arXiv subjects

Yongge Ma

Publications and source records attributed to Yongge Ma.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantum Oppenheimer-Snyder and Swiss Cheese models

By considering the quantum Oppenheimer-Snyder model in loop quantum cosmology, a new quantum black hole model whose metric tensor is a suitably deformed Schwarzschild one is derived. The quantum effects imply a lower bound on the mass of the black hole produced by the collapsing dust ball. For the case of larger masses where the event horizon does form, the maximal extension of the spacetime and its properties are investigated. By discussing the opposite scenario to the quantum Oppenheimer-Snyder, a quantum Swiss Cheese model is obtained with a bubble surrounded by the quantum universe. This model is analogous to black hole cosmology or fecund universes where the big bang is related to a white hole. Thus our models open a new window to cosmological phenomenology.

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arXiv2022

Realization of Dirac quantization in loop quantum gravity

The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In the framework of loop quantum gravity, the scalar constraint is promoted to a well-defined operator in a suitable Hilbert space of the coupled system, such that the physical Hamiltonian becomes a symmetric operator. By the deparametrized form, a general expression of the solutions to the quantum scalar constraint is obtained, and the observables on the space of solutions can be constructed. Moreover, the Dirac quantization procedure can be fully carried out in loop quantum gravity by this system.

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arXiv2022

Connection Dynamics of Reduced 5-dimensional Kaluza-Klein Theory and Its Deparametrization

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric model of the theory without introducing additional matter fields beyond the 5-dimensional gravity. Thus the physical time evolution and the physical spatial coordinate can be provided by the geometrical degrees of freedom in the higher dimensional spacetime.

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arXiv2021

The effective dynamics of weak coupling loop quantum gravity

By taking the limit that Newton's Gravitational constant tends to zero, the weak coupling loop quantum gravity can be formulated as a $U(1)^3$ gauge theory instead of the original $SU(2)$ gauge theory. In this paper, a parametrization of the $SU(2)$ holonomy-flux variables by the $U(1)^3$ holonomy-flux variables is introduced, and the Hamiltonian operator based on this parametrization is obtained for the weak coupling loop quantum gravity. It is shown that the effective dynamics obtained from the coherent state path integrals in $U(1)^3$ and $SU(2)$ loop quantum gravity respectively are consistent to each other in the weak coupling limit, provided that the expectation values of the Hamiltonian operators on the coherent states in these two theories coincide with their classical expressions respectively.

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arXiv2021

Loop quantum gravity and cosmological constant

An one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as special cases. The quantum bounce nature is tenable in the generalized cases. For positive value of the regularization parameter, the effective Hamiltonian leads to an asymptotic de-Sitter branch of the Universe connecting to the standard Friedmann branch by the quantum bounce. Remarkably, by suitably choosing the value of the regularization parameter, the observational cosmological constant can emerge at large volume limit from the effect of quantum gravity, and the effective Newtonian constant satisfies the experimental restrictions in the meantime.

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arXiv2021

Loop quantum Schwarzschild interior and black hole remnant

The interior of Schwarzschild black hole is quantized by the method of loop quantum gravity. The Hamiltonian constraint is solved and the physical Hilbert space is obtained in the model. The properties of a Dirac observable corresponding to the ADM mass of the Schwarzschild black hole are studied by both analytical and numerical techniques. It turns out that zero is not in the spectrum of this Dirac observable. This supports the existence of a stable remnant after the evaporation of a black hole. Our conclusion is valid for a general class of schemes adopted for loop quantization of the model.

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arXiv2021

Entropy of black holes with arbitrary shapes in loop quantum gravity

The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is successfully applied in the scheme to calculate the entropy by the $SO(1,1)$ BF boundary theory matching loop quantum gravity in the bulk. The generating function for calculating the microscopical degrees of freedom of a given isolated horizon is obtained. Numerical computations of small black holes indicate a new entropy formula containing the quantum correction related to the partition of the horizon. Further evidence shows that, for a given horizon area, the entropy decreases as a black hole deviates from the spherically symmetric one, and the entropy formula is also well suitable for big black holes.

