arXiv subjects

Johannes Münch

Publications and source records attributed to Johannes Münch.

13 recordsLinked to original sources

arXiv2024

On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC

In spatially non-compact minisuperpace models, spatial integrals in the Hamiltonian and symplectic form must be regularised by confining them to a finite volume $V_o$, known as the fiducial cell. As this restriction is unnecessary in the complete theory before homogeneous reduction, the physical significance of the fiducial cell has been largely debated, especially in the context of loop quantum cosmology. Understanding its role is in turn essential for assessing the minisuperspace description's validity and its connection to the full theory. In this work we present a systematic procedure for reduction to spatially homogeneous and isotropic minisuperspaces within the canonical framework and apply it to a massive scalar field theory and gravity. Our strategy consists in implementing spatial homogeneity via second-class constraints for discrete field modes over a partitioning of the spatial slice into countably many disjoint cells. The reduced theory's canonical structure is then given by the corresponding Dirac bracket. Importantly, the latter can only be defined on a finite number of cells patched together. This identifies a finite region, the fiducial cell, whose physical size acquires then a precise meaning already at the classical level as the scale over which homogenenity is imposed. Additionally, the procedure allows to track the information lost during reduction and how the error depends on $V_o$. We then move to the quantisation of the classically reduced theories, focusing on the relation between theories for different $V_o$, and study the implications for statistical moments, quantum fluctuations, and semiclassical states. In the case of a quantum scalar field, a subsector of the full quantum field theory where the results from the "first reduced, then quantised" approach can be reproduced is identified and the conditions for this to be a good approximation are also determined.

gr-qc↗

arXiv2023

The Physical Relevance of the Fiducial Cell in Loop Quantum Cosmology

A common way to avoid divergent integrals in homogeneous spatially non-compact gravitational systems is to introduce a fiducial cell by cutting-off the spatial slice at a finite region $V_o$. This is usually considered as an auxiliary regulator to be removed after computations by sending $V_o\to\infty$. In this paper, we analyse the dependence of the classical and quantum theory of homogeneous, isotropic and spatially flat cosmology on $V_o$. We show that each fixed $V_o$ regularisation leads to a different canonically independent theory. At the classical level, the dynamics of observables is not affected by the regularisation on-shell. For the quantum theory, however, this leads to a family of regulator dependent quantum representations and the limit $V_o\to\infty$ becomes then more subtle. First, we construct a novel isomorphism between different $V_o$-regularisations, which allows us to identify states in the different $V_o$-labelled Hilbert spaces to ensure equivalent dynamics for any value of $V_o$. The $V_o\to\infty$ limit would then correspond to choosing a state for which the volume assigned to the fiducial cell becomes infinite as appropriate in the late-time regime. As second main result of our analysis, quantum fluctuations of observables smeared over subregions $V\subset V_o$, unlike those smeared over the full $V_o$, explicitly depend on the size of the fiducial cell through the ratio $V/V_o$ interpreted as the (inverse) number of subcells $V$ homogeneously patched together into $V_o$. Physically relevant fluctuations for a finite region, as e.g. in the early-time regime, which would be unreasonably suppressed in a naïve $V_o\to\infty$ limit, become appreciable at small volumes. Our results suggest that the fiducial cell is not playing the role of a mere regularisation but is physically relevant at the quantum level and complement previous statements in the literature.

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arXiv2023

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.

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arXiv2022

Quantum Corrected Polymer Black Hole Thermodynamics: Mass Relations and Logarithmic Entropy Correction

In this paper, we continue the analysis of the effective model of quantum Schwarzschild black holes recently proposed by some of the authors in [1,2]. In the resulting spacetime the central singularity is resolved by a black-to-white hole bounce, quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon and classical geometry is approached asymptotically. This is the case independently of the relation between the black and white hole masses, which are thus freely specifiable independent observables. A natural question then arises about the phenomenological implications of the resulting non-singular effective spacetime and whether some specific relation between the masses can be singled out from a phenomenological perspective. Here we focus on the thermodynamic properties of the effective polymer black hole and analyse the corresponding quantum corrections as functions of black and white hole masses. The study of the relevant thermodynamic quantities such as temperature, specific heat and horizon entropy reveals that the effective spacetime generically admits an extremal minimal-sized configuration of quantum-gravitational nature characterised by vanishing temperature and entropy. For large masses, the classically expected results are recovered at leading order and quantum corrections are negligible, thus providing us with a further consistency check of the model. The explicit form of the corrections depends on the specific relation among the masses. In particular, a first-order logarithmic correction to the entropy is obtained for a quadratic mass relation. The latter corresponds to the case of proper finite length effects which turn out to be compatible with a minimal length generalised uncertainty principle associated with an extremal Planck-sized black hole.

