Manifold dimension of a causal set: Tests in conformally flat spacetimes

This paper describes an approach that uses flat-spacetime dimension estimators to estimate the manifold dimension of causal sets that can be faithfully embedded into curved spacetimes. The approach is invariant under coarse graining and can be implemented independently of any specific curved spacetime. Results are given based on causal sets generated by random sprinklings into conformally flat spacetimes in 2, 3, and 4 dimensions, as well as one generated by a percolation dynamics.

[1]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[2]  William H. Press,et al.  Numerical Recipes in FORTRAN - The Art of Scientific Computing, 2nd Edition , 1987 .

[3]  Karsten P. Ulland,et al.  Vii. References , 2022 .

[4]  R. Sorkin,et al.  Classical sequential growth dynamics for causal sets , 1999, gr-qc/9904062.

[5]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[6]  D. D. Reid.  Discrete quantum gravity and causal sets , 2001 .

[7]  D. Meyer.  The dimension of causal sets , 1988 .

[8]  I. Modena,et al.  GENERAL RELATIVITY AND GRAVITATIONAL PHYSICS , 1991, General Relativity and Gravitational Physics.

[9]  Bombelli,et al.  Space-time as a causal set. , 1987, Physical review letters.

[10]  Gregory,et al.  Structure of random discrete spacetime. , 1990, Physical review letters.

[11]  Walter L. Smith.  Probability and Statistics , 1959, Nature.