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arXiv2021

Loop quantum deparametrized Schwarzschild interior and discrete black hole mass

We present the detailed analyses of a model of loop quantum Schwarzschild interior coupled to a massless scalar field and extend the results in our previous rapid communication arXiv:2006.08313 to more general schemes. It is shown that the spectrum of the black hole mass is discrete and does not contain zero. This indicates the existence of a black hole remnant after Hawking evaporation due to loop quantum gravity effects. Besides to show the existence of a stable black hole remnant in the vacuum case, the quantum dynamics for the non-vacuum case is also solved and compared with the effective one.

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arXiv2021

Relating spin-foam to canonical loop quantum gravity by graphical calculus

The graphical calculus method is generalized to study the relation between covariant and canonical dynamics of loop quantum gravity. On one hand, a graphical derivation of the partition function of the generalized Euclidean Engle-Pereira-Rovelli-Livine (EPRL) spin-foam model is presented. On the other hand, the action of a Euclidean Hamiltonian constraint operator on certain spin network states is calculated by graphical method. It turns out that the EPRL model can provide a rigging map such that the Hamiltonian constraint operator is weakly satisfied on certain physical states for the Immirzi parameter $β=1$. In this sense, the quantum dynamics between the covariant and canonical formulations are consistent to each other.

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arXiv2020

Canonical loop quantization of the lowest-order projectable Horava gravity

The Hamiltonian formulation of the lowest-order projectable Horava gravity, namely the so-called $λ$-$R$ gravity, is studied. Since a preferred foliation has been chosen in projectable Horava gravity, there is no local Hamiltonian constraint in the theory. In contrast to general relativity, the constraint algebra of $λ$-$R$ gravity forms a Lie algebra. By canonical transformations, we further obtain the connection-dynamical formalism of the $λ$-R gravity theories with real $su(2)$-connections as configuration variables. This formalism enables us to extend the scheme of non-perturbative loop quantum gravity to the $λ$-$R$ gravity. While the quantum kinematical framework is the same as that for general relativity, the Hamiltonian constraint operator of loop quantum $λ$-$R$ gravity can be well defined in the diffeomorphism-invariant Hilbert space. Moreover, by introducing a global dust degree of freedom to represent a dynamical time, a physical Hamiltonian operator with respect to the dust can be defined and the physical states satisfying all the constraints are obtained.

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arXiv2020

Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term

The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized separately mimicking the treatment of full loop quantum gravity. The new quantum dynamics for the spatially flat Friedmann-Robertson-Walker model with a massless scalar field as an emergent time is studied. By semiclassical analysis, the effective Hamiltonian constraint is obtained, which indicates that the new quantum dynamics has the correct classical limit. The classical big-bang singularity is again replaced by a quantum bounce. Similar to the case of quantizing only the Euclidean term, the backward evolution of the cosmological model determined by the new effective Hamiltonian will be bounced to an asymptotic de Sitter universe coupled to a massless scalar field, while the problem of negative energy density of matter in the former case is resolved.

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arXiv2020

Polytopes in all dimensional loop quantum gravity

The Lasserre's reconstruction algorithm is extended to the D-polytopes with the construction of their shape space. Thus, the areas of d-skeletons $(1\leq d\leq D)$ can be expressed as functions of the areas and normal bi-vectors of the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints in all dimensional loop quantum gravity, the simple coherent intertwiners are employed to describe semiclassical D-polytopes. New general geometric operators based on D-polytopes are proposed by using the Lasserre's reconstruction algorithm and the coherent intertwiners. Such kind of geometric operators have expected semiclassical property by the definition. The consistent semiclassical limit with respect to the semiclassical D-polytopes can be obtained for the usual D-volume operator in all dimensional loop quantum gravity by fixing its undetermined regularization factor case by case.