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arXiv2021

Causal Structure of a recent Loop Quantum Gravity Black Hole Collapse Model

The causal structure of the recent loop quantum gravity black hole collapse model [1] is analysed. As the spacetime is only approximately diffeomorphism invariant up to powers of $\hbar$, it is not straight forwardly possible to find global conformally compactified coordinates and to construct the Penrose diagram. Therefore, radial in- and outgoing light rays are studied to extract the causal features and sketch a causal diagram. It was found that the eternal metric [2], which is the vacuum solution of the collapse model, has a causal horizon. However, in the collapsing case light rays travel through matter to causally connect the regions in- and outside the horizon -- the causal horizon is not present in the collapsing scenario. It is worked out that this is related to the shock wave and spacetime discontinuity, which allows matter travelling super-luminal along a space-like trajectory from the vacuum point of view, but remaining time-like from the matter perspective. The final causal diagram is a compact patch of a Reissner-Nordström causal diagram. Further, possibilities of a continuous matter collapse with only time-like evolution are studied. It was found that the time-reversed vacuum metric is also a solution of the dynamical equations and a once continuously differentiable matching of the vacuum spacetime across the minimal radius is possible. This allows an everywhere continuous and time-like collapse process at the cost of an infinite extended causal diagram. This solution is part of an infinitely extended eternal black hole solution with a bounce, whose global extension is constructed. Due to the analysis of radial light rays, it is possible to sketch causal diagrams of these spacetimes.

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arXiv2021

Effective Quantum Dust Collapse via Surface Matching

The fate of matter forming a black hole is still an open problem, although models of quantum gravity corrected black holes are available. In loop quantum gravity (LQG) models were presented, which resolve the classical singularity in the centre of the black hole by means of a black-to-white hole transition, but neglect the collapse process. The situation is similar in other quantum gravity approaches, where eternal non-singular models are available. In this paper, a strategy is presented to generalise these eternal models to dynamical collapse models by surface matching. Assuming 1) the validity of a static quantum black hole spacetime outside the collapsing matter, 2) homogeneity of the collapsing matter, and 3) differentiability at the surface of the matter fixes the dynamics of the spacetime uniquely. It is argued that these assumptions resemble a collapse of pressure-less dust and thus generalises the Oppenheimer-Snyder-Datt model, although no precise model of the matter has to be assumed. Hawking radiation is systematically neglected in this approach. The junction conditions and the spacetime dynamics are discussed generically for bouncing black hole spacetimes, as proposed by LQG, although the scheme is approach independent. Further, the equations are explicitly solved for the recent model [1] and a global spacetime picture of the collapse is achieved. The causal structure is discussed in detail and the Penrose diagram is constructed. The trajectory of the collapsing matter is completely constructed from an inside and outside observer point of view. The general analysis shows that the matter is collapsing and re-expanding and crosses the Penrose diagram diagonally. This way the infinite tower of Penrose diagrams, as proposed by several LQG models, is generically not cut out. Questions about different timescales of the collapse for in- and outside observers can be answered.

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arXiv2021

(b,v)-type variables for black to white hole transitions in effective loop quantum gravity

Quantum gravity effects in effective models of loop quantum gravity, such as loop quantum cosmology, are encoded in the choice of so-called polymerisation schemes. Physical viability of the models, such as an onset of quantum effects at curvature scales near the Planck curvature, severely restrict the possible choices. An alternative point of view on the choice of polymerisation scheme is to choose adapted variables so that the scheme is the simplest possible one, known as $μ_0$-scheme in loop quantum cosmology. There, physically viable models with $μ_0$-scheme polymerise the Hubble rate $b$ that is directly related to the Ricci scalar and the matter energy density on-shell. Consequently, the onset of quantum effects depends precisely on those parameters. In this letter, we construct similar variables for black to white hole transitions modelled using the description of the Schwarzschild interior as a Kantowski-Sachs cosmology. The resulting model uses the $μ_0$-scheme and features sensible physics for a broad range of initial conditions (= choices of black and white hole masses) and favours symmetric transitions upon invoking additional qualitative arguments. The resulting Hamiltonian is very simple and at most quadratic in its arguments, allowing for a straight forward quantisation.

