperspace quantizations. Then, we study the ABP model, and find that the inverse volume corrections become important only when the radius of the two-sphere is of the Planck size. For macroscopic black holes, the minimal radius obtained at the transition surface is always much larger than the Planck scale, and hence these corrections are always sub-leading. The transition surface divides the whole spacetime into two regions, and in one of them the spacetime is asymptotically Schwarzschild-like, while in the other region, the asymptotical behavior sensitively depends on the ratio of two spin numbers involved in the model, and can be divided into three different classes. In one class, the spacetime in the 2-planes orthogonal to the two spheres is asymptotically flat, and in the second one it is not even conformally flat, while in the third one it can be asymptotically conformally flat by properly choosing the free parameters of the model. In the latter, it is asymptotically de Sitter. However, in any of these three classes, sharply in contrast to the models obtained by the bottom-up approach, the spacetime is already geodesically complete, and no additional extensions are needed in both sides of the transition surface. In particular, identical multiple black hole and white hole structures do not exist.

Dirac Observables in the 4-Dimensional Phase Space of Ashtekar’s Variables and Spherically Symmetric Loop Quantum Black Holes

In this paper, we study a proposal put forward recently by Bodendorfer, Mele and Münch and García-Quismondo and Marugán, in which the two polymerization parameters of spherically symmetric black hole spacetimes are the Dirac observables of the four-dimensional Ashtekar’s variables. In this model, black and white hole horizons in general exist and naturally divide the spacetime into the external and internal regions. In the external region, the spacetime can be made asymptotically flat by properly choosing the dependence of the two polymerization parameters on the Ashtekar variables. Then, we find that the asymptotical behavior of the spacetime is universal, and, to the leading order, the curvature invariants are independent of the mass parameter m. For example, the Kretschmann scalar approaches zero as K≃A0r−4 asymptotically, where A0 is generally a non-zero constant and independent of m, and r the geometric radius of the two-spheres. In the internal region, all the physical quantities are finite, and the Schwarzschild black hole singularity is replaced by a transition surface whose radius is always finite and non-zero. The quantum gravitational effects are negligible near the black hole horizon for very massive black holes. However, the behavior of the spacetime across the transition surface is significantly different from all loop quantum black holes studied so far. In particular, the location of the maximum amplitude of the curvature scalars is displaced from the transition surface and depends on m; so does the maximum amplitude. In addition, the radius of the white hole is much smaller than that of the black hole, and its exact value sensitively depends on m, too.

Quasinormal modes of self-dual black holes in loop quantum gravity

We study the evolution of a test scalar field on the background geometry of a regular loop quantum black hole characterized by two loop quantum gravity correction parameters, namely, the polymeric function and the minimum area gap. The calculations of quasinormal frequencies in asymptotically flat spacetime are performed with the help of higher-order Wentzel-Kramers-Brillouin expansion and related Pad\'e approximants, the improved asymptotic iteration method, and time-domain integration. The effects of free parameters of the theory on the quasinormal modes are studied and deviations from those of the Schwarzschild black holes are investigated. We show that the loop quantum gravity correction parameters have opposite effects on the quasinormal frequencies and the loop quantum black holes are dynamically stable.

On the possible spacetime structures of rotating loop quantum black holes

To date, a mathematically consistent construction of effective rotating black hole models in the context of Loop Quantum Gravity (LQG) is still lacking. In this work, we start with the assumption that rotating LQG black hole metrics can be effectively obtained using Newman–Janis Algorithm. Then, based on a few extra fair assumptions on the seed metric functions, we make a conjecture on what a rotating LQG black hole would generically look like. Our general arguments and conclusions can be supported by some known specific examples in the literature.

