2012/01/15 by Shun'ya Mizoguchi, Shun’ya Mizoguchi, Shinya Tomizawa · 10 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dilaton #Duality (order theory) #Kaluza–Klein theory #Massless particle #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum mechanics #Spacetime #Supergravity #Supersymmetry #hep-th
paper · pdf · doi:10.1103/physrevd.86.024022
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 86(2) (American Physical Society) · 16 pages
arxiv created 2012/01/15 · openalex publication_date 2012/07/11 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The dimensional reduction of the bosonic sector of five-dimensional minimal supergravity to a Lorentzian four-dimensional spacetime leads to a theory with a massless axion and a dilaton coupled to gravity and two U(1) gauge fields and the dimensionally reduced equations of motion have SL(2,ℝ)/SO(2)-duality invariance. In our previous work, utilizing the duality invariance, we formulated solution-generation techniques within five-dimensional minimal supergravity. In this work, by choosing a timelike Killing vector, we consider dimensional reduction to a four-dimensional Euclidean space, in which the field equations have SL(2,ℝ)/SO(1,1) invariance. In the timelike case, we develop a new duality transformation technique, while in the spacelike case we have done that in the previous work. As an example, by applying it to the Rasheed solutions, we obtain rotating Kaluza-Klein black hole solutions in five-dimensional minimal supergravity. In general, in contrast to the spacelike case, the resulting dimensionally reduced solution includes the so-called NUT (Newman, Unti, and Tamburino) parameter, and therefore from a four-dimensional point of view, such a spacetime is not asymptotically flat. However, it is shown that in some special cases, it can describe ordinary Kaluza-Klein black holes.