Papers

For three-dimensional non-interacting multi-band metals, we show that important information about the shape and the quantum geometry of Fermi surfaces is encoded in the subleading logarithmic term of bipartite charge fluctuations. This logarithmic term is related to the dimensionless $|\mathbf{q}|^3$-coefficient of the structure factor in momentum space, and both quantities can be expressed as Fermi surface integrals of the Fermi surface curvature tensor and the quantum metric tensor. When the real-space partition surface is a quadric (i.e., sphere or ellipsoid), the logarithmic coefficient satisfies a topological bound depending only on the Euler characteristic and the Chern number of the Fermi surface, illustrating a non-trivial interplay between topology and quantum topology in multi-band metals.

We study local quantum field theories in Anti-de Sitter (AdS) space, with boundary conditions that break some of the bulk isometries. Specifically, we focus on conformal defects and we prove that their spectrum supports a displacement operator of protected dimension, despite the non-local nature of the conformal theory living at the boundary of AdS. If the defect breaks a global symmetry, a tilt operator is also present. The existence of a displacement was conjectured in arXiv:2508.08250 for Wilson loops in Yang-Mills theories in AdS. Our proof is valid in general and applies, in particular, to defects in long-range models, as we discuss in various examples. In the bulk, the modes sourced by the protected operators have Compton wavelength of order of the AdS radius: they constitute the AdS analogue of the Goldstone bosons for the spontaneous breaking of the corresponding symmetries.

In this study, a relativistic formulation of the $(q)$-deformed Dunkl-Fokker-Planck equation in $(1+1)$-dimensions is constructed within the reflection-deformed quantum framework. In this case, the formalism includes $(q)$-deformed Dunkl operators and reflection symmetry to build a generalized dynamical structure for a relativistic quantum systems framework. Moreover, the corresponding $(q)$-Wigner-Dunkl supersymmetric configuration is established via the construction of deformed ladder operators and supersymmetric algebraic relations, yielding a consistent spectral representation of the model within the algebraic framework. The analysis extends to the harmonic oscillator with centrifugal interaction, where exact algebraic solutions, similarity reduction techniques, and closed energy spectra are obtained analytically in detail. The role of the deformation parameter and reflection operator on spectral properties and wavefunction structure is examined systematically in detail. A generalized Foldy-Wouthuysen (FW) transformation is introduced within the deformed Dunkl framework to achieve relativistic decoupling of positive- and negative-energy sectors within the present theoretical formulation. In this case, this approach yields an effective reduced Hamiltonian, including higher-order relativistic and deformation-induced terms. Also, the associated Dunkl-Fokker-Planck dynamics generated through high-order FW reduction are examined in detail for reflection-deformed relativistic quantum systems. In this context, results obtained here yield a unified algebraic and relativistic description of $(q)$-deformed Dunkl structures and construct a consistent framework for investigating supersymmetric and relativistic properties in reflection-symmetric quantum models in general.

A comprehensive study of the phase structure of the two-flavor quark-meson-diquark model is presented within the nonperturbative functional renormalization group framework. The influence of mesonic fluctuations beyond the mean-field approximation is investigated, and two-point functions of the diquark fields are computed at finite real-time frequencies. Renormalization group consistency of the effective potential is ensured in order to avoid cutoff artifacts. Substantial modifications of the phase structure are found once mesonic fluctuations are included, and for sufficiently strong diquark couplings the dynamics become dominated by diquark condensation. These effects are elucidated through an analysis of the diquark pole mass and the Silver-Blaze property.

Generalized vector-tensor theories of gravity have drawn attention for admitting hairy black hole solutions, thereby circumventing the standard no-hair theorems. It remains an open question, however, how such black holes may form starting from reasonable initial conditions. It has been suggested that vector hair may grow spontaneously as a result of the field developing a negative effective mass squared $-$ the so-called spontaneous vectorization mechanism. We demonstrate that this is not possible if the initial state is a hairless black hole, a result that applies to essentially all stationary and axisymmetric solutions of interest in general relativity. More precisely, we prove that the appearance of a negative effective mass squared for the vector field must necessarily be accompanied by ghost- or gradient-type instabilities. Demanding the absence of such instabilities translates into interesting bounds on the coupling constants of the theory as functions of the black hole parameters. In particular, we discover that a Kerr black hole may become unstable when the spin increases above a certain critical value.

