A configuration space for quantum gravity and solutions to the Euclidean Einstein equations in a slab region

Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge equivalent connections. This calculus does not use any background fields (such as a metric) and thus well-suited to a fully non-perturbative treatment of quantum gravity. Using this framework, quantum geometry is examined. Fundamental excitations turn out to be one-dimensional, rather like polymers. Geometrical observables such as areas of surfaces and volumes of regions are purely discrete spectra. Continuum picture arises only upon coarse graining of suitable semi-classical states. Next, regulated quantum diffeomorphism constraints can be imposed in an anomaly-free fashion and the space of solutions can be given a natural Hilbert space structure. Progress has also been made on the quantum Hamiltonian constraint in a number of directions. In particular, there is a recent approach based on a generalized .Wick transformation which maps solutions to the Euclidean quantum constraints to those of the Lorentzian theory. These developments are summarized. Emphasis is on conveying the underlying ideas and overall pictures rather than technical details.

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Quantum Gravity Phenomenology from the Thermodynamics of Spacetime

Universe ◽

10.3390/universe8010050 ◽

2022 ◽

Vol 8 (1) ◽

pp. 50

Author(s):

Ana Alonso-Serrano ◽

Marek Liška

Keyword(s):

Quantum Gravity ◽

Big Bang ◽

Einstein Equations ◽

Logarithmic Term ◽

Quantum Gravity Phenomenology ◽

Gravity Effects ◽

Energy Quantum ◽

The Big Bang ◽

Big Bang Singularity ◽

Modified Dynamics

This work is based on the formalism developed in the study of the thermodynamics of spacetime used to derive Einstein equations from the proportionality of entropy within an area. When low-energy quantum gravity effects are considered, an extra logarithmic term in the area is added to the entropy expression. Here, we present the derivation of the quantum modified gravitational dynamics from this modified entropy expression and discuss its main features. Furthermore, we outline the application of the modified dynamics to cosmology, suggesting the replacement of the Big Bang singularity with a regular bounce.

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REGGE GRAVITY FROM SPINFOAMS

International Journal of Modern Physics D ◽

10.1142/s0218271813500016 ◽

2013 ◽

Vol 22 (02) ◽

pp. 1350001 ◽

Cited By ~ 11

Author(s):

ELENA MAGLIARO ◽

CLAUDIO PERINI

Keyword(s):

Fine Structure ◽

Quantum Gravity ◽

Scaling Limit ◽

Einstein Equations ◽

Quantum Corrections ◽

Semiclassical Regime ◽

Double Scaling Limit

We consider spinfoam quantum gravity in the flipped limit, which is the double scaling limit γ → 0, j → ∞ with γj = const. , where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. In this regime the amplitude for a 2-complex becomes effectively an integral over Regge-like metrics and seems to enforce Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs to zero when the fine structure of the foam is averaged. In addition to quantum corrections which vanish for ℏ → 0, we find new corrections due to the discreteness of geometric spectra.

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Quantum gravity as a metaphysical problem

Physics & Astronomy International Journal ◽

10.15406/paij.2017.01.00029 ◽

2017 ◽

Vol 1 (5) ◽

pp. 163-170

Author(s):

Ilja Schmelzer

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Degrees Of Freedom ◽

Einstein Equations ◽

Absolute Space ◽

Quantum Theories ◽

Approximation Techniques ◽

Metaphysical Problem ◽

Space And Time ◽

Important Argument

The problem with quantum gravity is usually presented as if it would be difficult to construct even a single quantum theory of relativistic gravity. This is shown to be wrong. A straightforward approach using standard, well-studied methods allows to construct mathematically well-defined quantum theories which give, in a certain classical limit, the Einstein equations of GR: GR may be transformed into a field theory on a fixed background by breaking diffeomorphism symmetry using harmonic coordinates. The resulting field theory may be regularized using standard lattice approximation techniques. The result is a well-defined canonical theory with a finite number of degrees of freedom, which can be quantized without problems in a canonical way. Why such a straightforward way to quantize gravity is simply ignored? We identify missing explanation of relativistic symmetry as an important argument, and propose a solution. evaluate possible explanations why this simple possibility to construct a theory of quantum gravity is ignored. While a lot of different metaphysical and sociological reasons play a role, we identify as a main point a preference of the scientific community for the relational philosophy behind the spacetime interpretation of GR, in opposition to the Newtonian concept of absolute space and time (substantivalism). We conclude that the quantization of gravity is not a problem of physics, but a metaphysical problem. It is a problem of the relational philosophy of space and time in the tradition of Descartes and Leibniz, which is the base of the spacetime interpretation of GR, because this philosophy is incompatible with the known examples of theories of quantum gravity.

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Black to white hole tunneling: An exact classical solution

International Journal of Modern Physics A ◽

10.1142/s0217751x15450153 ◽

2015 ◽

Vol 30 (28n29) ◽

pp. 1545015 ◽

Cited By ~ 7

Author(s):

Hal M. Haggard ◽

Carlo Rovelli

Keyword(s):

General Relativity ◽

Black Hole ◽

Quantum Theory ◽

Quantum Gravity ◽

Quantum Tunneling ◽

Einstein Equations ◽

White Hole ◽

Small Quantum ◽

Pile Up ◽

Over Time

We present a metric that describes conventional matter collapsing into a black hole, bouncing and emerging from a white hole, and that satisfies the vacuum Einstein equations everywhere, including in the interior of the black hole and the subsequent white hole, except for a small compact 4d “quantum tunneling” zone. This shows that a black hole can tunnel into a white hole without violating classical general relativity where this can be trusted. We observe that quantum gravity can affect the metric in a region outside the horizon without violating causality because small quantum effects might pile up over time. We study how quantum theory can determines the bouncing time.

