We study the concept of a dark energy star, which is assumed to be composed of both dark and conventional matter in a modified teleparallel gravity. After employing a specific viable stellar model, we build the corresponding equations of motion that govern our further analysis. We then calculate the analytical form of the spherical geometric function, accompanied by an embedding class I choice, which states that the 4-dimensional geometry can be placed in a 5-dimensional planar space. With the help of a specific dark energy state equation, we model our system to investigate the role of dark energy on key stellar characteristics, such as equilibrium, star mass, and compactness, among other aspects, in the presence of torsion terms. This will lead us to investigate the stable epochs of the corresponding stellar structure through parameters such as pressure, mass function, density, and surface redshift, among others. We will then calculate the maximum allowable stellar matter quantity by utilizing the M-R diagram. It is inferred that, under certain parametric geometric zones, torsion-based correction supports a realistic and singularity-free star model. The system is seen to obey all energy conditions and stability criteria proposed by some theoretical backgrounds.

Pakistan

Z. Yousaf

U.A. Khokhar

Uzbekistan

Javlon Rayimbaev

Otaboyev Sirajiddin

Aybek Seytov

Azerbaijan

M.Z. Bhatti

Existence of class-I dark energy stellar models

We propose a new kind of Dark Matter: Derivative Portal Dark Matter. This kind of Dark Matter connects to the Standard Model through a massive mediator, which links to the Standard Model in derivative form. The derivative of a mediator in momentum space corresponds to the mediated momentum, which vanishes in the zero momentum transfer limit. As a result, this kind of Dark Matter can evade stringent constraint from the Dark Matter direct detection while fitting the Dark Matter relic density observation naturally. We explore several UV complete models of this kind of Dark matter. What’s more, we show that these models also survive from Dark Matter indirect detection and collider search.

China

Yu-Pan Zeng

Derivative portal dark matter

We investigate a wide range of dynamical and observational signatures of spherically symmetric static black holes in the non-local Deser-Woodard gravity model, distinguished by a non-local parameter <italic>&#945;</italic> and an integer model order <italic>n</italic>. Starting from the modified metric functions, we derive the Klein&#8211;Gordon equation for a massless scalar field and transform it into a Schr&#246;dinger-like form using tortoise coordinates. We then compute the spectra of quasinormal modes (QNMs) employing both the sixth-order WKB approximation and its Pad&#233;-improved variants. We demonstrate that nonlocality systematically reduces the real frequencies of QNMs and increases damping. Additionally, we observe that the errors associated with the WKB approximation grow rapidly; however, the Pad&#233; method effectively reduces these errors to sub-percent levels. Next, we establish rigorous analytic lower bounds on greybody factors (GBFs) using the Visser&#8211;Boonserm method. This analysis demonstrates that an increase in either the parameter <italic>&#945;</italic> or the integer model order <italic>n</italic> serves to elevate and expand the effective potential barrier, which in turn suppresses transmission at mid-frequency ranges. We quantified the sparsity of Hawking radiation by calculating the dimensionless sparsity parameter, <italic>&#951;</italic>. Our findings indicate that nonlocal coupling, denoted by <italic>&#945;</italic>, significantly reduces the value of <italic>&#951;</italic>, which in turn accelerates the evaporation process. In contrast, higher values of <italic>n</italic> produce subtler effects. Notably, in all scenarios, we observe that <italic>&#951;</italic> approaches <italic>&#951;<inf>Sch</inf></italic> as the horizon radius increases. Finally, we analyse the epicyclic (radial and vertical) oscillation frequencies of near-circular orbits, presenting them in a closed form and discussing their potential as probes for nonlocal corrections in quasi-periodic oscillations of accretion discs. Our findings underscore distinct, observationally testable signatures of nonlocal gravity on black hole spectroscopy, greybody emission, and the dynamics of accretion discs.

