Holes In Loop Quantum Gravity Research Articles

The fate of a quantum-corrected collapsing star in General Relativity

We incorporate some corrections inspired by loop quantum gravity into the concept of gravitational collapse and propose a complete model of the dynamic process. The model carries the essence of a mass-independent upper bound on the curvature scalars, originally found as a crucial feature of black holes in loop quantum gravity. The quantum-inspired interior is immersed in a geometry filled with null radiation, and they are matched at a distinct boundary hypersurface. The ultimate fate of the process depends on the inhomogeneities of the metric tensor coefficients. We find a critical parameter λ embedded in the inhomogeneity of the conformal factor of the interior metric. Examples with λ< 0 enforce an eventual collapse to singularity, and λ> 0 cases produce a non-singular collapse resulting in a loop-quantum-corrected Schwarzschild geometry modulo a conformal factor. Interestingly, for λ< 0 as well, there exist situations where the quantum effects are able to cause a bounce but fall short of preventing the ultimate formation of a singularity. The trapped surface formation condition is studied for the λ<0 case to infer about the visibility of the final singularity. Interestingly, we find a possibility of the formation of three horizons during the course of the collapse. Eventually, all of them merge into a single horizon, which envelopes the final singularity. For the non-singular case, there is a possibility that the sphere can evolve into a wormhole throat whose radius is found to be inversely proportional to the critical parameter λ. Depending on the nature of evolution and the shell regions, the collapsing shells violate some standard energy conditions, which can be associated with quantum-inspired corrections.

Geodetic precession and shadow of quantum extended black holes

We study the circular motion of massive and massless particles in a recently proposed quantum-corrected Schwarzschild black hole in loop quantum gravity. This solution is supposed to introduce small but non-zero quantum corrections in the low curvature limit. In this paper, we confine our attention to the shadow of the black hole and the geodetic precession (GP) of a freely falling gyroscope in a circular orbit. Despite the mathematical complexity of the metric, our results are exact and show that the black hole shadow decreases slightly in this solution while the quantum corrections introduce a non-trivial term in the GP frequency of the gyroscope.

Smooth extensions of black holes in loop quantum gravity

Vacuum spherically symmetric loop quantum gravity in the midi-superspace approximation using inhomogeneous horizon-penetrating slices has been studied for a decade, and it has been noted that the singularity is eliminated. It is replaced by a region of high curvature and potentially large quantum fluctuations. It was recently pointed out that the effective semiclassical metric implies the existence of a shell of matter which violates energy conditions in regions where the curvature is largest. Here, we propose an alternative way of treating the problem that is free from the shells. The ambiguity in the treatment is related with the existence of new observables in the quantum theory that characterize the area excitations, and how the counterpart of diffeomorphisms in the discrete quantum theory is mapped to the continuum semiclassical picture. The resulting spacetime in the high curvature region inside the horizon is approximated by a metric of the type of the Simpson–Visser wormhole and it connects the black hole interior to a white hole in a smooth manner.

Semi-classical rotating black hole in loop quantum gravity

In the research paper [1], the analytical solution of semi-classical rotating black holes (BH) in loop quantum gravity theory (LQG) is obtained, but an unknown function H is still preserved. In this note, we obtain an expression for the unknown function H, which makes the space-time line element of the semi-classical rotating BH in the LQG theory sufficiently well-expressed and thus provides a basis for the study of such rotating BHs.

Axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity

Axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity

Periodic orbits and their gravitational wave radiations in a polymer black hole in loop quantum gravity

Periodic orbits and their gravitational wave radiations in a polymer black hole in loop quantum gravity

Finite-distance gravitational deflection of massive particles by a rotating black hole in loop quantum gravity

A rotating black hole in loop quantum gravity was constructed by Brahma, Chen, and Yeom based on a nonrotating counterpart using the revised Newman–Janis algorithm recently. For such spacetime, we investigate the weak gravitational deflection of massive particles to explore observational effects of the quantum correction. The purpose of this article is twofold. First, for Gibbons–Werner (GW) method, a geometric approach computing the deflection angle of particles in curved spacetimes, we refine its calculation and obtain a simplified formula. Second, by using GW method and our new formula, we work out the finite-distance weak deflection angle of massive particles for the rotating black hole in loop quantum gravity obtained by Brahma et al. An analysis to our result reveals the repulsive effect of the quantum correction to particles. What’s more, an observational constraint on the quantum parameter is obtained in solar system.

Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the galactic center

One of remarkable features of loop quantum gravity (LQG) is that it can provide resolutions to both the black hole and big bang singularities. In the mini-superspace approach based on the polymerization procedure in LQG, a quantum corrected black hole metric is constructed. This metric is also known as self-dual spacetime since the form of the metric is invariant under the exchange r ⟶ a 0/r with a 0 being proportional to the minimum area in LQG and r is the standard radial coordinate at asymptotic infinity. It modifies the Schwarzschild spacetime by the polymeric function P, purely due to the geometric quantum effects from LQG. Here P is related to the polymeric parameter δ which is introduced to define the paths one integrates the connection along to define the holonomies in the quantum corrected Hamiltonian constraint in the polymerization procedure in LQG. In this paper, we consider its effects on the orbital signatures of S0-2 star orbiting Sgr A* in the central region of our Milky Way, and compare it with the publicly available astrometric and spectroscopic data, including the astrometric positions, the radial velocities, and the orbital precession for the S0-2 star. We perform Monte Carlo Markov Chain (MCMC) simulations to probe the possible LQG effects on the orbit of S0-2 star. No significant evidence of the self-dual spacetime arisIng from LQG is found. We thus place an upper bounds at 95% confidence level on the polymeric function P < 0.043 and P < 0.056, for Gaussian and uniform priors on orbital parameters, respectively.

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.

Solar system constraints of a polymer black hole in loop quantum gravity

A new polymer black hole solution in loop quantum gravity was proposed recently. The difference between the polymer black hole and Schwarzschild black hole is captured by a quantum parameter $A$. In order to get the constraints on parameter $A$, we consider the observational constraints imposed on $A$ by using the Solar System experiments and calculate the deflection of light, Shapiro time delay, perihelion precession and obtain the effects associated with parameter $A$. Moreover, the parameterized post-Newtonian approach of this loop quantum gravity black hole was also carried out. It turns out the tightest constraint on $A$ can be improved to $0<A<4.0\times10^{-6}$.

Testing Loop Quantum Gravity from Observational Consequences of Nonsingular Rotating Black Holes

The lack of rotating black hole models, which are typically found in nature, in loop quantum gravity (LQG) substantially hinders the progress of testing LQG from observations. Starting with a nonrotating LQG black hole as a seed metric, we construct a rotating spacetime using the revised Newman-Janis algorithm. The rotating solution is nonsingular everywhere and it reduces to the Kerr black hole asymptotically. In different regions of the parameter space, the solution describes (1)a wormhole without event horizon (which, we show, is almost ruled out by observations), (2)a black hole with a spacelike transition surface inside the event horizon, or (3)a black hole with a timelike transition region inside the inner horizon. It is shown how fundamental parameters of LQG can be constrained by the observational implications of the shadow cast by this object. The causal structure of our solution depends crucially only on the spacelike transition surface of the nonrotating seed metric, while being agnostic about specific details of the latter, and therefore captures universal features of an effective rotating, nonsingular black hole in LQG.

A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes

We investigate the interior structure, perturbations, and the associated quasinormal modes of a quantum black hole model recently proposed by Bodendorfer, Mele, and Münch (BMM). Within the framework of loop quantum gravity, the quantum parameters in the BMM model are introduced through polymerization, consequently replacing the Schwarzschild singularity with a spacelike transition surface. By treating the quantum geometry corrections as an `effective' matter contribution, we first prove the violation of energy conditions (in particular the null energy condition) near the transition surface and then investigate the required junction conditions on it. In addition, we study the quasinormal modes of massless scalar field perturbations, electromagnetic perturbations, and axial gravitational perturbations in this effective model. As expected, the quasinormal spectra deviate from their classical counterparts in the presence of quantum corrections. Interestingly, we find that the quasinormal frequencies of perturbations with different spins share the same qualitative tendency with respect to the change of the quantum parameters in this model.

Quantum fields in the background spacetime of a polymeric loop black hole

The description of black holes in loop quantum gravity is a hard and tricky task. In this article, we focus on a minisuperspace approach based on a polymerization procedure. We consider the resulting effective metric and study the propagation of quantum fields in this background. The cross sections for scalar particles and fermions are explicitly calculated. The Teukolsky–Chandrasekhar procedure used to derived the fermionic radial equation of motion for usual spacetimes is entirely generalized to a much larger class. The resulting radial equation can be used in quite a lot of other contexts.

A Status Report on the Phenomenology of Black Holes in Loop Quantum Gravity: Evaporation, Tunneling to White Holes, Dark Matter and Gravitational Waves

The understanding of black holes in loop quantum gravity is becoming increasingly accurate. This review focuses on the possible experimental or observational consequences of the underlying spinfoam structure of space-time. It addresses both the aspects associated with the Hawking evaporation and the ones due to the possible existence of a bounce. Finally, consequences for dark matter and gravitational waves are considered.

