2001/04/27 by К. А. Бронников, Kirill A. Bronnikov · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Anti-de Sitter space #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #De Sitter universe #Field (mathematics) #General relativity #Mathematical physics #Mathematics #Minkowski space #Physics #Pure mathematics #Quantum mechanics #Scalar field #Schwarzschild radius #Spacetime #Universe #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.64.064013
published as Phys.Rev.D64:064013,2001 · Latex2e, 4 pages, 1 bezier figure
arxiv created 2001/04/27 · openalex publication_date 2001/08/27 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
I enumerate all possible types of spacetime causal structures that can appear in static, spherically symmetric configurations of a self-gravitating, real, nonlinear, minimally coupled scalar field \ensuremathφ in general relativity, with an arbitrary potential V(\ensuremathφ), not necessarily positive definite. It is shown that a variable scalar field adds nothing to the list of possible structures with a constant \ensuremathφ field, namely, Minkowski [or anti--de Sitter (AdS)], Schwarzschild, de Sitter, and Schwarzschild--de Sitter structures. It follows in particular that whatever V(\ensuremathφ) is, this theory does not admit regular black holes with flat or AdS asymptotics. It is concluded that the only possible globally regular, asymptotically flat solutions are solitons with a regular center, without horizons and with at least partly negative potentials V(\ensuremathφ). Extension of the results to more general field models is discussed.