Holes In Loop Quantum Gravity Research Articles

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.

Singularity Avoidance of Charged Black Holes in Loop Quantum Gravity

Based on spherically symmetric reduction of loop quantum gravity, quantization of the portion interior to the horizon of a Reissner-Nordstr\"{o}m black hole is studied. Classical phase space variables of all regions of such a black hole are calculated for the physical case $M^2> Q^2$. This calculation suggests a candidate for a classically unbounded function of which all divergent components of the curvature scalar are composed. The corresponding quantum operator is constructed and is shown explicitly to possess a bounded operator. Comparison of the obtained result with the one for the Swcharzschild case shows that the upper bound of the curvature operator of a charged black hole reduces to that of Schwarzschild at the limit $Q \rightarrow 0$. This local avoidance of singularity together with non-singular evolution equation indicates the role quantum geometry can play in treating classical singularity of such black holes.

Black holes in loop quantum gravity

We summarize recent results concerning the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution of the polymerized theory, that is expected to capture features of the semi-classical limit. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.

Self-dual black holes in loop quantum gravity: Theory and phenomenology

In this paper we have recalled the semiclassical metric obtained from a classical analysis of the loop quantum black hole (LQBH). We show that the regular Reissner--Nordstr\om-like metric is self-dual in the sense of $T$-duality: the form of the metric obtained in loop quantum gravity is invariant under the exchange $r\ensuremath{\rightarrow}{a}_{0}/r$ where ${a}_{0}$ is proportional to the minimum area in loop quantum gravity and $r$ is the standard Schwarzschild radial coordinate at asymptotic infinity. Of particular interest, the symmetry imposes that if an observer in $r\ensuremath{\rightarrow}+\ensuremath{\infty}$ sees a black hole of mass $m$ an observer in the other asymptotic infinity beyond the horizon (at $r\ensuremath{\approx}0$) sees a dual mass ${m}_{P}/m$. We then show that small LQBH are stable and could be a component of dark matter. Ultralight LQBHs created shortly after the big bang would now have a mass of approximately ${10}^{\ensuremath{-}5}{m}_{P}$ and emit radiation with a typical energy of about ${10}^{13}--{10}^{14}\text{ }\text{ }\mathrm{eV}$ but they would also emit cosmic rays of much higher energies, albeit few of them. If these small LQBHs form a majority of the dark matter of the Milky Way's Halo, the production rate of ultra-high-energy-cosmic-rays (UHECR) by these ultralight black holes would be compatible with the observed rate of the Auger detector.

Effective polymer dynamics ofD-dimensional black hole interiors

We consider two different effective polymerization schemes applied to $D$-dimensional, spherically symmetric black hole interiors. It is shown that polymerization of the generalized area variable alone leads to a complete, regular, single-horizon spacetime in which the classical singularity is replaced by a bounce. The bounce radius is independent of rescalings of the homogeneous internal coordinate, but does depend on the arbitrary fiducial cell size. The model is therefore necessarily incomplete. It nonetheless has many interesting features: After the bounce, the interior region asymptotes to an infinitely expanding Kantowski-Sachs spacetime. If the solution is analytically continued across the horizon, the black hole exterior exhibits asymptotically vanishing quantum corrections due to the polymerization. In all spacetime dimensions except four, the falloff is too slow to guarantee invariance under Poincar\'e transformations in the exterior asymptotic region. Hence, the four-dimensional solution stands out as the only example which satisfies the criteria for asymptotic flatness. In this case it is possible to calculate the quantum-corrected temperature and entropy. We also show that polymerization of both phase space variables, the area and the conformal mode of the metric, generically leads to a multiple horizon solution which is reminiscent of polymerized minisuperspace models of spherically symmetric black holes in loop quantum gravity.

Computing black hole entropy in loop quantum gravity from a conformal field theory perspective

Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity.

Fine-Grained State Counting for Black Holes in Loop Quantum Gravity

A state of a black hole in loop quantum gravity is given by a distribution of spins on punctures on the horizon. The distribution is of the Boltzmann type, with the area playing the role of the energy. In investigations where the total area was kept approximately constant, there was a kind of thermal equilibrium between the spins which have the same analogue temperature and the entropy was proportional to the area. If the area is precisely fixed, however, multiple constraints appear, different spins have different analogue temperatures and the entropy is not strictly linear in the area, but is bounded by a linear rise.

Black holes in loop quantum gravity: Recent advances

Black holes in equilibrium and the counting of their entropy within Loop Quantum Gravity are reviewed. In particular, we focus on the conceptual setting of the formalism, briefly summarizing the main results of the past 12 years. We then focus in recent results for small, Planck scale, black holes, where new structures have been shown to arise. This contribution is based on the invited talk given at the 6th International Conference on Gravitation & Cosmology (ICGC-07) December 17–21, 2007, IUCAA, Pune, India.

Entropy calculation for a toy black hole

In this paper, we carry out the counting of states for a black hole in loop quantum gravity, assuming however an equidistant area spectrum. We find that this toy-model is exactly solvable, and we show that its behavior is very similar to that of the correct model. Thus this toy-model can be used as a nice and simplifying ‘laboratory’ for questions about the full theory.

Toward explaining black hole entropy quantization in loop quantum gravity

In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this steplike behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking.

A note on renormalization and black hole entropy in loop quantum gravity

Microscopic state counting for a black hole in loop quantum gravity yields a result proportional to the horizon area, and inversely proportional to Newton's constant and the Immirzi parameter. It is argued here that before this result can be compared to the Bekenstein–Hawking entropy of a macroscopic black hole, the scale dependence of both Newton's constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds.

Quantum black holes: Entropy and entanglement on the horizon

We are interested in black holes in Loop Quantum Gravity (LQG). We study the simple model of static black holes: the horizon is made of a given number of identical elementary surfaces and these small surfaces all behaves as a spin- s system accordingly to LQG. The chosen spin- s defines the area unit or area resolution, which the observer uses to probe the space(time) geometry. For s = 1 / 2 , we are actually dealing with the qubit model, where the horizon is made of a certain number of qubits. In this context, we compute the black hole entropy and show that the factor in front of the logarithmic correction to the entropy formula is independent of the unit s. We also compute the entanglement between parts of the horizon. We show that these correlations between parts of the horizon are directly responsible for the asymptotic logarithmic corrections. This leads us to speculate on a relation between the evaporation process and the entanglement between a pair of qubits and the rest of the horizon. Finally, we introduce a concept of renormalisation of areas in LQG.

Entropy and area of black holes in loop quantum gravity

Simple arguments related to the entropy of black holes strongly constrain the spectrum of the area operator for a Schwarzschild black hole in loop quantum gravity. In particular, this spectrum is fixed completely by the assumption that the black hole entropy is maximum. Within the approach discussed, one arrives in loop quantum gravity at a quantization rule with integer quantum numbers n for the entropy and area of a black hole.