The European Physical Journal C

Gao, Leda; Shashank, Swarnim; Bambi, Cosimo

doi: 10.1140/epjc/s10052-026-15867-xpmid: N/A

X-ray reflection spectroscopy is a powerful tool for testing the Kerr hypothesis and probing the strong gravity regime around accreting black holes. Most tests of general relativity (GR) assume that the spacetime around a black hole is circular, meaning the metric possesses a specific symmetry structure common to the Kerr solution. However, deviations from circularity are predicted by various modified gravity theories and non-vacuum general relativity solutions. In this work, we test a specific non-circular metric constructed based on a locality principle, where the deviation from the Kerr spacetime is driven by the local spacetime curvature. To accurately model the reflection spectrum in this background, we implement a relativistic ray-tracing code in horizon-penetrating (ingoing Kerr) coordinates, which are favored for their ability to avoid introducing curvature singularities at the horizon in non-circular spacetimes. We apply this model to the high-quality NuSTAR spectrum of the Galactic black hole binary EXO 1846-031. Our spectral analysis reveals a source with a high inclination angle (ι≈76∘\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\iota \approx 76^{\circ }$$\end{document}) and a near-extremal spin parameter (a∗≈0.98\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$a_* \approx 0.98$$\end{document}). While we identify a global minimum in the parameter space suggesting a non-zero deformation (ℓNP≈0.12\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell _{\textrm{NP}} \approx 0.12$$\end{document}), the 99% confidence interval fully encompasses the Kerr limit (ℓNP=0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\ell _{\textrm{NP}}=0$$\end{document}). We conclude that the current X-ray reflection data for EXO 1846-031 are consistent with the Kerr hypothesis. This work demonstrates the feasibility of using X-ray reflection spectroscopy to constrain non-circular metrics and establishes a framework for future tests.

Araújo Filho, A. A.; Heidari, N.; Lobo, Iarley P.

doi: 10.1140/epjc/s10052-026-15859-xpmid: N/A

We investigate the propagation of gravitational waves in the presence of Lorentz- and diffeomorphism-violating operators within the linearized gravitational sector of the Standard Model Extension. Focusing on isotropic contributions, we analyze the combined effects of the CPT-even dimension-four coefficient k˚(I)(4)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathring{k}^{(4)}_{(I)}$$\end{document} and the CPT-odd dimension-five coefficient k˚(V)(5)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathring{k}^{(5)}_{(V)}$$\end{document} on tensorial gravitational radiation. The modified dispersion relation induces both a rescaling of the propagation speed and helicity-dependent corrections, leading to birefringence and polarization mixing without introducing additional propagating degrees of freedom. We derive the retarded Green function associated with the modified wave operator and obtain explicit expressions for the gravitational waveform generated by matter sources. As an application, we examine a binary black hole system and show how Lorentz violation alters the observed strain through shifted retarded times, amplitude rescaling, and higher derivative corrections to the quadrupole formula. Using GW170817/GRB 170817A, published GWTC-3 propagation tests, and conservative polarization consistency arguments, we translate existing observational constraints into bounds on k˚(I)(4)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathring{k}^{(4)}_{(I)}$$\end{document} and k˚(V)(5)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathring{k}^{(5)}_{(V)}$$\end{document}.

Garousi, Mohammad R.

doi: 10.1140/epjc/s10052-026-15848-0pmid: N/A

Recent studies suggest that applying the Buscher rules to the dimensional reduction of ten-dimensional, one-loop effective actions generate “purely stringy” couplings in nine dimensions that cannot be lifted to a local, covariant form in ten dimensions. We investigate this phenomenon at order α′3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha '^3$$\end{document} in type IIA string theory. By computing the circular reduction of the one-loop Chern–Simons term and pure-gravity couplings in type IIA theory and applying the T-duality transformation to the resulting couplings, we derive their counterparts in the type IIB effective action. We demonstrate that the resulting nine-dimensional type IIB couplings are invariant under S-duality without requiring contributions from the tree-level effective action or non-perturbative effects. As a consistency check, we show that the nine-dimensional type IIB couplings, when reduced on a K3 surface, reproduce the known heterotic string couplings on T5\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ T^5 $$\end{document} at order α′\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ \alpha ' $$\end{document}, via the duality between the two theories.

Zeng, Xiao-Xiong; Yang, Chen-Yu; He, Ke-Jian; Li, Li-Fang

doi: 10.1140/epjc/s10052-026-15827-5pmid: N/A

Using the ballistic approximation accretion flow model, this paper investigates the shadow and polarization images of a Kerr-like black hole surrounded by a cold dark matter halo. By numerically solving the geodesic and radiative transfer equations, we analyze the effects of the critical density rc\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r_c$$\end{document}, the scale radius of the dark matter halo rs\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r_s$$\end{document}, the spin parameter a, and the observer inclination θo\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta _o$$\end{document} on the resulting images. In all cases, a bright ring structure corresponding to higher-order images is observed, accompanied by an inner region of decreased intensity. The results show that both rc\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r_c$$\end{document} and rs\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$r_s$$\end{document} increase the size of the higher-order images, while the spin parameter a and inclination θo\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta _o$$\end{document} modify the image morphology, producing a crescent-shaped bright region on the left side. In the polarization maps, the linear polarization degree Po\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$P_o$$\end{document} is significantly lower in the higher-order image region, and the polarization vectors exhibit distinct distributions inside and outside the ring. Compared with the thin disk model, the thick disk model displays notable differences in both shadow and polarization images.

