A Gluing Construction Regarding Point Particles in General Relativity

• Published in: Annales Henri Poincaré Vol. 10; no. 8; pp. 1437 - 1486
• Main Author: Allen, Iva Stavrov
• Format: Journal Article
• Language: English
• Published: Basel SP Birkhäuser Verlag Basel 01-05-2010; Springer
• Subjects: Classical and Quantum Gravitation; Dynamical Systems and Ergodic Theory; Elementary Particles; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Other topics in mathematical methods in physics; Physics; Physics and Astronomy; Quantum Field Theory; Quantum Physics; Relativity Theory; Sciences and techniques of general use; Theoretical; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Point Particle; Hamiltonian Constraint; Constant Mean Curvature; Conformal Killing; Conformal Killing Vector; Stresses; Wald test; Limit point; General relativity; Einstein equation; Mathematical physics; Truncated solution
• ISSN: 1424-0637; 1424-0661
• DOI: 10.1007/s00023-010-0025-8

We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled “point-particle” limits analogous to those of Gralla and Wald (Class Quantum Grav 25:205009, 2008). In particular, we produce examples of initial data which generalize Schwarzschild–de Sitter initial data and gluing theorems of IMP-type (Isenberg et al. in Comm Math Phys 231:529–568).