Gravity coupled to a scalar field in extra dimensions

Abstract

In d+1 dimensions we solve the equations of motion for the case of gravity minimally or conformally coupled to a scalar field. For the minimally coupled system the equations can either be solved directly or by transforming vacuum solutions, as shown before in 3+1 dimensions by Buchdahl. In d+1 dimensions the solutions have been previously found directly by Xanthopoulos and Zannias. Here we first rederive these earlier results, and then extend Buchdahl's method of transforming vacuum solutions to d+1 dimensions. We also review the conformal coupling case, in which d+1 dimensional solutions can be found by extending Bekenstein's method of conformal transformation of the minimal coupling solution. Combining the extended versions of Buchdahl transformations and Bekenstein transformations we can in arbitrary dimensions always generate solutions of both the minimal and the conformal equations from known vacuum solutions.

v2, 10 pages, minor change, two more references, published version. Extended version of talk given at ERE2006, Palma de Mallorca, Spain, Sept. 4-8, 2006

References in corpus (5)

• Spherical Black Holes cannot Support Scalar Hair
• Black holes cannot support conformal scalar hair
• Dressing a black hole with non-minimally coupled scalar field hair
• "No-Scalar-Hair" Theorems for Nonminimally Coupled Fields with Quartic Self-Interaction
• Scalar fields in multidimensional gravity. No-hair and other no-go theorems

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• A Viable Dark Fluid Model
• Higher-dimensional Buchdahl and Janis-Robinson-Winicour transformations in the Einstein-Maxwell system with a massless scalar field
• Dilatonic effects near naked singularities
• Dilatonic effects on a falling test mass in scalar-tensor theory
• A field theoretic approach to the energy momentum tensor for theories coupled with gravity
• "Jordan's Scalar Stars" and Dark Matter
• Comment about the "Gravity coupled to a scalar field in extra dimensions" paper
• A note on "Algebraic approach to Casimir force between two $\delta$-like potentials" (K. Ziemian, Ann. Henri Poincaré, Online First, 2021)