We prove that any background-inert perturbative coupling $ \lambda $ in coincident $ f(Q) $ gravity exhibits a degeneracy with the clustering amplitude $ \sigma_{80} $, when using compressed CMB distance priors. This degeneracy is, in fact, a direct materialization of a deeper $ A_s-D_0(\lambda) $ degeneracy between the primordial amplitude $ A_s $ and the present day growth factor $ D_0(\lambda) $. We outline a consistency check scheme, whose logic extends to any model in which the coupling is background inert, by computing $ A_s $ per posterior sample, needed to reproduce the $ \sigma_{80} $ preferred by the sampler. We perform our analysis with two dataset pipelines, based on the coupled/decoupled $ f\sigma_8(z) $ data. To ensure theoretical diversity, we include $ \Lambda $CDM and the Hybrid model in the $ f(Q) $ framework. Our results illustrate that adding the $ \lambda_0\sqrt{QQ_0} $ correction to the models inflates $ \sigma_{80} $ by $ 5\%-8\% $ as compared to its vanilla variant, while the Bayesian evidence disfavors every alternative considered - $\Delta\log\mathcal{Z} = -0.5$ to $-2.6$ against $\Lambda$CDM on the same pipeline. Propagating this inflated $ \sigma_{80} $ through a per-sample computation of the implied primordial amplitude accounting for both the transfer function and the modified growth factor yields $\ln(10^{10}A_s)$ in $1.5\sigma-2.6\sigma$ tension with Planck 2018. Imposing the $ \ln(10^{10}A_s) $ constraint from Planck 2018 as an additional prior removes this inflation, pulling $ \sigma_{80} $ to the Planck value and $ \lambda_0 $ to values consistent with $ 0 $, with the implied amplitude recovering to within $ 0.2\sigma $ of Planck in every case. We find no model-dataset combination preferred over $ \Lambda $CDM.

In this work, we derive an exact black hole solution in higher-order curvature gravity by coupling an electromagnetic sector formulated within the ModMax framework to a quintessence dark energy component. Focusing on purely electrically charged configurations, we analyze the thermodynamic and geothermodynamic properties of the solution to investigate its stability and phase structure. Within this sector, the ModMax theory effectively reduces Maxwell electrodynamics up to a rescaling of the electric charge, and thus the obtained solution corresponds to a consistent subset of the broader nonlinear theory. Using thermodynamic geometry, we examine microscopic interactions and phase transitions, showing that divergences in the thermodynamic curvature coincide with the vanishing of the heat capacity, confirming the consistency of the phase structure. We further explore the optical properties of the black hole by studying null geodesics and determining the photon sphere and the corresponding shadow radius for different values of the quintessence state parameter $\omega$. Exact analytical expressions for the photon-sphere radius are derived, revealing that higher-order curvature corrections and quintessence significantly enhance the shadow size, whereas the electric charge has the opposite effect. Notably, quintessence is found to have a more pronounced impact on the shadow than the charge. These results highlight that dark energy and higher-order curvature corrections can yield potentially observable signatures in black hole shadows.

We present an analytic method for computing gravitational-wave fluxes from bound Schwarzschild geodesics with arbitrary eccentricity. Our approach systematically expands the Fourier coefficients of the emitted radiation in a Chebyshev basis, allowing them to be reduced to sums of Keplerian-like Fourier coefficients previously derived in the Quantum Spectral Method. Because the construction does not rely on a small-eccentricity expansion, it applies to a broad range of bound eccentric orbits. As an illustration, we implement the method using a $15$PN-expanded input and find that it reproduces the total flux for the case $(p,e)=(12.5,0.5)$ to relative accuracy $10^{-5}$, while for the stronger-field case $(p,e)=(10,0.8)$ it yields weighted mode-by-mode errors below $10^{-6}$ for the selected dominant modes analyzed. These results provide an analytic route to frequency-domain flux calculations relevant to extreme-mass-ratio inspirals.

