Search

In linear perturbation theory, a static perturber in the vicinity of a Schwarzschild black hole (BH) enhances [suppresses] the Gauss-Bonnet (GB) curvature invariant, $\mathcal{R}_{\rm GB}$, in the high [low] tide regions. By analysing exact solutions of the vacuum Einstein field equations describing one or two BHs immersed in a multipolar gravitational field, which is locally free of pathologies, including conical singularities, we study the corresponding non-linear tides on a fiducial BH, in full General Relativity (GR). We show that the tidal field due to a far away, or close by, static BH creates high/low tides that can deviate not only quantitatively but also qualitatively from the weak field/Newtonian pattern. Remarkably, the suppression in low tide regions never makes $\mathcal{R}_{\rm GB}$ negative on the BH, even though the horizon Gaussian curvature may become negative; but $\mathcal{R}_{\rm GB}$ can vanish in a measure zero set, a feature qualitatively recovered in a Newtonian analogue model. Thus, purely gravitational, static, tidal interactions in GR, no matter how strong, cannot induce GB$^-$ scalarization. We also show that a close by BH produces noticeable asymmetric tides on another (fiducial) BH., Comment: 13 pages, 13 figures

In the presence of certain non-minimal couplings between a scalar field and the Gauss-Bonnet curvature invariant, Kerr black holes can scalarize, as long as they are spinning fast enough. This provides a distinctive violation of the Kerr hypothesis, occurring only for some high spin range. In this paper we assess if strong magnetic fields, that may exist in the vicinity of astrophysical black holes, could facilitate this distinctive effect, by bringing down the spin threshold for scalarization. This inquiry is motivated by the fact that self-gravitating magnetic fields, by themselves, can also promote "spin-induced" scalarization. Nonetheless, we show that in the \textit{vicinity of the horizon} the effect of the magnetic field $B$ on a black hole of mass $M$, up to $BM\lesssim 1$, works \textit{against} spin-induced scalarization, requiring a larger dimensionless spin $j$ from the black hole. A geometric interpretation for this result is suggested, in terms of the effects of rotation $vs.$ magnetic fields on the horizon geometry., Comment: 8 pages, 2 figures