Non-extensive statistical mechanics and black hole entropy from quantum geometry

Using non-extensive statistical mechanics, the Bekenstein–Hawking area law is obtained from microstates of black holes in loop quantum gravity, for arbitrary real positive values of the Barbero–Immirzi parameter (γ). The arbitrariness of γ is encoded in the strength of the “bias” created in the horizon microstates through the coupling with the quantum geometric fields exterior to the horizon. An experimental determination of γ will fix this coupling, leaving out the macroscopic area of the black hole to be the only free quantity of the theory.

Semiclassical analysis of black holes in loop quantum gravity: Modeling Hawking radiation with volume fluctuations

We introduce the notion of fluid approximation of a quantum spherical black hole in the context of Loop Quantum Gravity. In this limit, the microstates of the black hole are intertwiners between "large" representations $s_i$ which typically scale as $s_i \sim \sqrt{a_H}$ where $a_H$ denotes the area of the horizon in Planck units. The punctures with large colors are, for the black hole horizon, similar to what are the fluid parcels for a classical fluid. We dub them puncels. Hence, in the fluid limit, the horizon is composed by puncels which are themselves interpreted as composed (in the sense of the tensor product) by a large number of more fundamental intertwiners. We study the spectrum of the euclidean volume acting on puncels and we compute its quantum fluctuations. Then, we propose an interpretation of black holes radiation based on the properties of the quantum fluctuations of the euclidean volume operator. We estimate a typical temperature of the black hole and we show that it scales as the Hawking temperature.

Gravitational lensing by self-dual black holes in loop quantum gravity

We study gravitational lensing by a recently proposed black hole solution in Loop Quantum Gravity. We highlight the fact that the quantum gravity corrections to the Schwarzschild metric in this model evade the `mass suppression' effects (that the usual quantum gravity corrections are susceptible to) by virtue of one of the parameters in the model being dimensionless, which is unlike any other quantum gravity motivated parameter. Gravitational lensing in the strong and weak deflection regimes is studied and a sample consistency relation is presented which could serve as a test of this model. We discuss that though the consistency relation for this model is qualitatively similar to what would have been in Brans-Dicke, in general it can be a good discriminator between many alternative theories. Although the observational prospects do not seem to be very optimistic even for a galactic supermassive black hole case, time delay between relativistic images for billion solar mass black holes in other galaxies might be within reach of future relativistic lensing observations.

Quantum shells in a quantum space-time

We study the quantum motion of null shells in the quantum space-time of a black hole in loop quantum gravity. We treat the shells as test fields and use an effective dynamics for the propagation equations. The shells propagate through the region where the singularity was present in the classical black hole space-time, but is absent in the quantum space-time, eventually emerging through a white hole to a new asymptotic region of the quantum space-time. The profiles of the shells get distorted due to the quantum fluctuations in the Planckian region that replaces the singularity. The evolution of the shells is unitary throughout the whole process.

Evolution of Primordial Black Holes in Loop Quantum Cosmology

In this work, we study the evolution of Primordial Black Holes within the context of Loop Quantum Gravity. First we calculate the scale factor and energy density of the universe for different cosmic era and then taking these as inputs we study evolution of primordial black holes. From our estimation it is found that accretion of radiation does not affect evolution of primordial black holes in loop quantum gravity even though a larger number of primordial black holes may form in early universe in comparison with Einstein's or scalar-tensor theories.

On the nature of black holes in loop quantum gravity

A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain the black hole thermodynamical properties. As for all quantum systems, a quantum realization of black holes requires an operator algebra of the fundamental observables of the theory which is introduced in this study based on aspects of loop quantum gravity. From the eigenvalue spectra of the quantum operators for the black hole area, charge and angular momentum, it is demonstrated that a strict bound on the extensive parameters, different from the relation arising in classical general relativity, holds, implying that the extremal black hole state can neither be measured nor can its existence be proven. This is, as turns out, a result of the specific form of the chosen angular momentum operator and the corresponding eigenvalue spectrum, or rather the quantum measurement process of angular momentum. Quantum-mechanical considerations and the lowest, non-zero eigenvalue of the loop quantum gravity black hole mass spectrum indicate, on the one hand, a physical Planck scale cutoff of the Hawking temperature law and, on the other hand, give upper and lower bounds on the numerical value of the Immirzi parameter. This analysis provides an approximative description of the behavior and the nature of quantum black holes.