We consider the “metric-affine-like” generalization of the Yang-Mills theory (mal-YM) which we first proposed earlier. In this model, the connection is no longer assumed to be compatible with the Hermitian form in the fibers. As a consequence, along with the usual YM potential $\boldsymbol{A}_a$ and the field strength tensor $\boldsymbol{F}_{ab}$, it contains non-trivially interacting fields $\boldsymbol{B}_a$, $\boldsymbol{h}$, and $\boldsymbol{G}_{ab}$, $\boldsymbol{N}_a$, forming a non-Abelian generalization of Stückelberg theory. Due to the spontaneous symmetry breaking $GL(n,\mathbb{C}) \to U(n)$, these new fields can be made massive and the limit $M\to\infty$ restores the standard YM theory. We perform a detailed analysis of this theory on the classical level. We discuss in detail geometric motivation for the model, field transformations, gauge symmetry and its spontaneous breaking, action, equations of motion, Noether identities, gauge fixing, and other issues.

We develop a rigorous evaluation of Dirac brackets for classical observables on the phase space of radiative gravitational modes at null infinity that naturally incorporates memory effects. Considering the Ashtekar-Streubel phase space, with boundary conditions in time given by vanishing news and purely electric shear, and taking into account the infinite dimensionality of the phase space, we identify the algebra of proper observables (understood as functions on phase space that can be associated with smooth symplectic flows). We show that the action of supertranslation charges generate the correct transformations on the shear. We also show that the conventional definition of the “Goldstone mode” adopted in the literature cannot be associated with a proper observable, but nevertheless there exists an infinite family of proper observables, which we call Goldstone probes, that are capable of measuring the Goldstone mode. We notice that there are no Goldstone probes constructed only out of the shear or the news, providing a possible explanation for why attempts to construct a (separable) Hilbert space with different memory states have failed so far. Finally, we derive formulas for distributional Dirac brackets between local shear and news, and show that they contain non-local corrections.

We investigate the structure and emission properties of a thin accretion disk around a rotating charged black hole described by an effective higher-curvature-inspired spacetime, constructed as a phenomenological deformation of the Kerr Newman geometry. In this framework, the deformation is introduced through a modification of the metric function $\Delta$ by an effective Gauss-Bonnet-like parameter $\alpha$, such that the spacetime reduces to the standard Kerr Newman solution in the limit $\alpha \to 0$. Adopting a kinematical approach, we use test-particle motion to derive the specific energy, specific angular momentum, and angular velocity of circular orbits, and analyze the effects of the parameters $\alpha$ and charge $Q$ on the innermost stable circular orbit (ISCO), radiative efficiency, radiation flux, temperature, and differential luminosity of the disk. We find that increasing $\alpha$ shifts the ISCO inward and enhances the disk's radiation flux and temperature, while the presence of charge suppresses these quantities due to electrostatic effects. Our results demonstrate that effective higher curvature deformations of rotating black hole spacetimes can lead to observable deviations from the Kerr case, highlighting accretion disks as sensitive probes of strong-gravity effects without relying on a specific underlying gravitational theory.