India

Y. Sekhmani

Oman

S.K. Maurya

J. Rayimbaev

Saudi Arabia

M. Altanji

I. Ibragimov

S. Muminov

Black hole quasinormal modes, greybody factors, sparsity of Hawking radiation and quasi-periodic oscillations in a tetrad-frame Deser–Woodard nonlocal gravity

We generalize the explicit construction of fields in orbifolds of products of <math altimg='si2.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></mrow></math> minimal models, developed by A. Belavin, V. Belavin and S. Parkhomenko to include minimal models with D and E-type modular invariants. It is shown that spectral flow twisting by the elements of admissible group <italic>G</italic> <inf>adm</inf>, which is used in the construction of the orbifold, is consistent with the nondiagonal pairing of D and E-type minimal models. We obtain the complete set of fields of the orbifold from the mutual locality and other requirements of the conformal bootstrap. The collection of mutually local primary fields is labeled by the elements of dual group <math altimg='si3.svg'><msubsup><mi>G</mi><mtext>adm</mtext><mo>*</mo></msubsup></math>. The permutation of <italic>G</italic> <inf>adm</inf> and <math altimg='si3.svg'><msubsup><mi>G</mi><mtext>adm</mtext><mo>*</mo></msubsup></math> is given by the mirror spectral flow construction of the fields and maps the space of states of the original <italic>G</italic> <inf>adm</inf> orbifold onto the space of states of <math altimg='si3.svg'><msubsup><mi>G</mi><mtext>adm</mtext><mo>*</mo></msubsup></math> orbifold. We show that this transformation is by construction a mirror isomorphism of spaces of states. Thus, mirror isomorphism of states is built into the construction. We illustrate our approach for the orbifolds of <math altimg='si4.svg'><mrow><msub><mi mathvariant='bold'>A</mi><mn>2</mn></msub><msubsup><mi mathvariant='bold'>E</mi><mn>7</mn><mn>3</mn></msubsup></mrow></math> model.

Russia

Boris Eremin

Sergej Parkhomenko

Explicit construction of states in orbifolds of products of <math altimg='si1.svg'><mrow><mi>N</mi><mo linebreak='goodbreak'>=</mo><mn>2</mn></mrow></math> superconformal ADE minimal models

This work employs the minimal geometric deformation decoupling scheme to derive interior stellar solutions in the background of an electrically charged BTZ ansatz as a seed metric in three dimensions. In this respect, we impose two different equations of state to determine the deformation function and the new material contributions emerging from the additional field source. Furthermore, we describe the finiteness of all thermodynamic quantities of the presented stellar solutions, including the effective thermodynamical quantities, for varying values of the deformation parameter and total electric charge. We explore the new interior astrophysical solutions in three-dimensional gravity by analyzing the charged BTZ metric, admitting circular symmetry through the principles of geometric deformation. This study examines the impact of radial-metric deformation on the charged BTZ geometry and underscores the importance of stellar decoupling within the context of electrically charged dense distributions. It is shown that new physically acceptable solutions by incorporating any known three-dimensional spacetime as the isotropic basis are possible, which in turn enable one to analyze the quantum effects due to low degrees of freedom at lower dimensions.

Japan

Kazuharu Bamba

Mansoor Alshehri

S. Khan

Physical features of geometrically deformed anisotropic charged three-dimensional BTZ black holes

In the present paper we consider the usage of associative Yang-Baxter equations in the theory of classical and quantum <italic>ABCD</italic> algebras [1]. Classical and quantum associative analogs of the generalized Fredel-Maillet equations for <italic>ABCD</italic> tensors [2, 3] are found. Two classes of examples &#8212; rational and trigonometric &#8212; of classical and quantum <italic>ABCD</italic> tensors satisfying these equations are considered in details.

Ukraine

T. Skrypnyk

On ABCD algebras and associative Yang-Baxter equations

In this paper, we have tested the non-unitary mixing hypothesis with the latest data from NO <italic>&#957;</italic>A and T2K experiments. We have also analysed their combined data. We have provided the best-fit values of the standard and non standard parameters after the analysis. 90% limits on the non-unitary mixing parameters have also been provided. The constraints on unitary violation is stronger, compared to the constraints obtained from previous data from NO <italic>&#957;</italic>A and T2K. The tension between NO <italic>&#957;</italic>A and T2K at the 1&#8201; <italic>&#963;</italic> for normal mass hierarchy can be reduced for non-unitary mixing due to <italic>&#945;</italic> <inf>10</inf>, albeit for a value of | <italic>&#945;</italic> <inf>10</inf>| larger than the present global 90% limit. Additionally a study of the future sensitivity of NO <italic>&#957;</italic>A, T2K and DUNE has been provided.

