Constraints for warped branes

Abstract

We investigate singular geometries which can be associated with warped branes in arbitrary dimensions. If the brane tension is allowed to be variable, the extremum condition for the action requires additional constraints beyond the solution of the field equations. In a higher dimensional world, such constraints arise from variations of the metric which are local in the usual four-dimensional spacetime, without changing the geometry of internal space. As a consequence, continuous families of singular solutions of the field equations, with arbitrary integration constants, are generically reduced to a discrete subset of extrema of the action, similar to regular spaces. As an example, no static extrema of the action with effective four-dimensional gravity exist for six-dimensional gravity with a cosmological constant. These findings explain why the field equations of the reduced four-dimensional theory are not consistent with arbitrary solutions of the higher dimensional field equations - consistency requires the additional constraints. The characteristic solutions for variable tension branes are non-static runaway solutions where the effective four-dimensional cosmological constant vanishes as time goes to infinity.

25 pages

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Cited by in corpus (6)

• Fermionic Kaluza-Klein modes in the string-cigar braneworld
• Dilatation symmetry in higher dimensions and the vanishing of the cosmological constant
• Dynamical Foundations of the Brane Induced Gravity
• The cosmological constant and higher dimensional dilatation symmetry
• Warping with dilatation symmetry and self-tuning of the cosmological constant
• General Solutions of Braneworlds under the Schwarzschild Ansatz