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A bstract We consider black holes generically sourced by quantum matter described by regular wavefunctions. This allows for integrable effective energy densities and the removal of Cauchy horizons in spherically symmetric configurations. Moreover, we identify the ultrarigid rotation of the Kerr spacetime as causing the existence of an inner horizon in rotating systems, and describe general properties for quantum matter cores at the centre of rotating black holes with integrable singularities and no Cauchy horizon.

We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.

Stealth solutions of scalar-tensor gravity and less-known de Sitter spaces that generalize them are analyzed regarding their possible role as thermal equilibria at non-zero temperature in the new first-order thermodynamics of scalar-tensor gravity. No stable equilibria are found, further validating the special role of general relativity as an equilibrium state in the landscape of gravity theories, seen through the lens of first-order thermodynamics.

We improve upon the results presented in Casadio et al. (Phys Rev D 105:124026, 2022) deriving a quantum-corrected Reissner–Nordström geometry containing an integrable singularity at its center while being devoid of spurious oscillations around the classical configuration. We further investigate some relevant physical observables, related to geodesics and quasinormal modes of scalar perturbations, associated with this geometry to complement our theoretical analysis.

It is now established that, contrary to common belief, (electro-)vacuum Brans–Dicke gravity does not reduce to general relativity (GR) for large values of the Brans–Dicke coupling ω . Since the essence of experimental tests of scalar–tensor gravity consists of providing lower bounds on ω , in light of the misguided assumption of the equivalence between the limit ω → ∞ and the GR limit of Brans–Dicke gravity, the parametrized post-Newtonian (PPN) formalism on which these tests are based could be in jeopardy. We show that, in the linearized approximation used by the PPN formalism, the anomaly in the limit to general relativity disappears. However, it survives to second (and higher) order and in strong gravity. In other words, while the weak gravity regime cannot tell apart GR and ω → ∞ Brans–Dicke gravity, when higher order terms in the PPN analysis of Brans–Dicke gravity are included, the latter never reduces to the one of GR in this limit. This fact is relevant for experiments aiming to test second order light deflection and Shapiro time delay.

After reviewing the definition of two differential operators which have been recently introduced by Caputo and Fabrizio and, separately, by Atangana and Baleanu, we present an argument for which these two integro-differential operators can be understood as simple realizations of a much broader class of fractional operators, i.e. the theory of Prabhakar fractional integrals. Furthermore, we also provide a series expansion of the Prabhakar integral in terms of Riemann–Liouville integrals of variable order. Then, by using this last result we finally argue that the operator introduced by Caputo and Fabrizio cannot be regarded as fractional. Besides, we also observe that the one suggested by Atangana and Baleanu is indeed fractional, but it is ultimately related to the ordinary Riemann–Liouville and Caputo fractional operators. All these statements are then further supported by a precise analysis of differential equations involving the aforementioned operators. To further strengthen our narrative, we also show that these new operators do not add any new insight to the linear theory of viscoelasticity when employed in the constitutive equation of the Scott–Blair model.

The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries.

Since, in Einstein gravity, a massless scalar field with lightlike gradient behaves as a null dust, one could expect that it can act as the matter source of Vaidya geometries. We show that this is impossible because the Klein–Gordon equation forces the null geodesic congruence tangent to the scalar field gradient to have zero expansion, contradicting a basic property of Vaidya solutions. By contrast, exact plane waves travelling at light speed and sourced by a scalar field acting as a null dust are possible.

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein’s field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.

Hypophosphatemia presents with highly variable clinical manifestations. Among the identified hypophosphatemic disorders, X-linked hypophosphatemia (XLH) and tumor-induced osteomalacia (TIO) are caused by persistent excess fibroblast growth factor 23 (FGF23), which leads to phosphate renal wasting and reduced phosphate availability. Traditional treatments involving oral phosphate and active vitamin D supplements have limitations and potential side effects. By targeting FGF23, burosumab directly addresses the underlying pathophysiology of both XLH and TIO. This narrative review describes the diagnosis and management of XLH and TIO, highlighting key gaps and barriers within Italian clinical practice, which are often common in international healthcare settings; pragmatic solutions are also proposed to optimize patient care. Early diagnosis and appropriate treatment of XLH and TIO are crucial for preventing disease progression and improving patient outcomes. However, XLH diagnosis is often delayed or mistaken due to nonspecific symptoms, while TIO diagnosis is complicated by the challenge of localizing small FGF23-secreting tumors, which requires extensive imaging. A general lack of awareness among healthcare professionals about these rare diseases may further delay diagnosis. Management of XLH and TIO also faces hurdles. Although burosumab is now the recommended first-line treatment for XLH patients, both between 1 and 17 years old and adults, its continuous use is often limited by strict eligibility criteria, and adequate follow-up of XLH patients is difficult to maintain during the critical transition period from pediatric age to adulthood. For TIO, tumor resection remains the definitive treatment, but its success depends on tumor localization and surgical expertise. In cases where surgery is not feasible, burosumab or conventional therapy may be used, but long-term management strategies are lacking. Improving the care of XLH and TIO patients requires increased awareness, better access to advanced diagnostic tools, and enhanced multidisciplinary collaboration. Improving networking to discuss clinical cases and share best practices are crucial steps to ensure optimal patient outcomes. Implementing standardized protocols while setting personalized treatment goals and follow-up strategies can significantly improve the quality of life for patients with these rare diseases.