We investigate the description of quark confinement in terms of confining strings or flux tubes. We show that compact QED with a topological $\theta$-term, in the dyon condensation phase, is described by a massive two-form field $B_{\mu\nu}$ that gives rise to a string theory with an IR Brazovskii-Lifshitz fixed point at strong coupling, reached along a double-scaling renormalization trajectory on which the cutoff can be removed. This corresponds to a UV-complete quantum string in (3+1) dimensions, representing the dual of asymptotic freedom in the UV. Contrary to critical strings, which correspond to trivial Gaussian fixed points, this string is stabilized by a finite thickness, determined by the mass of the $B_{\mu\nu}$ field, instead of living in a higher-dimensional space. Interestingly, it contains a world-sheet excitation, in addition to the Nambu-Goto phonons, whose nature depends on the sign of the string stiffness: for the negative stiffness favoured by lattice data it appears as a broad, overdamped mode rather than a sharp resonance, consistent with the broad phase shift seen in lattice $SU(N)$ scattering data. On the other hand, we determine the confining potential and show that it reproduces a generalized Arvis potential $V(L)= aL\sqrt{1-c/L^2}$ with running parameters $a(L), c(L)$. With this, we compute the mass difference ratios for the heaviest quarkonium and find 2.5% agreement with experiment already at the infrared fixed point, from a two-parameter fit of both the reduced quark mass and a boundary-condition parameter, to this fixed functional form. We also compute the intercept of Regge trajectories and find that the thickness of Brazovskii-Lifshitz strings tends to increase it from the Nambu-Goto value $\alpha_0= 1/12$. Overall, our findings strongly support Polyakov's longstanding conjecture on universality of confining gauge theories in the IR.

This essay discusses recent progress on Euclidean wormholes as candidate contributions to the Universe's initial quantum state. The comparison with the Hartle-Hawking no-boundary proposal highlights both a conceptual affinity and genuine advance: wormholes retain the relevance of Euclidean-saddles as encoders of properties of cosmological wavefunctions, while they broaden the class of regular saddles that are physically relevant for inflating universes and are capable of resolving issues that plague the no-boundary proposal. The principal achievement of the wormhole program is to enlarge the semiclassical initial-condition land-scape in a way that is physically rich, conforms with Holographic expectations and as such becomes increasingly relevant for early-universe model building, within UV complete theories of quantum gravity.

It is often stated that a phase of standard, decelerated cosmological expansion is characterised by the absence of global event horizons, while a phase of accelerated expansion is associated with the absence of particle horizons. This is not necessarily true because such horizons, being non-local properties of the spacetime geometry, depend on the full (past and future) history of the given cosmological background. We provide examples of various different scenarios for the case in which the final asymptotic phase of standard expansion and decreasing curvature is connected, through a regular bounce, with an initial (and possibly infinitely extended in time) regime of growing curvature.

In this work, we address the unresolved type III cases of the algebraic reconstruction theorem by integrating crossed product algebras and semiclassical approximations. We first derive that the relative entropy in crossed product algebras factorizes into contributions from the original algebra and observer wavefunctions. By constructing “holographic” crossed product algebras for “bulk” and “boundary” type III factors, we extend the algebraic reconstruction theorem to include the algebraic Ryu-Takayanagi (RT) formula semiclassically, which provides a complete algebraic description of the reconstruction theorem, as an intrinsic framework for the algebraic version of bulk-boundary correspondences in holographic duality.

We revisit the Schwarzschild singularity in a semiclassical setting where the background geometry is classical and quantum effects enter through Bohmian (quantal) trajectories associated with a Klein Gordon wave packet. Using the Madelung-Bohm decomposition of the Klein Gordon wavefunction, we show that the quantum-modified motion is equivalent to geodesic motion in an effective metric conformally related to Schwarzschild, with a conformal factor fixed by the wavefunction amplitude. Solving the wavefunction equation near $r\to 0$ determines this factor and yields finite curvature invariants, in suitable coordinates the interior extends smoothly and the effective spacetime is geodesically complete. This suggests that quantum dynamics on a fixed classical background can regularize the Schwarzschild singularity without a full theory of quantum gravity.

We argue that if de Sitter space is indeed represented by a finite dimensional quantum system, then semi-classical considerations, combined with the fundamental principles of quantum measurement theory, imply that any theoretical model of it is ambiguous. If our own universe asymptotes to such a de Sitter state, and if a model of it as a finite system can be embedded in a sequence of models that converges to a non-perturbative completion of a unique superstring model in asymptotically flat space, then one might be able to find a very precise mathematical model of our universe. However, even the most comprehensive experiments possible to local detectors in the universe cannot measure more than a tiny fraction of the total number of q-bits in the system.

