Regge calculus: a brief review and bibliography

Presents a brief review of the theory and applications of Regge calculus in classical and quantum gravity, followed by a comprehensive bibliography which the author hopes will be of use to workers in the subject.

[1]  J. Hartle.  Simplicial minisuperspace I. General discussion , 1985 .

[2]  J. Barrett.  The Einstein tensor in Regge's discrete gravity theory , 1986 .

[3]  Semilocality of one-dimensional simplicial quantum gravity , 1987 .

[4]  T. Regge.  General relativity without coordinates , 1961 .

[5]  Ruth M. Williams,et al.  Dynamics of the friedmann universe using regge calculus , 1973 .

[6]  THREE-DIMENSIONAL REGGE QUANTUM GRAVITY AND 6J SYMBOLS , 1983 .

[7]  H. Waelbroeck.  2+1 lattice gravity , 1990 .

[8]  Regge calculus and observations. II. Further applications , 1984 .

[9]  The time-symmetric initial value problem for a homogeneous, anisotropic, empty, closed universe, using Regge calculus , 1985 .

[10]  J. Porter.  Calculation of relativistic model stars using Regge calculus , 1987 .

[11]  Null-strut calculus. II. Dynamics. , 1990, Physical review. D, Particles and fields.

[12]  Bander.  Hamiltonian lattice gravity. II. Discrete moving-frame formulation. , 1988, Physical review. D, Particles and fields.

[13]  S. M. Lewis.  Two cosmological solutions of Regge calculus , 1982 .

[14]  Hamber.  Phases of four-dimensional simplicial quantum gravity. , 1992, Physical review. D, Particles and fields.

[15]  Leo Brewin.  An application of a first-order formulation of the Regge calculus , 1988 .

[16]  Richard Friedberg,et al.  Lattice gravity near the continuum limit , 1984 .

[17]  M. Dubal.  Initial data for time-symmetric gravitational radiation using Regge calculus , 1989 .

[18]  Regge-Palatini calculus , 1986 .

[19]  H. Nielsen,et al.  Diffeomorphism Symmetry in Simplicial Quantum Gravity , 1986 .

[20]  M. Caselle,et al.  Regge Calculus as a Local Theory of the Poincare Group , 1989 .

[21]  Ruth M. Williams,et al.  NONPERTURBATIVE SIMPLICIAL QUANTUM GRAVITY , 1985 .

[22]  Williams,et al.  Three-plus-one formulation of Regge calculus. , 1986, Physical review. D, Particles and fields.

[23]  J. Friedman,et al.  3+1 Regge calculus with conserved momentum and Hamiltonian constraints , 1986 .

[24]  R. Sorkin.  Time-evolution problem in regge calculus , 1975 .

[25]  M. Roček,et al.  The quantization of Regge calculus , 1984 .

[26]  Jourjine.  Discrete gravity without coordinates. , 1987, Physical review. D, Particles and fields.

[27]  Berg.  Exploratory numerical study of discrete quantum gravity. , 1985, Physical review letters.

[28]  A correlation decay theorem at high temperature , 1984 .

[29]  林 憲二,et al.  C. W. Misner, K. S. Thorne. and J. A. Wheeler : Gravitation, W. H. Freeman, San Francisco, 1973, 1279ページ, 26×21cm, $39.50. , 1975 .

[30]  T. Piran,et al.  Solutions of the Regge equations , 1986 .

[31]  Ruth M. Williams.  Quantum Regge calculus in the Lorentzian domain and its Hamiltonian formulation , 1986 .

[32]  V. Khatsymovsky.  Tetrad and self-dual formulations of Regge calculus , 1989 .

[33]  J Porter,et al.  A new approach to the Regge calculus: I. Formalism , 1987 .

[34]  On the continuum limit of curvature squared actions in the regge calculus , 1989 .

[35]  V. Khatsymovsky.  Continuous time Regge gravity in the tetrad-connection variables , 1991 .

[36]  Warner A. Miller.  The geometrodynamic content of the Regge equations as illuminated by the boundary of a boundary principle , 1986 .

[37]  J. Barrett.  The fundamental theorem of linearised Regge calculus , 1987 .

[38]  Bander.  Hamiltonian lattice gravity. Deformations of discrete manifolds. , 1987, Physical review. D, Particles and fields.

[39]  J. Ambjorn.  2d gravity, random surfaces and all that , 1991 .

[40]  H. Hamber.  Phases of simplicial quantum gravity , 1992 .

[41]  Lattice gravity and strings , 1985 .

[42]  B. Berg.  Entropy versus energy on a fluctuating four-dimensional Regge skeleton , 1986 .

[43]  Rafael D. Sorkin,et al.  The electromagnetic field on a simplicial net , 1975 .

[44]  J. Louko,et al.  Regge calculus in anisotropic quantum cosmology , 1992 .

[45]  Three-dimensional Einstein gravity and Regge calculus , 1985 .

[46]  Godfrey,et al.  Simplicial quantum gravity in more than two dimensions. , 1991, Physical review. D, Particles and fields.

[47]  M. Roček,et al.  Quantum regge calculus , 1981 .

[48]  L. Brewin,et al.  A continuous time formulation of the Regge calculus , 1988 .

[49]  D. Foerster.  Nonperturbative d = 2 euclidean gravity without a lattice , 1987 .

[50]  Don Weingarten.  Geometric formulation of electrodynamics and general relativity in discrete space–time , 1977 .

