Black Hole Quasinormal Modes: Contamination by Massless Scalar Fields

Gravitational wave detections from black hole mergers have opened a new window to test General Relativity (GR) in strong-field regimes. A key technique involves analyzing the "ringdown" phase, the final stage of coalescence where the remnant black hole settles into its stable state, emitting gravitational waves with characteristic frequencies known as quasinormal modes (QNMs). Traditionally, research has focused on searching for shifts in these QNM frequencies from those predicted by GR's Kerr metric. However, recent work suggests that ringdown analysis might be more complex than anticipated. If new fields, beyond those described by GR, exist and couple non-minimally to gravity, their own quasinormal modes could "contaminate" the ringdown signal. This implies that observed deviations might not solely be due to shifts in the GR QNM frequencies, but also to the presence of additional QNMs associated with these new fields. Researchers investigated this concept within the framework of the shift-symmetric Horndeski action, which describes interactions between a massless scalar field and gravity, leading to second-order equations. Using a perturbative analysis, expanding in the scalar charge per unit black hole mass (q), they demonstrated that, up to order q², the coupling between the scalar and the Gauss-Bonnet invariant is the only term contributing to both frequency shifts and contamination. Both effects appear at the same perturbative order. If the assumption about the scalar amplitude being suppressed by q is relaxed, contamination can appear at leading order in q, dominating over frequency shifts and receiving additional corrections from other couplings. This finding underscores the importance of considering the potential presence of scalar fields when interpreting black hole ringdown signals.

Page curve in cosmological horizons reveals quantum information escape

Researchers have addressed a question analogous to the black hole information paradox, but applied to cosmological horizons: when does an individual Hawking pair begin to carry information out of a de Sitter horizon? This study, employing two-dimensional flow geometries that smoothly interpolate between an asymptotic AdS₂ boundary and a dS₂ static patch, models the emission of a Hawking pair via a probe state constructed from local operators and their modular conjugates. To achieve this, the scientists promoted the centaur algebra of observables to a Type II∞ factor through the crossed-product construction. This allowed them to compute the entropy difference between a thermofield-double reference state and the Hawking-pair state. The results show that this difference traces a characteristic "mini-Page curve" for the cosmological horizon: it starts near zero, reaches a minimum near τ ≈ β/8, and then increases again. The location of this minimum is interpreted as the time at which quantum information begins to escape the cosmological horizon. Extending the analysis to the microcanonical ensemble, it was shown that the algebraic entropy coincides with the generalized entropy of an entanglement wedge cut that tracks the emitted particle along the horizon. Furthermore, the relative modular flow generated between the two states yields a Lyapunov exponent λ = 2π/β. This finding identifies the scrambling time as the scale at which the information carried by the pair becomes accessible to a static-patch observer. This work represents a significant advance in understanding how quantum information behaves in extreme cosmological environments.