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arXiv2021

Mass and Horizon Dirac Observables in Effective Models of Quantum Black-to-White Hole Transition

In the past years, black holes and the fate of their singularity have been heavily studied within loop quantum gravity. Effective spacetime descriptions incorporating quantum geometry corrections are provided by the so-called polymer models. Despite the technical differences, the main common feature shared by these models is that the classical singularity is resolved by a black-to-white hole transition. In a recent paper, we discussed the existence of two Dirac observables in the effective quantum theory respectively corresponding to the black and white hole mass. Physical requirements about the onset of quantum effects then fix the relation between these observables after the bounce, which in turn corresponds to a restriction on the admissible initial conditions for the model. In the present paper, we discuss in detail the role of such observables in black hole polymer models. First, we revisit previous models and analyse the existence of the Dirac observables there. Observables for the horizons or the masses are explicitly constructed. In the classical theory, only one Dirac observable has physical relevance. In the quantum theory, we find a relation between the existence of two physically relevant observables and the scaling behaviour of the polymerisation scales under fiducial cell rescaling. We present then a new model based on polymerisation of new variables which allows to overcome previous restrictions on initial conditions. Quantum effects cause a bound of a unique Kretschmann curvature scale, independently of the relation between the two masses.

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arXiv2020

Vanishing torsion coupling of the Maxwell field in canonical gauge theory of gravity

The Maxwell field can be viewed as a $U(1)$-gauge theory, therefore, generalizing it to form-invariance in dynamical spacetime backgrounds should take this symmetry into account. This is of essential importance when generalizations of general relativity to theories with non-vanishing torsion are considered. Despite the many statements in literature that a $U(1)$-gauge field cannot couple to torsion, this issue was recently revived. In this letter we contribute to the discussion by demonstrating via a canonical transformation within the framework of the DeDonder-Weyl Hamiltonian formalism that a $U(1)$-gauge field does not couple to torsion.

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arXiv2019

Effective Quantum Extended Spacetime of Polymer Schwarzschild Black Hole

The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches. In the context of loop quantum gravity (LQG), one of the major candidates for a non-perturbative background-independent quantisation of general relativity, considerable effort has been devoted to construct effective models in which these questions can be studied. In these models, classical singularities are replaced by a "bounce" induced by quantum geometry corrections. Undesirable features may arise however depending on the details of the model. In this paper, we focus on Schwarzschild black holes and propose a new effective quantum theory based on polymerisation of new canonical phase space variables inspired by those successful in loop quantum cosmology. The quantum corrected spacetime resulting from the solutions of the effective dynamics is characterised by infinitely many pairs of trapped and anti-trapped regions connected via a space-like transition surface replacing the central singularity. Quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon. The effective quantum metric describes also the exterior regions and asymptotically classical Schwarzschild geometry is recovered. We however find that physically acceptable solutions require us to select a certain subset of initial conditions, corresponding to a specific mass (de-)amplification after the bounce. We also sketch the corresponding quantum theory and explicitly compute the kernel of the Hamiltonian constraint operator.

gr-qc↗

arXiv2019

Is limiting curvature mimetic gravity an effective polymer quantum gravity?

A recently proposed version of mimetic gravity incorporates a limiting curvature into general relativity by means of a specific potential depending on the d'Alembertian of the scalar field. In the homogeneous and isotropic setting, the resulting theory agrees with the simplest incarnation of effective loop quantum cosmology (LQC) once the limiting curvature is identified with a multiple of the Planck scale. In this paper, we answer the question of whether such a relation can hold in the context of Bianchi I models. Our result is negative: it turns out to be impossible to view the Hamiltonian of limiting curvature mimetic gravity as an effective LQC Hamiltonian due to the appearance of terms that cannot be supported on the polymer Hilbert space underlying LQC. The present analysis complements a related result in the context of spherical symmetry.

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arXiv2019

A note on the Hamiltonian as a polymerisation parameter

In effective models of loop quantum gravity, the onset of quantum effects is controlled by a so-called polymerisation scale. It is sometimes necessary to make this scale phase space dependent in order to obtain sensible physics. A particularly interesting choice recently used to study quantum corrected black hole spacetimes takes the generator of time translations itself to set the scale. We review this idea, point out errors in recent treatments, and show how to fix them in principle.

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arXiv2018

Holographic Signatures of Resolved Cosmological Singularities II: Numerical Investigations

A common strategy to investigate the fate of gravitational singularities in asymptotically AdS spacetimes is to translate the question from the gravitational side to a dual field theory using the gauge/gravity correspondence and to do a field theory computation. Given recent progress in singularity resolution via non-perturbative quantum gravity, it is natural to now turn the question around and to ask about field theory signatures of resolved singularities. An investigation along this line has been initiated in a companion paper, where a finite-distance pole exhibited by the two-point correlator in the dual field theory, which has previously been linked directly to the gravitational bulk singularity, has been resolved in this way. In order to perform analytic computations, some simplifications were necessary. In this paper, we lift these restrictions by tackling the problem numerically. Our analysis shows that the pole in the two-point correlator gets resolved in the same manner as before.

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