We investigate the structure and radial oscillations of anisotropic compact stars composed of dark energy, using the vanishing complexity factor formalism within general relativity. This novel approach establishes a direct link between the energy density and anisotropic factor, providing a robust framework for studying these exotic stellar objects. Employing an Extended Chaplygin Gas equation of state, we numerically compute interior solutions for both isotropic and anisotropic stars, revealing distinct differences in their properties. Additionally, we examine the oscillation modes and frequencies of these stars, highlighting the impact of anisotropy on their pulsational behaviour. Our results reveal distinct differences in the stellar properties, such as the metric potentials, pressure, speed of sound, and relativistic adiabatic index, between the two cases. Furthermore, we calculate the large frequency separation for the fundamental and first excited modes, offering insights relevant for future asteroseismology studies. Our findings shed light on the complex interplay of gravity, matter, and anisotropy in compact stars, providing a new perspective on dark energy's role in their structure and dynamics.

Chile

Grigoris Panotopoulos

Spain

Ángel Rincón

Portugal

Ilídio Lopes

Anisotropic dark energy stars within vanishing complexity factor formalism: Hydrostatic equilibrium, radial oscillations, and observational implications

In the present work, we perform a comparative study of different interacting dark energy (DE) models using the Statefinder diagnostics. In particular, 17 different forms of the energy transfer rate Q between DE and dark matter (DM) were focused on, belonging to the following categories: (i) linear models in energy densities of DE and DM, (ii) non-linear models, (iii) models with a change of direction of energy transfer between DE and DM, (iv) models involving derivatives of the energy densities, (v) parametrized interactions through a function of the coincidence parameter  $$\tilde{r}$$  <math> <mover> <mi>r</mi> <mo>~</mo> </mover> </math>  , and finally we also consider (vi) two kinds of models with a self-interaction between DM, without DE. These models have been already studied in the literature and constrained with observational data available at that time. In order to discriminate between them at background level, we use the Statefinder diagnostic, based on the computation and study of the so-called Statefinder parameters r, s in addition to the deceleration parameter q. We plot the evolution trajectories for the several interacting models on the  $$r-q$$  <math> <mrow> <mi>r</mi> <mo>-</mo> <mi>q</mi> </mrow> </math>  ,  $$r-s$$  <math> <mrow> <mi>r</mi> <mo>-</mo> <mi>s</mi> </mrow> </math>   planes, and we find some distinctive features and departures from  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM and other DE models, as Quintessence, Chaplygin Gas, running vacuum models (RVM) and Galileon.

Brazil

Raul Carrasco

Joel Saavedra

Nelson Videla

Discriminating interacting dark energy models using Statefinder diagnostic

In this work, we prove that every f(R) gravity can be represented as a scale-dependent one, but not every scale-dependent gravity can be represented in the f(R) framework. Therefore, the f(R) formalism is strictly included in the scale-dependent approach. This scale-dependent representation of f(R) gravity allows for a novel approach toward both theories. In particular, we obtain a novel dynamical characterization of light rings for f(R(r)) theories and we have shown that some previous solutions of f(R) theories correspond to solutions of scale-dependent gravity. Finally, new solutions to scale-dependent gravity are identified with the help of the f(R) representation.

Pelayo Calzada

Pedro Bargueño

Comparing f(R) and scale-dependent gravities

In this work, we investigate for the first time Nariai-like black hole solutions in four dimensional space time with spherical symmetry in the context of scale-dependent gravity. In particular, we construct self-consistent solutions in such a way that the classical one that coming from Einstein theory) is also contained into our new results. We start by considering a truncated effective Einstein–Hilbert action with cosmological constant in which both the gravitational and the cosmological couplings are elevated to scale-dependent functions (instead of being coupling constants), taking advantage of the scale-dependent scenario, which is a concrete and simple approach strongly inspired by asymptotically safe gravity. We briefly discuss black hole thermodynamics and and compare it with its classical counterpart. The impact of non-Einsteinian features is encoded by the scale-dependent parameter,  $$\epsilon $$  <math> <mi>ϵ</mi> </math>  . A few comments regarding the topology of the solution and their impact are also mentioned.

