The authors construct a model in which a piecewise mass function describes a Schwarzschild black hole surrounded by a finite, electromagnetically inert dark-matter distribution. The dark matter is treated as an effective addition to the black hole’s mass, with separate parameters for the mass ratio ΔM/M, the shell’s inner boundary rs and its thickness Δrs. The authors state that the framework can represent dark matter bound in a galactic halo as well as locally captured objects such as brown dwarfs, stellar-mass black holes, primordial black holes and non-radiating dust.

For the non-rotating case, the analysis identifies a critical shell mass beyond which the metric develops an additional pair of horizons. With rs/M = 2 and Δrs/M = 200, the critical values are r*/M = 152 and ΔM/M = 800/9, or about 88.9. Below that threshold, the original event horizon remains in place, although the photon sphere and shadow radius can change slightly. Above it, the outermost root becomes a new event horizon enclosing the central black hole and part of the dark-matter shell, while the photon-sphere and shadow scales increase substantially.

The authors then generalize the static model to an axisymmetric rotating spacetime using the Newman–Janis Algorithm. The resulting metric returns to the Kerr solution when ΔM = 0 and to the static configuration when the spin parameter is zero. They report that the metric satisfies the Einstein field equations and derive corresponding dark-matter density and pressure profiles. The surface stress-energy at the interfaces of the piecewise mass distribution is found to vanish.

In the rotating model, the critical dark-matter mass depends on spin and shell geometry. For an extremal black hole with a/M = 1 and Δrs/M = 200, the reported threshold is ΔM/M = 88.3 at r*/M = 150.5. Models above this threshold develop an enlarged outer horizon and additional roots in the stationary-limit equation, changing the locations and number of ergosphere layers. The reported changes concern the horizon, ergosphere, critical photon-orbit and shadow scales; the study does not establish a general expansion of every physical scale in the system.

Null geodesics are used to locate the unstable circular photon orbits that define the shadow boundary. In the high-mass regime, the critical photon orbits lie outside the dark-matter shell, where the mass function is constant and the geometry has the Kerr form with a much larger total mass. At a fixed spin, rotation and frame-dragging then have less influence relative to the enlarged shadow scale. The calculated distortion parameter consequently approaches zero, producing a nearly circular shadow even at high spin. This circularization is a model prediction rather than an observed black-hole feature.

The study also estimates the high-frequency absorption cross section from the average shadow radius and uses the surface gravity of the outer horizon to calculate Hawking temperature and thermal energy emission. At fixed dark-matter mass, the model predicts a lower emission rate as spin increases. Dark-matter masses below the critical threshold have a marginal effect, whereas above the threshold the calculated Hawking temperature becomes very small and the emission rate is strongly suppressed.

The authors compare predicted shadow diameters with EHT values of dsh/M = 11 ± 1.5 for M87* and dsh/M = 9.77 ± 0.67 for Sagittarius A*. For M87*, all theoretically allowed dark-matter masses in the plotted compatible region satisfy both the 1σ and 2σ observational intervals. For Sagittarius A*, the full allowed region satisfies the 2σ interval, while a 1σ upper limit emerges and decreases as spin rises. At a/M = 0.9, the reported constraint is ΔM/M ≤ 22.3853.

Because the high-mass branch predicts a shadow diameter beyond the EHT-compatible range, the model disfavors dark-matter configurations large enough to trigger the new outer-horizon branch near the two observed black holes. Within the study’s assumptions, the dark matter must either be absent from the immediate vicinity or have a localized mass below the relevant critical value. These limits are conditional on the piecewise, electromagnetically inert shell model, its chosen shell geometry and the adopted horizon and shadow calculations, rather than being general constraints on all possible dark-matter distributions.

Subject of Research: Theoretical modeling of rotating black holes surrounded by finite dark-matter shells and their observable shadows

Article Title: Shadow of rotating black hole surrounded by dark matter

Article References: Feng, H., Cai, Z., Yang, R.-J., & Zhang, J. (2026). Shadow of rotating black hole surrounded by dark matter. The European Physical Journal C, 86(10), Article 1180. https://doi.org/10.1140/epjc/s10052-026-16437-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16437-x

Keywords: black holes, dark matter, black hole shadows, Kerr spacetime, Event Horizon Telescope, null geodesics, Newman–Janis Algorithm, M87*, Sagittarius A*, Hawking radiation, Shadow, rotating

To understand why the shadow effect matters, it helps to picture how single-crystal castings are made. Directional solidification technology works by withdrawing a ceramic mold from a hot furnace zone into a cooler region, so that molten alloy solidifies from the bottom upward along a carefully controlled temperature gradient. The goal is for a single crystal orientation to propagate through the entire component. But when a cluster of large-caliber castings is arranged together in the furnace, the components block each other’s view of the cooling surfaces. One casting literally casts a thermal shadow on its neighbor, disrupting the local heat flow and the temperature gradient that the solidification front depends on. The result is one of the primary causes of casting defects in Ni-base single-crystal superalloy castings, including stray grains, freckles, and solidification pores that force manufacturers to scrap otherwise valuable parts.