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arXiv2020

Alternative dynamics in loop quantum Brans-Dicke cosmology

To inherit more features of full loop quantum Brans-Dicke theory, the Euclidean and Lorentzian terms of the Hamiltonian constraint are quantized independently in loop quantum Brans-Dicke cosmology. An alternative Hamiltonian constraint operator and its effective expression are obtained in the cosmological model. A residual quantum correction term is found in the effective Hamiltonian constraint, which has no analog in the effective Hamiltonian of the loop quantum cosmology from general relativity. The dynamics driven by this effective Hamiltonian constraint is analyzed in detail. For the physically interesting case of $ω\gg 1$, this effective Hamiltonian drives a bouncing evolution which evolves from a de Sitter universe to a classical Brans-Dicke solution.

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arXiv2020

Mechanics of Isolated Horizons in Scalar-Tensor Theories

Based on the first-order action for scalar-tensor theories with the Immirzi parameter, the symplectic form for the spacetimes admitting a weakly isolated horizon as internal boundary is derived by the covariant phase space approach. The first law of thermodynamics for the weakly isolated horizons with rotational symmetry is obtained. It turns out that the Immirzi parameter appears in the expression of the angular momentum of isolated horizon, and the scalar field contributes to the horizon entropy.

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arXiv2020

General geometric operators in all dimensional loop quantum gravity

Two strategies for constructing general geometric operators in all dimensional loop quantum gravity are proposed. The different constructions are mainly come from the two different regularization methods for the de-densitized dual momentum, which play the role of building block for the spatial geometry. The first regularization method is a generalization of the regularization of the length operator in standard $(1+3)$-dimensional loop quantum gravity, while the second method is a natural extension of those for standard (D-1)-area and D-volume operators. Two versions of general geometric operators to measure arbitrary $m$-areas are constructed, and their properties are discussed and compared. They serve as valuable candidates to study the quantum geometry in arbitrary dimensions.

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arXiv2019

Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity

Although the physical Hamiltonian operator can be constructed in the deparameterized model of loop quantum gravity coupled to a scalar field, its property is still unknown. This open issue is attacked in this paper by considering an operator $\hat{H}_v$ representing the square of the physical Hamiltonian operator acting nontrivially on two-valent spin networks. The Hilbert space $\mathcal{H}_v$ preserved by the graphing changing operator $\hat{H}_v$ is consist of spin networks with a single two-valent non-degenerate vertex. The matrix element of $\hat{H}_v$ are explicitly worked out in a suitable basis. It turns out that the operator $\hat{H}_v$ is essentially self-adjoint, which implies a well-defined physical Hamiltonian operator in $\mathcal{H}_v$ for the deparameterized model.

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arXiv2019

Consistency check on the fundamental and alternative flux operators in loop quantum gravity

There are different constructions of the flux of triad in loop quantum gravity, namely the fundamental and alternative flux operators. In parallel to the consistency check on the two versions of operator by the algebraic calculus in the literature, we check their consistency by the graphical calculus. Our calculation based on the original Brink graphical method is obviously simpler than the algebraic calculation. It turns out that our consistency check fixes the regulating factor $κ_{\rm reg}$ of the Ashtekar-Lewandowski volume operator as $\frac12$, which corrects its previous value in the literature.

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arXiv2019

Loop quantum cosmology from an alternative Hamiltonian

In this paper, a new Hamiltonian constraint operator for loop quantum cosmology is constructed by using the Chern-Simons action. The quantum dynamics of the $k=0$ cosmological model with respect to a massless scalar field as an emergent time is determined by a difference equation. The semiclassical analysis shows that the new quantum dynamics has the correct classical limit, and the classical big-bang singularity is again replaced by the quantum bounce. Interestingly, the inverse time evolution of the flat Friedmann-Robertson-Walker cosmological model determined by the effective Hamiltonian will be bounced to an asymptotic de Sitter universe.

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