Evaluating quantum loop corrections to curvature perturbations in non-attractor inflation presents theoretical ambiguities. A crucial aspect of this challenge lies in the unconstrained finite contributions in renormalization counterterms and regularization scheme dependence. In this work, we derive exact Ward identities via the path integral formalism based on the large gauge symmetry of the background-perturbation split. These identities are shown to impose strict, model-independent constraints on the renormalization procedure. Provided the ultraviolet completion respects this symmetry, the Ward identities non-perturbatively govern the infrared evolution of the power spectrum. This symmetry-based framework offers a systematic resolution to recent theoretical discrepancies concerning one-loop corrections in ultra-slow-roll inflation.

This paper aims to clarify conceptual aspects of emergent structure in IKKT-type matrix models. Even without any adjustable parameters in the action, non-trivial matrix vacua do acquire a meaningful coupling constant, as well as two distinct uncertainty scales: a) the scale of noncommutativity of the matrix background, and b) the scale of quantum fluctuations of the matrices under the path integral. These scales are estimated for two prototypes of matrix backgrounds, known as Moyal-Weyl quantum plane and covariant quantum spacetime. Their relative importance separates two regimes: 1) the semi-classical regime interpreted in terms of semi-classical noncommutative geometry, and 2) the deep quantum regime usually interpreted in terms of holography. The quantum fluctuations around the background are shown to be negligible in the weak coupling regime. This justifies a basic assumption in previous work on the emergent 3+1-dimensional semi-classical geometry and (quantum) gravity in suitable vacua.

We consider the two-fermion $F_a F_b$ productions and decays via one mediator exchange at the $e^+e^-$ collider. With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix, we prove that the trace ${\rm Tr} [C]$ of the spin correlation matrix $C$ is an invariant quantity, and is invariant under basis rotations. Thus, for the exchanges of one mediator such as scalar and gauge boson, we can determine the product of the spin-analyzing powers for $F_a F_b$ via ${\rm Tr} [C]$, and reconstruct the spin correlation matrix. With the CHSH-Horodecki criterion, we can probe the Bell non-locality, and evade the no-go theorem. To be concrete, we study the Bell non-locality for the $\Lambda \bar \Lambda$ productions and decays at the BESIII experiment. In addition, the invariant ${\rm Tr} [C]$ is a new physics observable to probe the new physics beyond the Standard Model (SM) and study the SM precision measurements. Moreover, for the scalar exchanges, we discuss the general invariants of the spin correlation matrices and the related phenomenological consequences.

The traversable wormhole protocol in coupled Sachdev-Ye-Kitaev (SYK) systems produces a transmission signal C(t) widely interpreted as evidence of holographic dynamics. Recent work has questioned this interpretation, showing that similar signals arise in generic thermalizing systems. We address what the signal actually probes by systematically destroying quantum chaos in the SYK model via random coupling deletion, while monitoring the transmission signal across the chaos-to-integrable transition. Using exact diagonalization of the doubled SYK model at N=10 with 50 disorder realizations per sparsity, supplemented by Krylov-subspace extensions to N=20, we find that the ensemble-averaged peak height varies by less than 1.1% across a 50-fold sparsification range, even as the underlying spectrum transitions from Gaussian-unitary-ensemble to sub-Poisson statistics. A 1,200-instance sweep over the inter-system coupling mu confirms that the signal is controlled by mu alone, with no dependence on internal chaos. We further verify that the thermofield double state retains its thermal structure under sparsification despite substantial changes to the state vector, providing a structural explanation for the invariance. These results indicate that the transmission signal diagnoses inter-system coupling fidelity rather than holographic dynamics, and that future quantum-simulation experiments require independent chaos diagnostics to substantiate gravitational claims. As a practical consequence, the invariance implies that 98% of the Hamiltonian's coupling terms can be discarded (with variance rescaling of the survivors), reducing the gate count per Trotter step by approximately 50x at N=10 and bringing larger traversable-wormhole simulations within experimental reach.

