METAPHOR: Metabolic evaluation through phasor-based hyperspectral imaging and organelle recognition for mouse blastocysts and oocytes.

Only 30% of embryos from in vitro fertilized oocytes successfully implant and develop to term, leading to repeated transfer cycles. To reduce time-to-pregnancy and stress for patients, there is a need for a diagnostic tool to better select embryos and oocytes based on their physiology. The current standard employs brightfield imaging, which provides limited physiological information. Here, we introduce METAPHOR: Metabolic Evaluation through Phasor-based Hyperspectral Imaging and Organelle Recognition. This non-invasive, label-free imaging method combines two-photon illumination and AI to deliver the metabolic profile of embryos and oocytes based on intrinsic autofluorescence signals. We used it to classify i) mouse blastocysts cultured under standard conditions or with depletion of selected metabolites (glucose, pyruvate, lactate); and ii) oocytes from young and old mouse females, or in vitro-aged oocytes. The imaging process was safe for blastocysts and oocytes. The METAPHOR classification of control vs. metabolites-depleted embryos reached an area under the ROC curve (AUC) of 93.7%, compared to 51% achieved for human grading using brightfield imaging. The binary classification of young vs. old/in vitro-aged oocytes and their blastulation prediction using METAPHOR reached an AUC of 96.2% and 82.2%, respectively. Finally, organelle recognition and segmentation based on the flavin adenine dinucleotide signal revealed that quantification of mitochondria size and distribution can be used as a biomarker to classify oocytes and embryos. The performance and safety of the method highlight the accuracy of noninvasive metabolic imaging as a complementary approach to evaluate oocytes and embryos based on their physiology.

Infinite Quantum Twisting at the Cauchy Horizon of Rotating Black Holes.

We present a numerical calculation of the expectation value of the quantum angular-momentum current flux density for a scalar field in the Unruh state near the inner horizon of a Kerr-de Sitter black hole. Our results indicate that this flux diverges as V_{-}^{-1} in a suitable Kruskal coordinate such that V_{-}=0 at the inner horizon. Depending on the parameter values of the scalar field and black hole that we consider, and depending on the polar angle (latitude), this flux can have different signs. In the near extremal cases considered, the angle average of the expectation value of the quantum angular momentum current flux is of the opposite sign as the angular momentum of the background itself, suggesting that, in the cases considered, quantum effects tend to decrease the total angular momentum of the spheres away from the extremal value. We also numerically calculate the energy flux component, which provides the leading order divergence of the quantum stress energy tensor, dominant over the classical stress energy tensor, at the inner horizon. Taking our expectation value of the quantum stress tensor as the source in the semiclassical Einstein equation, our analysis suggests that the spheres approaching the inner horizon can undergo an infinite twisting due to quantum effects along latitudes separating regions of infinite expansion and contraction.

Quantum Fluxes at the Inner Horizon of a Spinning Black Hole.

Rotating or charged classical black holes in isolation possess a special surface in their interior, the Cauchy horizon, beyond which the evolution of spacetime (based on the equations of General Relativity) ceases to be deterministic. In this Letter, we study the effect of a quantum massless scalar field on the Cauchy horizon inside a rotating (Kerr) black hole that is evaporating via the emission of Hawking radiation (corresponding to the field being in the Unruh state). We calculate the flux components (in Eddington coordinates) of the renormalized stress-energy tensor of the field on the Cauchy horizon, as functions of the black hole spin and of the polar angle. We find that these flux components are generically nonvanishing. Furthermore, we find that the flux components change sign as these parameters vary. The signs of the fluxes are important, as they provide an indication of whether the Cauchy horizon expands or crushes (when backreaction is taken into account). Regardless of these signs, our results imply that the flux components generically diverge on the Cauchy horizon when expressed in coordinates which are regular there. This is the first time that irregularity of the Cauchy horizon under a semiclassical effect is conclusively shown for (four-dimensional) spinning black holes.

Spinning Black Holes Fall in Love.

The open question of whether a black hole can become tidally deformed by an external gravitational field has profound implications for fundamental physics, astrophysics, and gravitational-wave astronomy. Love tensors characterize the tidal deformability of compact objects such as astrophysical (Kerr) black holes under an external static tidal field. We prove that all Love tensors vanish identically for a Kerr black hole in the nonspinning limit or for an axisymmetric tidal perturbation. In contrast to this result, we show that Love tensors are generically nonzero for a spinning black hole. Specifically, to linear order in the Kerr black hole spin and the weak perturbing tidal field, we compute in closed form the Love tensors that couple the mass-type and current-type quadrupole moments to the electric-type and magnetic-type quadrupolar tidal fields. For a dimensionless spin ∼0.1, the nonvanishing quadrupolar Love tensors are ∼2×10^{-3}, thus showing that black holes are particularly "rigid" compact objects.

High-order asymptotics for the spin-weighted spheroidal equation at large real frequency.

The spin-weighted spheroidal eigenvalues and eigenfunctions arise in the separation by variables of spin-field perturbations of Kerr black holes. We derive a large, real-frequency asymptotic expansion of the spin-weighted spheroidal eigenvalues and eigenfunctions to high order. This expansion corrects and extends existing results in the literature and we validate it via a high-precision numerical calculation.

Quantum Backreaction on Three-Dimensional Black Holes and Naked Singularities.

We analytically investigate backreaction by a quantum scalar field on two rotating Bañados-Teitelboim-Zanelli (BTZ) geometries: that of a black hole and that of a naked singularity. In the former case, we explore the quantum effects on various regions of relevance for a rotating black hole space-time. We find that the quantum effects lead to a growth of both the event horizon and the radius of the ergosphere, and to a reduction of the angular velocity, compared to the unperturbed values. Furthermore, they give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the case of a naked singularity, we find that quantum effects lead to the formation of a horizon that shields it, thus supporting evidence for the rôle of quantum mechanics as a cosmic censor in nature.

Spectroscopy of the Schwarzschild black hole at arbitrary frequencies.

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.