Canada

Xin Yue Yu

Zishen Guan

Ushak Rahaman

Nikolina Ilic

Update on non-unitary mixing in the recent NO <italic>&#957;</italic>A and T2K data

We discuss in this paper the lattice discretizations of all topological defect lines (TDLs) for diagonal, minimal CFTs, using integrable restricted solid-on-solid (RSOS) models. For these CFTs, the TDLs can be labeled by the Kac labels. In the case of (1, <italic>s</italic>) TDLs, lines that are exactly topological on the lattice can be obtained using the centralizer of the underlying Temperley-Lieb algebra, all the other lines become topological in the continuum limit only. Our general construction relies on insertions of rows/columns of faces with modified spectral parameters, and can therefore be studied using integrability techniques. We determine the regions of spectral parameters realizing the different ( <italic>r, s</italic>) TDLs, and in particular calculate analytically all the associated eigenvalues (and degeneracy factors). We also show how fusion of TDLs can be obtained from fusion hierarchies in the algebraic approach to the Bethe-ansatz. All our results are checked numerically in detail for several minimal CFTs.

United States

Madhav Sinha

Brazil

Thiago Silva Tavares

Ananda Roy

France

Hubert Saleur

Integrability and lattice discretizations of all topological defect lines in minimal CFTs

In this work, we derive a new class of analytic black hole solutions within the framework of <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity, where the black hole is surrounded by an anisotropic fluid acting as the matter source. We consider both linear and nonlinear forms of the function <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math>, enabling a detailed exploration of how anisotropic pressures and different <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> influence the spacetime structure. Furthermore, we derive the conditions on the coupling parameters ( <italic>&#946;</italic> <inf>1</inf>, <italic>&#946;</italic> <inf>2</inf>, <italic>&#946;</italic> <inf>3</inf>) under which the energy condition is satisfied. Utilising these constraints, we then investigate the thermodynamic behaviour of the resulting black hole solutions in the presence of various matter fields. An important outcome of this study is that the results obtained deviate from those predicted by standard General Relativity. It is also observed that these deviations depend explicitly on the interaction between the matter Lagrangian <math altimg='si9.svg'><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub></math> and the trace <italic>T</italic> of the energy-momentum tensor.

Aniruddha Ghosh

Ujjal Debnath

The new black hole solution with anisotropic fluid in <math altimg='si8.svg'><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>,</mo><msub><mi mathvariant='script'>L</mi><mi>m</mi></msub><mo>,</mo><mi>T</mi><mo>)</mo></mrow></math> gravity: Thermodynamics

We investigate exact charged and uncharged black hole solutions in a (2+1)-dimensional spacetime within the framework of quadratic form of <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> symmetric teleparallel gravity, where <math altimg='si15.svg'><mi mathvariant='double-struck'>Q</mi></math> is the non-metricity scalar. By adopting spherical symmetry and considering both vanishing and non-vanishing electromagnetic fields, we derive new classes of black hole solutions and analyze their geometric and physical properties. The study demonstrates that the inclusion of quadratic corrections in the gravitational Lagrangian significantly modifies the structure of solutions, producing deviations from the standard BTZ geometry. Invariants such as curvature and non-metricity scalars are calculated to classify the singularity structure and spacetime behavior. Thermodynamic quantities, including Hawking temperature, entropy, and heat capacity, are computed, showing consistency with the first law of black hole thermodynamics. Furthermore, we examine the geodesic motion of test particles and derive the effective potential to explore the stability of photon orbits. A notable outcome is the identification of weaker black hole singularities in comparison to General Relativity, attributed to the non-metricity corrections. The possibility of multi-horizon configurations is also explored. This study provides a comprehensive analysis of the gravitational, thermodynamic, and dynamical features of lower-dimensional black holes in <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> gravity and highlights their distinct characteristics with respect to General Relativity.

Egypt

Gamal G.L. Nashed

Italy

Salvatore Capozziello

Stable black holes in lower dimensional <math altimg='si2.svg'><mrow><mi>f</mi><mo>(</mo><mi mathvariant='double-struck'>Q</mi><mo>)</mo></mrow></math> non-metric gravity