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**Area Regge Calculus and Discontinuous Metrics(****arXiv****)**

**Author : **Chris Wainwright, Ruth M. Williams

**Abstract : **Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a triangulated lattice and find that on a spacelike hypersurface no such discontinuity can arise. On a null hypersurface however, we can have such a situation and the resulting metric can be interpreted as a so-called refractive wave

**2.Dynamical Regge Calculus as Lattice Quantum Gravity (****arXiv****)**

**Author : **Hiroyuki Hagura

**Abstract :** We propose a hybrid model of simplicial quantum gravity by performing at once dynamical triangulations and Regge calculus. A motive for the hybridization is to give a dynamical description of topology-changing processes of Euclidean spacetime. In addition, lattice diffeomorphisms as invariance of the simplicial geometry are generated by certain elementary moves in the model. We attempt also a lattice-theoretic derivation of the black hole entropy using the symmetry. Furthermore, numerical simulations of 3D pure gravity are carried out,exhibiting a large hysteresis between two phases. We also measure geometric properties of Euclidean `time slice’ based on a geodesic distance, resulting in a fractal structure in the strong-coupling phase. Our hybrid model not only reproduces numerical results consistent with those of dynamical triangulations and Regge calculus, but also opens a possibility of studying quantum black hole physics on the lattice.

**3.On the length expectation values in quantum Regge calculus (****arXiv)**

**Author : **V. M. Khatsymovsky

**Abstract :** Regge calculus configuration superspace can be embedded into a more general superspace where the length of any edge is defined ambiguously depending on the 4-tetrahedron containing the edge. Moreover, the latter superspace can be extended further so that even edge lengths in each the 4-tetrahedron are not defined, only area tensors of the 2-faces in it are. We make use of our previous result concerning quantisation of the area tensor Regge calculus which gives finite expectation values for areas. Also our result is used showing that quantum measure in the Regge calculus can be uniquely fixed once we know quantum measure on (the space of the functionals on) the superspace of the theory with ambiguously defined edge lengths. We find that in this framework quantisation of the usual Regge calculus is defined up to a parameter. The theory may possess nonzero (of the order of Plank scale) or zero length expectation values depending on whether this parameter is larger or smaller than a certain value. Vanishing length expectation values means that the theory is becoming continuous, here {it dynamically} in the originally discrete framework

**4. (arXiv)**

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**5. (arXiv)**

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