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Title: Non-linear tides and Gauss-Bonnet scalarization
Author: Annulli, Lorenzo
Herdeiro, Carlos A.R.
Issue Date: 2023
Publisher: Elsevier
Abstract: In linear perturbation theory, a static perturber in the vicinity of a Schwarzschild black hole (BH) enhances [suppresses] the Gauss-Bonnet (GB) curvature invariant, RGB, 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 RGB negative on the BH, even though the horizon Gaussian curvature may become negative; but RGB 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.
Peer review: yes
DOI: 10.1016/j.physletb.2023.138137
ISSN: 0370-2693
Appears in Collections:CIDMA - Artigos
GGDG - Artigos

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