Zhao, Xing-Meng; Wang, Liu-Lin; He, Ying-Bo; Wang, Xiao-Yun; Liu, Xiao-Hai

doi: 10.1140/epjc/s10052-026-15861-3pmid:

Li, Zonghai; Gao, Xiao-Jun

doi: 10.1140/epjc/s10052-026-15822-wpmid: N/A

In gravitational lensing under the weak-field approximation, the usual viewpoint is that light bending measures how a ray deviates from a straight line in Euclidean space. In this work, we take the opposite perspective: we ask how a straight line bends in a curved space, such as optical geometry–that is, how it deviates from geodesics. Using the Gauss–Bonnet theorem, we show that, at leading order, the deflection angle can be written as the integral of the geodesic curvature of a straight line in curved space. This reformulation emphasizes the global, coordinate-independent nature of the deflection angle and provides a complementary way of understanding the classical Gibbons–Werner method. To illustrate the idea, we apply it to three familiar spacetimes–Schwarzschild, Reissner–Nordström, and Kerr–and recover the well-known results. Furthermore, we extend the method to massive particles using the Jacobi metric, and illustrate it with the Reissner–Nordström spacetime.

Kwasnitza, Thomas; Stöckinger, Dominik; Voigt, Alexander; Wünsche, Johannes

doi: 10.1140/epjc/s10052-026-15750-9pmid: N/A

We perform an extensive analysis of the light CP-even Higgs boson pole mass in the MSSM and its dependencies on various parameters based on the 3-loop FlexibleEFTHiggs hybrid calculation which is implemented and publicly available since recently in FlexibleSUSY. Our focus lies on the study of the robustness of the approach in scenarios of highly non-degenerate SUSY mass spectra. Also, we present an improved Higgs mass calculation in the NMSSM based on the same approach, which is published in the new version 2.9.0 of FlexibleSUSY as well. The calculation provides a treatment in the full-model parametrization, leading to an advantageous resummation of QCD-enhanced terms in the stop-mixing parameter and includes important 2-loop contributions as well as 3-loop QCD contributions in the MSSM limit. We assess the reliability of this new calculation by applying it to several distinct NMSSM scenarios. In this context, special attention is devoted to the estimation of NMSSM-specific theory uncertainty.

Khan, Saeed Ullah; Rayimbaev, Javlon; Hayat, Haidar; Chen, Zhi-Min; Abdullaev, Mardon; Murodov, Sardor; Wang, Weiwei

doi: 10.1140/epjc/s10052-026-15830-wpmid: N/A

In this article, we develop a framework to study particle dynamics and quasi-periodic oscillations (QPOs) in a Kerr-like rotating Simpson–Visser black hole endowed with a modified gravity (MOG) coupling α\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\alpha $$\end{document} and a regularization parameter b. We study the horizon structure under the influence of these parameters, including the black hole spin. Using the Hamiltonian approach, we derive the equation of motion. Then, by exploiting the Kerr separability structure, we derive closed-form expressions for the effective potential. We examine the effective force, angular momentum, and energy to obtain information about particle motion. In addition, we calculated the Keplerian, radial, and vertical frequencies. We investigate the behavior of black hole parameters as a function of frequency and QPOs. We show how the modified rotating Simpson–Visser MOG black hole alters the spacetime geometry, particle dynamics, and QPOs.

de Souza, F. E. A.; Tahim, M. O.; Junior, R. I. de Oliveira; Macêdo, I. M.

doi: 10.1140/epjc/s10052-026-15903-wpmid: N/A

In this work we analyze the classical confinement of relativistic and supersymmetric spinning particles in higher-codimension braneworlds. Considering warped backgrounds generated by string-like n=2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ n=2$$\end{document} and global scalar defects n≥3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$ n \ge 3$$\end{document}, we derive the effective radial dynamics from a Polyakov-type action. For spinless particles, the effective potential is monotonically decreasing, leading to repulsive behavior and the absence of confinement. In contrast, for N=1,2\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$N=1,2 $$\end{document} spinning particles, spin-curvature coupling modifies the potential, allowing the emergence of stable equilibrium points. Depending on the coupling parameter, particles may be confined on the membrane or in nearby regions, exhibiting bounded or satellite-like motion. These results emphasize the role of spin in localization mechanisms.

Iyer, Karthik; Chakraborty, Chandrachur

doi: 10.1140/epjc/s10052-026-15834-6pmid: N/A

We study the orbital structure and precession dynamics of neutral test particles in the magnetized Kerr black hole (MKBH) spacetime – an exact electrovacuum solution of the Einstein–Maxwell equations that self-consistently incorporates the curvature effects of an external magnetic field. This geometry allows a unified treatment of gravitational and magnetic influences across weak to ultra-strong regimes. The analysis reveals a critical magnetic field strength Bcr(a∗)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$B_{\textrm{cr}}(a_*)$$\end{document} above which no circular geodesics, timelike or null, can exist, establishing an upper magnetic bound for orbital motion. For subcritical fields, the photon circular orbit admits two real roots, the outer of which defines an outermost stable circular orbit (OSCO), complementing the conventional innermost stable circular orbit (ISCO) and confining stable motion within a finite radial domain. Exact expressions for the orbital, radial, and vertical epicyclic frequencies, and their associated precession rates, show substantial deviations from Kerr behavior, including a magnetically induced reversal of periastron precession (Ωper<0\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\Omega _{\textrm{per}} < 0$$\end{document}) within a finite radial range. For astrophysically relevant magnetic field strengths, the retrograde precession could be observable at large radii around astrophysical BHs, offering a potential diagnostic of large-scale magnetization. These findings highlight the geometric influence of magnetic curvature on strong-field dynamics, providing a self-consistent framework to interpret quasi-periodic oscillation phenomenology and potential magnetic imprints in precision timing observations of compact objects.