Spherically symmetric solutions in dimensionally reduced spacetimes

Details Spherically symmetric solutions in dimensionally reduced spacetimes Spherically symmetric solutions in dimensionally reduced spacetimes

Jul 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cqgra...6..987m&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 6, July 1, 1989, p. 987-1002. Research supported by the Royal Society.

Statistics

Computation

51

Computational Astrophysics, Einstein Equations, Relativity, Space-Time Functions, Differential Equations, Schwarzschild Metric, Singularity (Mathematics), Symmetry, Vacuum

Scientific paper

Consideration is given to static solutions of the vacuum Einstein equations in D = m + n + 2 dimensions which have the following symmetries: the solutions are spherically symmetric in (m + 2) dimensions, (or more generally the m-sphere is replaced by an abitrary m-dimensional Einstein space), while the internal space is any 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. Apart from the trivial case of the Schwarzschild solution with constant scalar field, all solutions are found to contain naked singularities or else not to be asymptotically flat, as would be expected from the 'no hair' theorems.

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