[51]  Bander.  Functional measure for lattice gravity. , 1986, Physical review letters.

[52]  J. Hartle.  Simplical minisuperspace. III. Integration contours in a five‐simplex model , 1989 .

[53]  H. Ren.  Matter fields in lattice gravity , 1988 .

[54]  P. E. Parker,et al.  Smooth Limits of Piecewise-Linear Approximations , 1994 .

[55]  Ruth M. Williams,et al.  TWO-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY , 1986 .

[56]  H. Nielsen,et al.  Pregeometric quantum lattice: A general discussion , 1986 .

[57]  H. Romer,et al.  Functional integration and the diffeomorphism group in Euclidean lattice quantum gravity , 1986 .

[58]  Ninomiya,et al.  Functional formulation of Regge gravity. , 1986, Physical Review D, Particles and fields.

[59]  Brewin.  Marginally trapped surfaces in a simplicial space. , 1988, Physical review. D, Particles and fields.

[60]  Ruth M. Williams,et al.  A 3+1 Regge calculus model of the Taub universe , 1988 .

[61]  L. Brewin,et al.  Friedmann cosmologies via the Regge calculus , 1987 .

[62]  Quasi-regular singularities based on null planes , 1987 .

[63]  P. Tuckey.  Independent variables in 3+1 Regge calculus , 1989 .

[64]  Robert Schrader,et al.  On the curvature of piecewise flat spaces , 1984 .

[65]  Herbert W. Hamber.  Simulations of Discrete Quantized Gravity , 1991, Int. J. High Perform. Comput. Appl..

[66]  N. Warner.  The application of Regge calculus to quantum gravity and quantum field theory in a curved background , 1982, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[67]  T. Piran,et al.  Inflation in universes with a massive scalar field , 1985 .

[68]  Exterior differentiation in the Regge calculus , 1986 .

[69]  H. Hamber.  CRITICAL BEHAVIOR IN SIMPLICIAL QUANTUM GRAVITY , 1991 .

[70]  L. Brewin.  Equivalence of the Regge and Einstein equations for almost flat simplicial space-times , 1989 .

[71]  D. Weingarten.  Euclidean quantum gravity on a lattice , 1982 .

[72]  J. Barrett.  The geometry of classical Regge calculus , 1987 .

[73]  Kheyfets,et al.  Pseudo-Riemannian geometry on a simplicial lattice and the extrinsic curvature tensor. , 1989, Physical review. D, Particles and fields.

[74]  C. Wong.  Application of Regge Calculus to the Schwarzschild and Reissner‐Nordstro/m Geometries at the Moment of Time Symmetry , 1971 .

[75]  M. Gross,et al.  Critical properties of two-dimensional simplicial quantum gravity , 1991 .

[76]  J. Barrett,et al.  The convergence of lattice solutions of linearised Regge calculus , 1988 .

[77]  B. Hasslacher,et al.  Spin networks are simplicial quantum gravity , 1981 .

[78]  L. Budach.  On the Combinatorial Foundations of Regge-Calculus† , 1989 .

[79]  J. Vickers,et al.  The large-scale bending of cosmic strings , 1990 .

[80]  Jourjine.  Dimensional phase transitions: Coupling of matter to the cell complex. , 1985, Physical review. D, Particles and fields.

[81]  S. Hawking,et al.  Space-Time Foam , 1979 .

[82]  Bergfinnur Durhuus,et al.  THREE-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY AND GENERALIZED MATRIX MODELS , 1991 .

[83]  Richard Friedberg,et al.  Derivation of Regge's action from Einstein's theory of general relativity☆ , 1984 .

[84]  V. Bezerra.  Einstein gravity in the loop variable approach , 1988 .

[85]  Ruth M. Williams,et al.  APPLICATION OF REGGE CALCULUS TO THE AXIALLY SYMMETRIC INITIAL-VALUE PROBLEM IN GENERAL RELATIVITY. , 1972 .

[86]  L. Brewin,et al.  The Riemann and extrinsic curvature tensors in the Regge calculus , 1988 .

[87]  Ruth M. Williams,et al.  Conserved constraints in three-plus-one Regge calculus , 1990 .

[88]  Ruth M. Williams,et al.  Regge-calculus model for the Tolman universe , 1974 .

[89]  J. Hartle.  Simplicial minisuperspace. II. Some classical solutions on simple triangulations , 1986 .

[90]  Alan L. Yuille,et al.  Non-Rigid Motion and Regge Calculus. , 1989 .

[91]  Null-strut calculus. I. Kinematics. , 1990, Physical review. D, Particles and fields.

[92]  J. Barrett.  A convergence result for linearised Regge calculus , 1988 .

[93]  G. Ellis,et al.  Regge calculus and observations. I. Formalism and applications to radial motion and circular orbits , 1981 .

[94]  W. Miller,et al.  A few insights into the nature of classical and quantum gravity via null-strut calculus , 1989 .

[95]  J. Hartle.  Unruly topologies in two-dimensional quantum gravity , 1985 .

[96]  Ruth M. Williams,et al.  Simplicial quantum gravity with higher derivative terms: Formalism and numerical results in four dimensions , 1986 .

[97]  J Porter,et al.  A new approach to the Regge calculus: II. Application to spherically symmetric vacuum spacetimes , 1987 .

[98]  R. Sorkin,et al.  Boundary terms in the action for the Regge calculus , 1981 .

[99]  Ruth M. Williams,et al.  Higher derivative quantum gravity on a simplicial lattice , 1984 .