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Bertotti-Robinson type solutions to Dilaton-Axion Gravity

Gerard Clement·Dmitri Gal'tsov
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Abstract

We present a new solution to dilaton-axion gravity which looks like a rotating Bertotti-Robinson (BR) Universe. It is supported by an homogeneous Maxwell field and a linear axion and can be obtained as a near-horizon limit of extremal rotating dilaton-axion black holes. It has the isometry $SL(2,R)\times U(1)$ where U(1) is the remnant of the SO(3) symmetry of BR broken by rotation, while $SL(2,R)$ corresponds to the $AdS_2$ sector which no longer factors out of the full spacetime. Alternatively our solution can be obtained from the D=5 vacuum counterpart to the dyonic BR with equal electric and magnetic field strengths. The derivation amounts to smearing it in D=6 and then reducing to D=4 with dualization of one Kaluza-Klein two-form in D=5 to produce an axion. Using a similar dualization procedure, the rotating BR solution is uplifted to D=11 supergravity. We show that it breaks all supersymmetries of N=4 supergravity in D=4, and that its higher dimensional embeddings are not supersymmetric either. But, hopefully it may provide a new arena for corformal mechanics and holography. Applying a complex coordinate transformation we also derive a BR solution endowed with a NUT parameter.

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Gerard Clement, Dmitri Gal'tsov. 2001-02-06. Bertotti-Robinson type solutions to Dilaton-Axion Gravity. https://doi.org/10.1103/physrevd.63.124011

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