Abstract
External magnetic fields can probe the composite structure of black holes in string theory. With this motivation we study magnetised four-charge black holes in the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. We employ solution generating techniques to obtain Melvin backgrounds, and black holes in these backgrounds. For an initially electrically charged static black hole immersed in magnetic fields, we calculate the resultant angular momenta and analyse their global structure. Examples are given for which the ergoregion does not extend to infinity. We calculate magnetic moments and gyromagnetic ratios via Larmor's formula. Our results are consistent with earlier special cases. A scaling limit and associated subtracted geometry in a single surviving magnetic field is shown to lift to $AdS_3\times S^2$. Magnetizing magnetically charged black holes give static solutions with conical singularities representing strings or struts holding the black holes against magnetic forces. In some cases it is possible to balance these magnetic forces.
Highlights
Maxwell fields, and black holes may carry k generalised electric and k generalised magnetic charges
Explicit solutions are available for all eight charges [4] in a theory often referred to as the STU model, which is N = 2 supergravity coupled to 3 additional vector multiplets. (See [5, 6] for the results for just four charges.) If this is reduced to three dimensions on a Killing symmetry, the bosonic sector of the resulting theory can be cast into the form of a scalar sigma model with a global O(4, 4) symmetry coupled to gravity
In the case of Einstein-Maxwell theory, it was found that a static magnetically charged but electrically neutral Reissner-Nordstrom black hole seed remains static and non-accelerating upon magnetization, but the metric exhibits a conical singularity along the axis of symmetry which represents a cosmic string whose tension is tuned so as to prevent acceleration
Summary
In the case of two non-zero equal charges, say, Q1 = Q2 = Q and Q3 = Q4 = 0, we obtain the following nonzero gyromagnetic matrix coefficients: g11 = g22 = 2 , g33 = g44 = 2 c2 , g34. In the case of three non-zero equal charges, say, Q1 = Q2 = Q3 = Q and Q4 = 0, we get the following nonzero gyromagnetic matrix coefficients: g11 = g22 = g33 = 2 + tanh δ , g44 = 3c2 − 1 , gi. Even though Q4 = 0, a nonzero μ4 is induced, since g4jQj = − tanh δ(2 + tanh δ) and g4 = − tanh δ(2 + tanh δ) Another explicit example can be obtained with pair-wise equal charges, say, Q1 = Q3 and Q2 = Q3.
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