We review a framework for the conformal bootstrap that does not rely on positivity and treats the infinite tower of high-dimension OPE contributions to conformal correlators through dispersion relations and neural networks. We apply it to scalar thermal two-point functions on $S^1\times \mathbb R^{d-1}$. We discuss the stability properties of the relevant non-convex optimisation scheme and potential relations to recent discussions of smoothness properties in CFT correlators. We illustrate the numerical application of the method to Generalized Free Fields and 4d holographic CFTs. This is a proceedings contribution to the “Athens Workshop in Theoretical Physics: 10th Anniversary", held at the National and Kapodistrian University of Athens on December 17-19 2025.

We propose a novel gravitational signature to detect Primordial Black Hole (PBH) dark matter by treating interstellar hydrogen as a quantum sensor for spacetime curvature. Focusing on H II regions, we demonstrate that the Riemann tidal tensor of an asteroid-mass PBH induces a symmetric splitting of the $2P_{3/2}$ state in bound hydrogen atoms. This relativistic effect redistributes $9.9\,\mathrm{GHz}$ absorption line into a gravitational spectral radio forest with a bandwidth $\sim 2\,\mathrm{GHz}$. By accounting for active accretion of Hydrogen atoms and the resulting density-squared emission measure within the Bondi radius, we find a relatively enhanced absorption spectrum. This feature presents a concrete, high-contrast target for upcoming radio-surveys to constrain PBH populations in the dark matter sector.

We investigate gravitational waveforms from compact binary systems in Einstein-scalar-Maxwell (ESM) theories, where a scalar field $\phi$ couples to a $U(1)$ gauge field $A_\mu$ through a field-dependent function $\mu(\phi)$. In this framework, compact objects – black holes (BHs), neutron stars (NSs), and exotic compact objects (ECOs) – can carry both vector and scalar charges, with the latter arising as secondary hair induced by the former. Modeling the binary as electrically charged point particles with scalar-field-dependent masses, we derive the conservative dynamics in the near zone and compute the radiative fields in the far zone. The tensor waveform is modified through the effective dynamics and radiation-reaction-driven phase evolution, while scalar and vector modes introduce additional energy-loss channels. From the energy fluxes of tensor, scalar, and vector radiation, we construct the frequency-domain waveform using the stationary phase approximation. Dipole radiation sourced by differences in scalar and vector charge-to-mass ratios yields a leading $-1$ post-Newtonian correction. The deviation from general relativity is characterized by a single parameter $b$, which controls both amplitude and phase modifications. We further examine constraints from the orbital-period decay of binary pulsars, showing that current observations already place stringent bounds on $b$ for neutron star binaries. In addition, we evaluate $b$ for representative BH-BH, NS-NS, ECO-ECO binaries realized in ESM theories. Our results provide a unified framework for gravitational-wave signatures of charged compact binaries and offer a means of testing dark-sectorscalar and vector charges with current and future observations.

I review the Feynman-Wiener path-integral formalism for diffusion with drift and jumps.

