Spherically symmetric solutions in dimensionally reduced spacetimes with a higher-dimensional cosmological constant

Details Spherically symmetric solutions in dimensionally reduced spacetimes with a higher-dimensional cosmological constant Spherically symmetric solutions in dimensionally reduced spacetimes with a higher-dimensional cosmological constant

Aug 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..44.1100w&link_type=abstract

Physical Review D (Particles, Fields, Gravitation, and Cosmology), Volume 44, Issue 4, 15 August 1991, pp.1100-1114

Mathematics

Logic

39

Scientific paper

Certain static solutions of D-dimensional gravity with a higher-dimensional cosmological constant Λ are studied. The solutions are taken to be spherically symmetric in the physical (m+2)-dimensional spacetime, where D=m+n+2 (or more generally the m-sphere is replaced by an arbitrary Einstein space), while the internal space is an arbitrary n-dimensional Einstein space. The global properties of all such solutions are derived by considering the equivalent dimensionally reduced system in m+2 dimensions, and by using techniques from the theory of dynamical systems after a judicious choice of variables. All solutions with a nonzero Λ are either found to contain naked singularities or not be asymptotically flat, as would be expected from the ``no-hair'' theorems. A recent ``black-hole'' solution derived by Kim and Cho in the context of these models is shown to be incorrect.

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