2017/08/31 by К. А. Бронников, K. A. Bronnikov, K. A. Baleevskikh +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Dark energy #Energy condition #Exotic matter #General relativity #Geometry #Isotropy #Mathematical physics #Mathematics #Perfect fluid #Physics #Quantum mechanics #Spacetime #Tensor (intrinsic definition) #Theoretical physics #Wormhole #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.96.124039
published as Phys. Rev. D 96, 124039 (2017) · 13 pages, 13 figures. A new section on traversability and lensing has been added, as well as new comments and references. To appear in Phys. Rev. D
arxiv created 2017/12/12 · openalex publication_date 2017/12/29 · arxiv updated 2018/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For static, spherically symmetric space-times in general relativity (GR), a no-go theorem is proved: it excludes the existence of wormholes with flat and/or anti--de Sitter asymptotic regions on both sides of the throat if the source matter is isotropic, i.e., the radial and tangential pressures coincide. It explains why in all previous attempts to build such solutions it was necessary to introduce boundaries with thin shells that manifestly violate the isotropy of matter. Under a simple assumption on the behavior of the spherical radius r(x), we obtain a number of examples of wormholes with isotropic matter and one or both de Sitter asymptotic regions, allowed by the no-go theorem. We also obtain twice asymptotically flat wormholes with anisotropic matter, both symmetric and asymmetric with respect to the throat, under the assumption that the scalar curvature is zero. These solutions may be on equal grounds interpreted as those of GR with a traceless stress-energy tensor and as vacuum solutions in a brane world. For such wormholes, the traversability conditions and gravitational lensing properties are briefly discussed. As a byproduct, we obtain twice asymptotically flat regular black hole solutions with up to four Killing horizons. As another byproduct, we point out intersection points in families of integral curves for the function A(x)=gtt, parametrized by its values on the throat.