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DISCRETE QUANTUM GRAVITY: A MECHANISM FOR SELECTING THE VALUE OF FUNDAMENTAL CONSTANTS

International Journal of Modern Physics D ◽

10.1142/s0218271803004018 ◽

2003 ◽

Vol 12 (09) ◽

pp. 1775-1781 ◽

Cited By ~ 13

Author(s):

RODOLFO GAMBINI ◽

JORGE PULLIN

Keyword(s):

Quantum Gravity ◽

Selection Process ◽

Einstein Equations ◽

Fundamental Constants ◽

Fundamental Physical Constants ◽

Physical Constants ◽

Random Fashion ◽

The One ◽

The Universe ◽

Fundamental Physical

Smolin has put forward the proposal that the universe fine tunes the values of its physical constants through a Darwinian selection process. Every time a black hole forms, a new universe is developed inside it that has different values for its physical constants from the ones in its progenitor. The most likely universe is the one which maximizes the number of black holes. Here we present a concrete quantum gravity calculation based on a recently proposed consistent discretization of the Einstein equations that shows that fundamental physical constants change in a random fashion when tunneling through a singularity.

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DUALISM BETWEEN PHYSICAL FRAMES AND TIME IN QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732304014756 ◽

2004 ◽

Vol 19 (20) ◽

pp. 1519-1527 ◽

Cited By ~ 11

Author(s):

SIMONE MERCURI ◽

GIOVANNI MONTANI

Keyword(s):

Quantum Gravity ◽

Reference Frame ◽

Path Integral ◽

Classical Limit ◽

Quantum Dynamics ◽

Einstein Equations ◽

Quantum Level ◽

Dust Fluid ◽

Lapse Function ◽

Canonical Quantum

In this work we present a discussion of the existing links between the procedures of endowing the quantum gravity with a real time and of including in the theory a physical reference frame. More precisely, as a first step, we develop the canonical quantum dynamics, starting from the Einstein equations in presence of a dust fluid and arrive at a Schrödinger evolution. Then, by fixing the lapse function in the path-integral of gravity, we get a Schrödinger quantum dynamics, of which eigenvalues problem provides the appearance of a dust fluid in the classical limit. The main issue of our analysis is to claim that a theory, in which the time displacement invariance, on a quantum level, is broken, is indistinguishable from a theory for which this symmetry holds, but a real reference fluid is included.

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Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

Symmetry ◽

10.3390/sym10070287 ◽

2018 ◽

Vol 10 (7) ◽

pp. 287 ◽

Cited By ~ 7

Author(s):

Claudio Cremaschini ◽

Massimo Tessarotto

Keyword(s):

Gravitational Field ◽

Quantum Gravity ◽

Cosmological Constant ◽

Proper Time ◽

Theoretical Background ◽

Space Time ◽

Einstein Equations ◽

Field Equations ◽

Metric Tensor ◽

Covariant Quantum

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

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A parametrix for quantum gravity?

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816500602 ◽

2016 ◽

Vol 13 (05) ◽

pp. 1650060

Author(s):

Giampiero Esposito

Keyword(s):

Quantum Gravity ◽

Hyperbolic System ◽

Wave Operator ◽

Wave Equations ◽

Inverse Operator ◽

Einstein Equations ◽

Poisson Brackets ◽

Maxwell Theory ◽

Kirchhoff Type ◽

Nonlinear Hyperbolic System

In the 60s, DeWitt discovered that the advanced and retarded Green functions of the wave operator on metric perturbations in the de Donder gauge make it possible to define classical Poisson brackets on the space of functionals that are invariant under the action of the full diffeomorphism group of spacetime. He therefore tried to exploit this property to define invariant commutators for the quantized gravitational field, but the operator counterpart of such classical Poisson brackets turned out to be a hard task. On the other hand, in the mathematical literature, it is by now clear that, rather than inverting exactly an hyperbolic (or elliptic) operator, it is more convenient to build a quasi-inverse, i.e. an inverse operator up to an operator of lower order which plays the role of regularizing operator. This approximate inverse, the parametrix, which is, strictly, a distribution, makes it possible to solve inhomogeneous hyperbolic (or elliptic) equations. We here suggest that such a construction might be exploited in canonical quantum gravity provided one understands what is the counterpart of classical smoothing operators in the quantization procedure. We begin with the simplest case, i.e. fundamental solution and parametrix for the linear, scalar wave operator; the next step are tensor wave equations, again for linear theory, e.g. Maxwell theory in curved spacetime. Last, the nonlinear Einstein equations are studied, relying upon the well-established Choquet-Bruhat construction, according to which the fifth derivatives of solutions of a nonlinear hyperbolic system solve a linear hyperbolic system. The latter is solved by means of Kirchhoff-type formulas, while the former fifth-order equations can be solved by means of well-established parametrix techniques for elliptic operators. But then the metric components that solve the vacuum Einstein equations can be obtained by convolution of such a parametrix with Kirchhoff-type formulas. Some basic functional equations for the parametrix are also obtained, that help in studying classical and quantum version of the Jacobi identity.

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Einstein equations and Fierz-Pauli equations with self-interaction in quantum gravity

Foundations of Physics ◽

10.1007/bf02067656 ◽

1994 ◽

Vol 24 (6) ◽

pp. 949-962 ◽

Cited By ~ 2

Author(s):

H. -H. v. Borzeszkowski ◽

H. -J. Treder

Keyword(s):

Quantum Gravity ◽

Einstein Equations

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