2001/10/31 by Sean M. Carroll, James Geddes, Mark B. Hoffman +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Curvature #Extra dimensions #General relativity #Geometry #Homogeneous #Homogeneous space #Isotropy #Manifold (fluid mechanics) #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Space (punctuation) #Spacetime #Stability (learning theory) #Statistical physics #Theoretical physics #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.66.024036
published as Phys.Rev. D66 (2002) 024036 · 25 pages; minor changes, improved references
arxiv created 2002/04/29 · openalex publication_date 2002/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
If spacetime possesses extra dimensions of size and curvature radii much larger than the Planck or string scales, the dynamics of these extra dimensions should be governed by classical general relativity. We argue that in general relativity it is nontrivial to obtain solutions where the extra dimensions are static and are dynamically stable to small perturbations. We also illustrate that intuition on equilibrium and stability built up from nongravitational physics can be highly misleading. For all static, homogeneous solutions satisfying the null energy condition, we show that the Ricci curvature of space must be non-negative in all directions. Much of our analysis focuses on a class of spacetime models where space consists of a product of homogeneous and isotropic geometries. A dimensional reduction of these models is performed, and their stability to perturbations that preserve the spatial symmetries is analyzed. We conclude that the only physically realistic examples of classically stabilized large extra dimensions are those in which the extra-dimensional manifold is positively curved.