We investigate five-dimensional rotating primordial black holes (PBHs) as dark matter candidates within the Dark Dimension (DD) scenario motivated by the Swampland Program. In this framework, a micron-scale extra dimension suppresses Hawking evaporation, allowing PBHs with initial masses \(M \gtrsim 10^{10}\,\mathrm{g}\) to survive to the present epoch. Moreover, the memory burden effect, a quantum-gravitational suppression of the evaporation rate by \(S^{-p}\), significantly prolongs PBH lifetimes and enlarges the allowed parameter space. We compute the evaporation dynamics for rotating 5D PBHs, derive the enhanced lifetime for \(p=2\), and establish the dark matter window \(10^{10}\,\mathrm{g} \lesssim M \lesssim 10^{21}\,\mathrm{g}\). The curvature perturbations responsible for PBH formation also generate a stochastic gravitational wave background through second-order scalar-induced effects. Assuming a log-normal primordial power spectrum with \(\sigma=1\) and \(f_{\mathrm{PBH}}=1\), we calculate the present-day energy density \(\Omega_{\mathrm{GW}}h^2\) across the Dark Dimension window. The predicted signals peak at frequencies from nHz to Hz, within the sensitivity ranges of LISA and DECIGO/BBO, while remaining consistent with current CMB spectral distortion bounds. Fisher forecasts show that future observatories can constrain the PBH mass, dark matter fraction, spectral width, and memory burden exponent with percent-level precision. A detection of the predicted gravitational wave background would provide simultaneous evidence for a micron-sized extra dimension, PBH dark matter, and the memory burden effect, offering a decisive test of quantum gravity and extra-dimensional physics.

In his 1999 preprint "Universal Lie Algebra", P. Vogel put forward a hypothesis on the existence of a universal Lie algebra. Although this hypothesis remains open, it is known that many quantities in Lie theory admit universal descriptions. Remarkably, almost all such universal formulas have been obtained through the representation theory of simple Lie (super)algebras, whereas Vogel's original framework was based on a more abstract diagrammatic algebra. Nevertheless, the diagrammatic approach has received little attention over the past two decades, since the last contributions by P. Vogel and J. Kneissler. In this work, we revive the diagrammatic technique grounded in Vogel's $\Lambda$-algebra and show that it enables truly universal computations. We examine numerous examples and discuss them.

We reinterpret the lukewarm sector of four-dimensional Reissner–Nordström–de Sitter black holes as the exact zero-dissipation thermal manifold of an effective two-horizon nonequilibrium system. In the fixed-charge sector, the inter-horizon thermal affinity controls the entropy production and vanishes precisely on the lukewarm branch. The corresponding linearized thermal mode is governed by an exact relaxation coefficient \(K_L(\rho)\), with \(\rho=r_+/r_c\), and changes stability at the critical ratio \[ \rho_*=\frac{1+\sqrt{3}-\sqrt{2}\,3^{1/4}}{2}\approx 0.4354, \] where the relaxation time diverges as \(\tau\sim |\rho-\rho_*|^{-1}\). We then encode this critical structure in a minimal Bragg–Williams functional and an Onsager–Machlup action for the effective trajectories of the thermal mode. In this way, the lukewarm branch is promoted from a geometric equal-temperature locus to a critical inter-horizon thermal manifold.

External matter distributions can substantially reshape the strong field environment of compact objects, yet this effect is usually neglected in idealized isolated models. In this work, we investigate geometrically thin, optically thick relativistic accretion onto a static axisymmetric space-time that describes a slightly deformed compact object immersed in an external quadrupolar field as an exact solution of vacuum Einstein field equations. Our aim is to determine whether such locally geometries can produce distinctive accretion signatures and, more broadly, to identify the physically meaningful radial domain over which the local solution remains self-consistent. We show that the external quadrupolar distortion leaves a clear imprint on both orbital dynamics and accretion structure. We further find that the outer edge of the radiating region is closely tied to the transition between radiation pressure and gas pressure dominance, which may link the geometry to the thermodynamic properties of the flow. Therefore, the local nature of the distorted spacetime is not merely a formal geometric feature, but has observable consequences for the morphology and emission properties of accretion flows.

We formulate out-of-equilibrium jet momentum broadening in QCD effective kinetic theory through a moment expansion of the medium distribution function, a method traditionally used to derive relativistic viscous hydrodynamics from kinetic theory. We explicitly compute the leading near-equilibrium contribution to the spatial jet broadening tensor $\hat q^{ij}$ within the 14-moment approximation, and show that it is controlled by the medium shear-stress tensor. This provides a direct map from QCD effective kinetic theory to event-by-event viscous hydrodynamic simulations, converting local shear-stress fields into anisotropic corrections to jet broadening in heavy-ion collisions.