The research team, led by Donghan Fan, Naicheng Sheng, and Yizhou Zhou of the University of Science and Technology of China and the Institute of Metal Research, Chinese Academy of Sciences, in collaboration with AECC Shenyang Liming Aero-Engine Co., Ltd, investigated a novel central cooling and heating process as a way to fight back against this thermal shadowing. Instead of relying solely on the conventional withdrawal-based cooling from the outside, the CCH process introduces controlled cooling and heating from the center of the casting cluster. This central intervention changes the radiation heat transfer dynamics inside the furnace, so that each component in the cluster receives a more balanced share of the heat exchange. The approach effectively rewrites the thermal geometry of the casting environment, preventing any single casting from being thermally starved by its neighbors.

The experimental results are striking. In CCH-processed castings, the size of the S-pores—solidification pores that form during directional solidification and act as stress concentrators during service—is significantly reduced. Even more dramatically, the freckles are eliminated. Freckles are chains of equiaxed grains that form when segregated interdendritic liquid becomes buoyantly unstable in the mushy zone, the semi-solid region between fully liquid and fully solid material. These freckle chains are catastrophic for single-crystal integrity because they introduce grain boundaries into a component that is supposed to have none. Previous studies have linked freckle formation to geometric features such as edges, curvature, and abrupt cross-section changes in castings, and the mushy zone width plays a decisive role in whether the segregated liquid can destabilize. By narrowing the mushy zone, the CCH process removes the conditions that allow freckles to nucleate in the first place.

Simulation results provide quantitative backing for these experimental observations. The numerical analysis shows that the mushy zone width of CCH-processed castings is shortened by 47.9 percent—a nearly halving of the vulnerable semi-solid region where defects incubate. The temperature field distribution also becomes more uniform across the casting cluster, meaning that the solidification front advances more evenly and the local thermal gradients stay within the safe range for single-crystal growth. A narrower mushy zone reduces the time that segregated liquid spends in the buoyantly unstable state, suppressing the interdendritic fluid flow that drives freckle formation and the shrinkage feeding problems that generate pores.

To clarify exactly how much control the CCH process achieves over the shadow effect, the researchers performed an in-depth deduction of the view factor, a geometric quantity from radiation heat transfer theory that describes how efficiently two surfaces exchange thermal radiation. The view factor analysis demonstrates the radiation heat transfer efficiency inside the furnace and quantifies the level of control over the shadow effect achieved by the central cooling and heating process. In conventional cluster casting, the view factors between neighboring components and the cooling surfaces are distorted by shadowing, so some castings radiate heat inefficiently and solidify under degraded gradients. The CCH process corrects this distortion by inserting central thermal elements that rebalance the radiation exchange, ensuring that the heat extraction from each component stays within the controlled range needed for defect-free directional solidification.

The benefits extend beyond the casting stage into the mechanical performance of the finished crystals. During deformation, a hexagonal dislocation network forms at the deformed gamma/gamma-prime interface in CCH-processed castings. The gamma-prime phase is the ordered intermetallic precipitate that strengthens nickel-base superalloys, and the gamma/gamma-prime interface is where plastic deformation concentrates at high temperatures. Hexagonal dislocation networks at this interface are a well-known signature of effective creep resistance, because they lock the interface and impede dislocation motion through the crystal. The formation of this network enhances the rupture life of the castings, meaning that components produced with the CCH process can withstand high-temperature stress for longer before failing. This is a crucial advantage for turbine blades, which must survive thousands of hours of creep loading at temperatures approaching the melting point of the alloy.

The significance of this work becomes clear when considering the economics of superalloy casting. Single-crystal superalloy components contain expensive alloying elements such as rhenium, and every rejected casting represents a substantial loss of both material and furnace time. The shadow effect is inevitable when directional solidification technology is employed to fabricate a cluster of large-caliber castings, which means that manufacturers have historically accepted high rejection rates as the cost of doing business. A process that suppresses the shadow effect and improves the yield rate of the castings directly translates into lower production costs, less material waste, and more reliable supply chains for the aerospace industry. The CCH process achieves this without requiring changes to the alloy chemistry itself, making it compatible with existing superalloy compositions and casting infrastructure.

