Buchdahl and Tolman Oppenheimer Volkoff limits for d-dimensional star-like solutions with a cosmological constant

Details Buchdahl and Tolman Oppenheimer Volkoff limits for d-dimensional star-like solutions with a cosmological constant Buchdahl and Tolman Oppenheimer Volkoff limits for d-dimensional star-like solutions with a cosmological constant

Feb 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cqgra..26c5021z&link_type=abstract

Classical and Quantum Gravity, Volume 26, Issue 3, pp. 035021 (2009).

Mathematics

Logic

Scientific paper

In this paper, we investigate the conditions for a (non-)regular perfect fluid with a cosmological constant in hydrostatic equilibrium for d-dimensional spacetime. The generalized Tolman Oppenheimer Volkoff equation is derived and a bound for the cosmological constant is given for the various geometries. We also follow Buchdahl's method to get a bound for the degree of compactification and show that it is valid only for regular spherical topology solutions, and for d = 3 toroidal/planar topology solutions. We also study the regions where the toroidal/planar topology solution in d = 3 is in hydrostatic equilibrium.

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