Shadow of Quantum Extended Kruskal Black Hole and its Super-Radiance Property

We perform the shadow calculation of the loop quantum gravity motivated regular black hole recently proposed by Ashtekar, Olmedo and Singh (will be termed AOS black hole hereafter). In the process, we also construct the rotating loop quantum gravity inspired solution of the originally proposed static spherically symmetric AOS black hole by applying the modified Newman-Janis algorithm. We study the quantum effects on the shadows of both the non-rotating and rotating loop quantum black hole solutions. It is observed that the general shape of the shadow for non-rotating AOS black hole is circular in shape as is expected for its classical counter part too, but the presence of loop quantum gravity inspired modification contracts the shadow radius and the effect reduces with the increase in the mass of the black hole. On a similar note, in the rotating situation, we find contraction in shadow radius due to quantum effects and the tapered nature of the shadow as expected from the classical Kerr case. However, instead of the symmetrical contraction, like non-rotating one, we found more contraction on one side relative to the other when we compare our result with the shadow of the Kerr black hole. We finally studied super-radiance in rotating AOS background and observed that the super-radiance condition for massless scalar field is identical to that of the Kerr case with the rotation of the BH being more compared to Kerr in the low mass regime. With an increase in mass of the rotating AOS black hole, the difference from Kerr starts to become insignificant.

Quasinormal modes of a massive scalar field nonminimally coupled to gravity in the spacetime of self-dual black hole

In this work, we investigate the quasinormal modes for a massive scalar field with a nonminimal coupling with gravity in the spacetime of a loop quantum black hole, known as the self-dual black hole. In this way, we have calculated the characteristic frequencies using the 3rd order WKB approach, where we can verify a strong dependence with the mass of scalar field, the parameter of nonminimal coupling with gravity, and parameters of the loop quantum gravity. From our results, we can check that the self-dual black hole is stable under the scalar perturbations when assuming small values for the parameters. Also, such results tell us that the quasinormal modes assume different values for the cases where the mass of field is null and the nonminimal coupling assumes xi =0 and xi =1/6, i.e., a possible breaking of the conformal invariance can be seen in the context of loop quantum black holes.

Beyond General Relativity: Models for Quantum Gravity, Loop Quantum Cosmology and Black Holes

In the past two decades, we have witnessed extraordinary progress in precision measurements in cosmology [...]

Shadow and quasinormal modes of a rotating loop quantum black hole

In this paper, we construct an effective rotating loop quantum black hole (LQBH) solution, starting from the spherical symmetric LQBH by applying the Newman-Janis algorithm modified by Azreg-A\"{i}nou's non-complexification procedure, and study the effects of loop quantum gravity { (LQG) on its shadow}. Given the rotating {LQBH}, we discuss its horizon, ergosurface, and regularity {as} $r \to 0$. Depending on the values of the specific angular momentum $a$ and the polymeric function $P$ arising from {LQG}, we {find} that the rotating solution we obtained can represent a regular black hole, a regular extreme black hole, or a regular spacetime {without horizon (a non-black-hole solution)}. We also {study} the effects of {LQG} and rotation, and {show} that, in addition to the specific angular momentum, the polymeric function {also} causes deformations in the size and shape of the black hole shadow. Interestingly, for a given value of $a$ and inclination angle $\theta_0$, the apparent size of the shadow monotonically decreases, and the shadow gets more distorted with increasing $P$. We also {consider the effects of $P$ on the deviations from the circularity of the shadow, and find} that the deviation from circularity increases with increasing $P$ for fixed values of $a$ and $\theta_0$. Additionally, we explore the observational implications of $P$ in comparison with the latest Event Horizon Telescope (EHT) observation of the supermassive black hole, M$87$. The connection between the shadow radius and quasinormal modes in the eikonal limit as well as {the} deflection of massive particles are also considered.

Gravitational axial perturbations and quasinormal modes of loop quantum black holes

Loop quantum gravity (LQG) is a theory that proposes a way to model the behavior of the spacetime in situations where its atomic characteristic arises. Among these situations, the spacetime behavior near the Big Bang or black hole’s singularity. The detection of gravitational waves, on the other hand, has opened the way to new perspectives in the investigation of the spacetime structure. In this work, by the use of a WKB method introduced by Schutz and Will (Astrophys J 291:L33, 1985), and after improved by Iyer and Will (Phys Rev D 35:3621, 1987), we study the gravitational wave spectrum emitted by loop quantum black holes, which correspond to a quantized version of the Schwarzschild spacetime by LQG techniques. From the results obtained, loop quantum black holes have been shown stable under axial gravitational perturbations.