Gas falling into a black hole (BH) from large distances is unaware of BH spin direction, and misalignment between the accretion disc and BH spin is expected to be common. However, the physics of tilted discs (e.g. angular momentum transport and jet formation) is poorly understood. Using our new GPU-accelerated code h-amr, we performed 3D general relativistic magnetohydrodynamic simulations of tilted thick accretion discs around rapidly spinning BHs, at the highest resolution to date. We explored the limit where disc thermal pressure dominates magnetic pressure, and showed for the first time that, for different magnetic field strengths on the BH, these flows launch magnetized relativistic jets propagating along the rotation axis of the tilted disc (rather than of the BH). If strong large-scale magnetic flux reaches the BH, it bends the inner few gravitational radii of the disc and jets into partial alignment with the BH spin. On longer time-scales, the simulated disc–jet system as a whole undergoes Lense–Thirring precession and approaches alignment, demonstrating for the first time that jets can be used as probes of disc precession. When the disc turbulence is well resolved, our isolated discs spread out, causing both the alignment and precession to slow down.

The positive-negative axis of emotional valence has long been recognized as fundamental to adaptive behavior, but its origin and underlying function have largely eluded formal theorizing and computational modeling. Using deep active inference, a hierarchical inference scheme that rests on inverting a model of how sensory data are generated, we develop a principled Bayesian model of emotional valence. This formulation asserts that agents infer their valence state based on the expected precision of their action model—an internal estimate of overall model fitness (“subjective fitness”). This index of subjective fitness can be estimated within any environment and exploits the domain generality of second-order beliefs (beliefs about beliefs). We show how maintaining internal valence representations allows the ensuing affective agent to optimize confidence in action selection preemptively. Valence representations can in turn be optimized by leveraging the (Bayes-optimal) updating term for subjective fitness, which we label affective charge (AC). AC tracks changes in fitness estimates and lends a sign to otherwise unsigned divergences between predictions and outcomes. We simulate the resulting affective inference by subjecting an in silico affective agent to a T-maze paradigm requiring context learning, followed by context reversal. This formulation of affective inference offers a principled account of the link between affect, (mental) action, and implicit metacognition. It characterizes how a deep biological system can infer its affective state and reduce uncertainty about such inferences through internal action (i.e., top-down modulation of priors that underwrite confidence). Thus, we demonstrate the potential of active inference to provide a formal and computationally tractable account of affect. Our demonstration of the face validity and potential utility of this formulation represents the first step within a larger research program. Next, this model can be leveraged to test the hypothesized role of valence by fitting the model to behavioral and neuronal responses.

Luminous active galactic nuclei and X-ray binaries often contain geometrically thin, radiatively cooled accretion discs. According to theory, these are – in many cases – initially highly misaligned with the black hole equator. In this work, we present the first general relativistic magnetohydrodynamic simulations of very thin (h/r ∼ 0.015–0.05) accretion discs around rapidly spinning (a ∼ 0.9) black holes and tilted by 45°–65°. We show that the inner regions of the discs with h/r ≲ 0.03 align with the black hole equator, though out to smaller radii than predicted by analytic work. The inner aligned and outer misaligned disc regions are separated by a sharp break in tilt angle accompanied by a sharp drop in density. We find that frame dragging by the spinning black hole overpowers the disc viscosity, which is self-consistently produced by magnetized turbulence, tearing the disc apart and forming a rapidly precessing inner sub-disc surrounded by a slowly precessing outer sub-disc. We find that the system produces a pair of relativistic jets for all initial tilt values. At small distances, the black hole launched jets precess rapidly together with the inner sub-disc, whereas at large distances they partially align with the outer sub-disc and precess more slowly. If the tearing radius can be modeled accurately in future work, emission model independent measurements of black hole spin based on precession-driven quasi-periodic oscillations may become possible.

Active inference offers a first principle account of sentient behavior, from which special and important cases—for example, reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design—can be derived. Active inference finesses the exploitation-exploration dilemma in relation to prior preferences by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this letter, we consider a sophisticated kind of active inference using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about “what would happen if I did that” to “what I would believe about what would happen if I did that.” The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states as opposed to states per se. We illustrate the competence of this scheme using numerical simulations of deep decision problems.

Black hole (BH) accretion is one of nature’s most efficient energy extraction processes. When gas falls in, a significant fraction of its gravitational binding energy is either converted into radiation or flows outwards in the form of BH-driven jets and disc-driven winds. Recently, the Event Horizon Telescope (EHT), an Earth-sized submillimetre radio interferometer, captured the first images of M87’s BH. These images were analysed and interpreted using general relativistic magnetohydrodynamics (GRMHD) models of accretion discs with rotation axes aligned with the BH spin axis. However, since infalling gas is often insensitive to the BH spin direction, misalignment between accretion disc and BH spin may be a common occurrence in nature. In this work, we use the general relativistic radiative transfer code bhoss to calculate the first synthetic radio images of (highly) tilted disc/jet models generated by our GPU-accelerated GRMHD code h-amr . While the tilt does not have a noticeable effect on the system dynamics beyond a few tens of gravitational radii from the BH, the warping of the disc and jet can imprint observable signatures in EHT images on smaller scales. Comparing the images from our GRMHD models to the 43 and 230 GHz EHT images of M87, we find that M87 may feature a tilted disc/jet system. Further, tilted discs and jets display significant time variability in the 230 GHz flux that can be further tested by longer-duration EHT observations of M87.