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Abstract: We investigate singular geometries which can be associated with warped branesin arbitrary dimensions. If the brane tension is allowed to be variable, theextremum condition for the action requires additional constraints beyond thesolution of the field equations. In a higher dimensional world, suchconstraints arise from variations of the metric which are local in the usualfour-dimensional spacetime, without changing the geometry of internal space. Asa consequence, continuous families of singular solutions of the fieldequations, with arbitrary integration constants, are generically reduced to adiscrete subset of extrema of the action, similar to regular spaces. As anexample, no static extrema of the action with effective four-dimensionalgravity exist for six-dimensional gravity with a cosmological constant. Thesefindings explain why the field equations of the reduced four-dimensional theoryare not consistent with arbitrary solutions of the higher dimensional fieldequations - consistency requires the additional constraints. The characteristicsolutions for variable tension branes are non-static runaway solutions wherethe effective four-dimensional cosmological constant vanishes as time goes toinfinity.



Author: C.Wetterich

Source: https://arxiv.org/







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