The research builds on a growing body of work on defect control in directional solidification. Earlier studies by the same group examined freckle formation during casting single crystal superalloys through the central cooling and heating process, published in the Journal of Alloys and Compd in 2025, and the effect of wall thickness on residual stress and microstructural evolution in multi-blade casting. Other researchers have developed thermal uniformity-based downward directional solidification technologies, non-uniform thickness molds for controlling temperature gradients, and digital twin models for single-crystal turbine blade solidification. The CCH process adds a new dimension to this toolkit by attacking the shadow effect at its geometric root—the distorted radiation exchange within casting clusters—rather than merely compensating for its downstream consequences.

Looking ahead, the combination of experimental validation, quantitative simulation, and view factor analysis demonstrated in this study offers a template for rational process design in superalloy casting. By deducing the radiation heat transfer efficiency from first principles, engineers can now predict how different furnace geometries and central thermal interventions will affect the shadow effect before committing to expensive trial castings. As the demand for single-crystal superalloy components grows with the expansion of commercial aviation and gas turbine power generation, processes like CCH that improve yield rates while enhancing rupture life will become increasingly valuable. The shadow effect has haunted superalloy casting for decades; with central cooling and heating, it may finally be losing its grip.

Subject of Research: Materials Science

Article Title: Suppression of the shadow effect during casting single-crystal superalloys through a central cooling and heating process

Article References: Fan, D., Sheng, N., Chu, Z., Liu, J., Sun, S., Fan, S., Hou, G., Li, J., Zhu, S., & Zhou, Y. (2026). Suppression of the shadow effect during casting single-crystal superalloys through a central cooling and heating process. Journal of Materials Science, 61(43), 33878-33895. https://doi.org/10.1007/s10853-026-13496-z

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13496-z

Keywords: single-crystal superalloys, directional solidification, shadow effect, central cooling and heating, freckles, S-pores, mushy zone, view factor, turbine blades, nickel-base superalloys, Suppression, shadow

The concept of the algorithmic unconscious builds on earlier work by philosopher Luigi Possati, who argued in 2020 that psychoanalysis offers tools for understanding AI that pure computer science cannot supply. Just as Freud and Jung claimed that human behavior is driven by forces beneath conscious awareness, the authors contend that machine learning systems harbor latent structures — biases embedded in training data, opaque feature interactions in deep networks, emergent behaviors that surprise even their creators — that operate below the level of deliberate design. The black box problem, long treated as a technical challenge of interpretability, is reframed here as something closer to an analytic problem: the hidden contents of these systems act on human minds whether or not anyone understands them, much as repressed material acts on a patient.

The Jungian framework supplies the vocabulary. Jung, the Swiss psychiatrist who broke with Freud and developed the theory of the collective unconscious, proposed that human psyches share inherited archetypal patterns — primordial images such as the Hero, the Wise Old Man, the Trickster and the Shadow — that surface in dreams, myths and cultural products. The authors focus on two archetypes in particular. The Trickster, a boundary-crossing figure of chaos, deception and unexpected creativity, maps onto the way generative AI systems confound expectations, produce hallucinations with total confidence, and destabilize established categories of authorship, truth and expertise. The Shadow, the repressed and disowned aspects of the personality, maps onto the way AI systems absorb and amplify the darkest contents of human culture: the prejudices, cruelty and distortions present in the data on which they are trained.

This Shadow reading gives technical teeth to a well-documented empirical problem. Research on algorithmic bias has shown that machine learning models reproduce discrimination across domains, from translation tools that encode gender stereotypes to applications that perpetuate unfair outcomes against animals and marginalized groups. Filter bubbles and recommendation engines curate reality in ways that polarize publics, as studies of social media manipulation during events such as Brexit have demonstrated. The authors’ point is that these are not mere engineering defects to be patched. In Jungian terms, the Shadow is precisely the material a person refuses to acknowledge; a society that trains its machines on its own unexamined output and then treats the resulting systems as neutral oracles is engaging in a collective act of disavowal, outsourcing its self-knowledge to entities that return its darkness in amplified form.

Equally central to the analysis is the phenomenon of projection. In Jungian practice, projection occurs when a person unconsciously attributes their own expectations, fears or desires to another person or object, failing to recognize them as their own. The authors argue that human-AI relationships are saturated with projection. Users who feel that a chatbot “understands” them, that a virtual assistant has betrayed them, or that an algorithm is wise or malicious are, on this account, encountering their own psychic contents reflected back. Prior work cited in the paper includes research on perceived betrayal by virtual assistants affecting consumer behavior, studies of belief projection in explainable AI, and psychological analyses of films such as Ex Machina that dramatize the human tendency to project otherness and soul onto machines. The magic mirror metaphor, developed by scholars of depth psychology and AI, captures the structure: the machine reflects, and we mistake the reflection for an other.

