On the Bogomol'nyi bound in Einstein-Maxwell-dilaton gravity

Abstract

It has been shown that the 4-dimensional Einstein-Maxwell-dilaton theory allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant $\alpha$, and that the bound is saturated if and only if the (asymptotically flat) spacetime admits a nontrivial spinor satisfying the gravitino and the dilatino Killing spinor equations. The present paper revisits this issue and argues that the dilatino equation fails to ensure the dilaton field equation unless the solution is purely electric/magnetic, or the dilaton coupling constant is given by $\alpha =0,\sqrt{3}$, corresponding to the Brans-Dicke-Maxwell theory and the Kaluza-Klein reduction of 5-dimensional vacuum gravity, respectively. A systematic classification of the supersymmetric solutions reveals that the solution can be rotating if and only if the solution is dyonic or the coupling constant is given by $\alpha =0,\sqrt{3}$. This implies that the theory with $\alpha \ne 0,\sqrt{3}$ cannot be embedded into supergravity except for the static truncation. Physical properties of supersymmetric solutions are explored from various points of view.

v2: 23 pages, typos corrected, minor modifications, to appear in CQG

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• New family of C-metrics in $\mathcal{N}=2$ gauged supergravity
• Stringy Stability of Charged Dilaton Black Holes with Flat Event Horizon
• Exact convoluted solutions in higher-dimensional Einstein-Maxwell theory
• Static spacetimes haunted by a phantom scalar field II: dilatonic charged solutions
• Modeling scalar fields consistent with positive mass
• Divergence equations and uniqueness theorem of static black holes
• Discreteness of dyonic dilaton black holes
• Positive mass theorem in extended supergravities
• Exact helicoidal and catenoidal solutions in Einstein-Maxwell theory
• A New Class of Exact Solutions in Einstein-Maxwell-dilaton Theory
• Bianchi IX geometry and the Einstein-Maxwell theory
• Minimal Surfaces and Generalized Einstein-Maxwell-dilaton Theory
• NUT Solutions in Einstein-Maxwell-scalar-Gauss-Bonnet Gravity
• M-Branes on Minimal Surfaces
• Supersymmetry of the Robinson-Trautman solution
• Supergravity $p$-branes with scalar charge