Nariai-like black holes in light of scale-dependent gravity

In this article, using gravitational decoupling by means of minimal geometric deformation approach, we obtain a new spherically symmetric and static black hole solution. To progress, we close the system by assuming that the average pressure of the  $$\theta $$  <math> <mi>θ</mi> </math>  -sector is vanishing. Also, we tackle the problem regarding how, for a given minimally deformed black hole solution, one can connect it to a wormhole space–time.

Francisco Tello-Ortiz

A. Alvarez

India

Saibal Ray

Gravitationally decoupled non-Schwarzschild black holes and wormhole space–times

Within Einstein’s General Relativity we study exotic stars made of dark energy assuming an extended Chaplygin gas equation-of-state. Taking into account the presence of anisotropies, we employ the formalism based on the complexity factor to solve the structure equations numerically, obtaining thus interior solutions describing hydrostatic equilibrium. Making use of well-established criteria we demonstrate that the solutions are well behaved and realistic. A comparison with another, more conventional approach, is made as well.

Anisotropic stars made of exotic matter within the complexity factor formalism

In the present work, we investigate the consequences of running gravitational coupling on the properties of the three-dimensional BTZ black hole. We take as starting point the functional form of gravitational coupling obtained in the context of asymptotic safe gravity theory. By using the standard scale setting relation where     $$k\sim \xi /r^n$$  <math> <mrow> <mi>k</mi> <mo>∼</mo> <mi>ξ</mi> <mo>/</mo> <msup> <mi>r</mi> <mi>n</mi> </msup> </mrow> </math>  , we compute the solution of the Einstein field equations. We get and analyze the horizon and the thermodynamic properties of this new class of black hole solutions. The impact of the scale-dependent parameter     $$\xi $$  <math> <mi>ξ</mi> </math>   on the cosmological “constant” and metric functions are briefly discussed. We find that the null energy condition is also violated in this setup when scale-dependent gravity and Newton’s coupling (coming from the asymptotic safety scenario of gravity) are simultaneously taken into account.

Austria

Benjamin Koch

Netherlands

Cristobal Laporte

Felipe Canales

Norman Cruz

The effects of running gravitational coupling on three dimensional black holes

In this work, the role of a time-varying Newton constant under the scale-dependent approach is investigated in the thermodynamics of the Friedman equations. In particular, we show that the extended Friedman equations can be derived either from equilibrium thermodynamics when the non-matter energy momentum tensor is interpreted as a fluid or from non-equilibrium thermodynamics when an entropy production term, which depends on the time-varying Newton constant, is included. Finally, a comparison between black hole and cosmological thermodynamics in the framework of scale-dependent gravity is briefly discussed.

Ecuador

Ernesto Contreras

Thermodynamics of scale-dependent Friedmann equations

We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton’s constant is allowed to vary with the radial coordinate throughout the star. Assuming (1) a linear equation-of-state in the MIT bag model for quark matter, and (2) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditions are fulfilled. Our results show that a decreasing Newton’s constant throughout the objects leads to slightly more massive and more compact stars.

Interior solutions of relativistic stars with anisotropic matter in scale-dependent gravity

In this work, we investigate the quasinormal frequencies of a class of regular black hole solutions which generalize Bardeen and Hayward spacetimes. In particular, we analyze scalar, vector and gravitational perturbations of the black hole with the semianalytic WKB method. We analyze in detail the behaviour of the spectrum depending on the parameter p/q of the black hole, the quantum number of angular momentum and the s number. In addition, we compare our results with the classical solution valid for  $$p = q = 1$$  <math> <mrow> <mi>p</mi> <mo>=</mo> <mi>q</mi> <mo>=</mo> <mn>1</mn> </mrow> </math>  .