From projection flows one of the paper’s most striking concepts: pseudo-individuation. In Jungian theory, individuation is the lifelong psychological process by which a person integrates conscious and unconscious contents to become a distinct, self-aware whole. The authors observe that AI systems create the impression of being subjects with their own personalities — they converse, remember, express preferences and seem to develop — while lacking self-consciousness and reflexive capacity. They appear to individuate without actually doing so. This pseudo-individuation is not harmless. It encourages humans to treat AI as a genuine other, a companion or authority, and to surrender forms of judgment and reflection that should remain their own. The authors connect this to concerns about digital dementia, the erosion of traditional values, and the documented psychological toll of social media use, particularly among adolescents, whose developing psyches are especially vulnerable to symbolic confusion.

To ground the theory, the authors apply it to a case study of Italian Brainrot, an explicitly AI-mediated internet phenomenon in which absurdist, AI-generated characters and imagery spread virally among young users. Related scholarship on “brain rot” as a genre of participation among teenagers suggests that such content is not merely noise; it functions as a shared symbolic field in which young people play with meaning, identity and absurdity. Through the Jungian lens, the authors read Italian Brainrot as an intensified expression of the algorithmic unconscious: archetypal imagery — trickster figures, grotesque hybrids, chaotic narrative fragments — generated and circulated by machines, absorbed by a generation, and reflecting collective psychic tensions that no single actor designed or intended. The phenomenon illustrates how AI-mediated culture can become a stage on which collective unconscious material is performed at unprecedented speed and scale.

The ethical payoff of the analysis is a shift in where we look for risk. Standard AI ethics focuses on the properties of systems: fairness metrics, transparency requirements, robustness against adversarial attack. The authors do not dismiss these, but they insist that the deepest risks arise in the relational space between humans and machines — in projection, in pseudo-individuation, in the seduction of treating mirrors as minds. A user who projects wisdom onto a language model may defer to its errors; a society that projects menace onto AI may misdirect its fears; a generation raised on AI-generated archetypal content may develop symbolic lives structured by commercial optimization systems rather than by human culture. Understanding the algorithmic unconscious, the authors argue, enables diagnostic insight and heightened sensitivity to these ethical risks, offering developmental self-reflection for human societies rather than merely technological optimization.

The paper is careful about what it does not claim. It does not assert that AI systems have an unconscious in any literal psychological sense, nor does it attribute agency or interiority to machines. The algorithmic unconscious is a heuristic, a way of naming the latent dynamics of AI systems and the unconscious dynamics they activate in humans. Its value is practical: it gives policymakers, designers and users a richer language for phenomena — hallucination, parasocial attachment to chatbots, collective panic and euphoria about AI — that resist purely technical description. As AI’s capabilities appear to surprise humanity on what the authors describe as a weekly basis, they contend that a timely and accurate understanding of its nature has become an urgent requirement for individuals and nations alike.

The deeper message is a reversal of the usual framing of the AI debate. The question that dominates public discourse — will machines become conscious? — may be less urgent than its mirror image: what will humans do with a technology that reflects their own unconscious so faithfully and so powerfully? By reconceptualizing AI as a mirror of individual and collective psychic dynamics, the authors suggest that the path to safe and humane AI runs not only through better alignment algorithms but through a kind of collective self-examination. The machines are, in this view, showing us ourselves. Whether we can bear to look — and integrate what we see rather than projecting it outward — may determine whether the algorithmic unconscious remains a diagnostic tool or becomes a source of escalating collective pathology.

Subject of Research: A Jungian psychoanalytic analysis of the algorithmic unconscious, archetypal projection and ethical risks in human-AI relations

Article Title: Jungian analysis of the algorithmic unconscious: From archetypal theory and projection to ethical risks in human-AI relations

Article References: Nguyen, D.-H., Ho, M.-T., Pham, T.-Q., Ngo, D.-T., & Nguyen, H.-K. T. (2026). Jungian analysis of the algorithmic unconscious: From archetypal theory and projection to ethical risks in human-AI relations. AI & SOCIETY. https://doi.org/10.1007/s00146-026-03311-3

Image Credits: AI Generated

DOI: 10.1007/s00146-026-03311-3

Keywords: artificial intelligence, Jungian psychology, algorithmic unconscious, archetypes, Shadow, Trickster, projection, pseudo-individuation, AI ethics, human-AI relationship, Italian Brainrot, collective unconscious