Roberto D. Alba Q., Javier Chagoya, and Armando A. Roque

Abstract

We investigate static, spherically symmetric solutions in Einstein-scalar-Gauss-Bonnet gravity nonminimally coupled to a massless real scalar field, both in vacuum and in the presence of fermionic matter. Focusing on a specific quadratic scalar–Gauss–Bonnet coupling, we identify two distinct classes of compact objects: one with a regular scalar field at the origin—connected to general relativity in an appropriate limit—and another one with a divergent scalar field at the origin but a regular geometry. We analyze both purely scalar and matter-supported (hybrid) configurations, showing that the former can describe a broad class of compact objects, while the latter can reproduce neutron starlike masses even when modeled with a simple polytropic equation of state. Furthermore, we highlight distinctive phenomenological signatures, including the ability of these stars to exceed known compactness limits and their potential to act as gravitational wave superemitters. We also examined the motion of test particles nonminimally coupled to the scalar field and showed the existence of stable circular orbits within the Schwarzschild’s ISCO and static configurations at finite radii for particles with zero angular momentum.

Wilfredo Yupanqui Carpio and Octavio Obregón 

Abstract

Starting from the eigenvalue equation for the mass of a black hole derived by Mäkelä and Repo, we show that, by reparametrizing the radial coordinate and the wave function, it can be rewritten as the eigenvalue equation of a quantum harmonic oscillator. We then study the interior of a Schwarzschild black hole using two quantization approaches. In the standard quantization, the area and mass spectra are discrete, characterized by a quantum number, but the wave function is not square-integrable, limiting its physical interpretation. In contrast, a minimal-uncertainty quantization approach yields an area spectrum that grows as n^2, and consequently the mass M also increases. In this framework, the wave function is finite and square-integrable, with convergence requiring that the deformation parameter \beta be regulated by a discrete quantum number m. The wave function exhibits quantum tunneling connecting the black hole interior with both its exterior and a white hole region, effects that disappear in the limit \beta \to 0. These results demonstrate how minimal-length effects both regularize the wave function and modify the semiclassical structure of the black hole.

Flavio C. Sánchez, Armando A. Roque, and Javier Chagoya

Abstract

We investigate the effects of Einsteinian cubic gravity in the strong gravitational regime. In the first part, we explore analytical solutions for a static, spherically symmetric metric, establishing the existence of maximally symmetric de Sitter solutions, as well as asymptotically de Sitter solutions, with an effective cosmological constant. We also study, analytically and numerically, how the horizon properties are affected by cubic gravity. Our results reveal that a positive coupling constant reduces the horizon size, while a negative one increases it. In the second part, we analyze potential observational signatures of cubic terms, focusing on their effects on the bending of light. Specifically, we investigate the angular difference, related to the deflection angle but valid near the source, along with the behavior of the photon sphere. Our findings show that the strongest effects of the cubic terms occur in the strong gravity regime, and there exists a direct relationship between the value of the coupling constant and the photon sphere position, opening up the possibility to constrain cubic gravity with black hole shadows.

Mario H Amante, Andrés Lizardo, Javier Chagoya and C Ortiz

Abstract

We analyze cosmography as a tool to constrain modified gravity theories. We take four distinct models and obtain their parameters in terms of the cosmographic parameters favored by observational data of strong gravitational lensing. We contrast with the values obtained by direct comparison between each model and the observational data. In general, we find consistency between the two approaches at 2σ for all models considered in this work. Our study bridges the gap between theoretical predictions of modified gravity and empirical observations of strong gravitational lensing, providing a simple methodology to test the validity of these models.

Nana Cabo Bizet, Octavio Obregón, and Wilfredo Yupanqui Carpio

Abstract

In a previous study, it was shown that the generalized uncertainty principle can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as in the literature. This finding reveals an intriguing connection between non-extensive statistics and quantum gravity. In the present work, we extend our previous result and derive a generalized energy-time uncertainty relation based on a measure of non-extensive entropies. Consequently, the dispersion relation undergoes modifications consistent with those obtained in other approaches to quantum gravity. We interpret these modifications as evidence of the non-extensive behavior of spacetime fluctuations at scales close to the Planck scale. While these effects are significant in this regime, they become negligible in the classical one, i.e., at low energies where the spacetime is smooth. As a consequence of the non-extensive behavior exhibited by spacetime at very small scales, the black hole radiation temperature undergoes quantum-level corrections, increasing in the case of and decreasing for the case of. Moreover, the modified uncertainty relation derived here predicts a maximum uncertainty in energy, of the order of Planck energy, and a minimum time interval, of the order of the Planck time, offering new insights into the fundamental structure of spacetime in the quantum regime.

Tonatiuh Tiscareño, Benito Rodríguez, and Javier Chagoya

Abstract

We apply the Kosambi–Cartan–Chern theory to perform an extensive examination of Jacobi stability of geodesics around rotating black hole solutions to dynamical Chern–Simons gravity, a theory that introduces modifications to General Relativity via a scalar field non-minimally coupled to curvature scalars. We present a comparative study between Jacobi and Lyapunov stability, pointing out the advantages of the more geometrical method over the usual Lyapunov approach

Javier Chagoya, I. Díaz-Saldaña, Mario H. Amante, J.C. López-Domínguez, and M. Sabido

Abstract

In this work, we derive a generalized modified Friedmann equation based on an entropy-area relation that incorporates established modifications, such as volumetric, linear, and logarithmic terms, in addition to novel entropic modifications that might yield to relevant cosmological implications at different stages of the evolution of the Universe. Some of these modifications are capable of mimicking the effects of dark energy and describing the current state of accelerated expansion of the Universe. We study particular cases of the generalized Friedmann equation and constrain the free parameters using observational datasets, including Hubble parameter measurements, baryon acoustic oscillations, and strong lensing systems. Our findings indicate that the proposed models align well with current observational data, particularly in low-redshift regimes; furthermore, these models are compatible with the value of 𝐻0 obtained by the SH0ES program.

Emmanuel Chávez Nambo, Alberto Diez-Tejedor, Edgar Preciado-Govea, Armando A. Roque, and Olivier Sarbach

Abstract

In this paper we follow an effective theory approach to study the nonrelativistic limit of a self-gravitating and self-interacting massive vector field. Our effective theory is characterized by three parameters: the field’s mass 𝑚0 and the self-interaction constants 𝜆𝑛 and 𝜆𝑠. For definiteness, we focus on a systematic study of the equilibrium configurations, commonly referred to as Proca stars when they have finite energy. We identify two different types of Proca stars, depending on the specific sector of the effective theory that we are exploring. In the generic sector, defined by 𝜆𝑠 ≠0, all equilibrium configurations are stationary states described by wave functions that evolve harmonically in time. However, in the symmetry-enhanced sector, for which 𝜆𝑠 =0, there exist multifrequency states whose wave functions oscillate with two or three distinct frequencies in addition to the stationary states. We determine the conditions under which a ground state configuration with fixed particle number exists. When these conditions are met, we prove that the lowest energy is reached by a stationary spherically symmetric configuration of constant polarization that is linear or circular depending on the sign of 𝜆𝑠. We numerically construct some illustrative examples of spherical stationary and multifrequency solutions, analyze their properties, and compare them with our analytical predictions. Unlike stationary states and other soliton configurations, which form a discrete set in the solution space associated with fixed particle number, the symmetry-enhanced sector exhibits a continuum of solutions with multifrequency states connecting stationary states of constant polarization.

Emmanuel Chávez Nambo, Alberto Diez-Tejedor, Armando A. Roque, and Olivier Sarbach

Abstract

In this paper, we study the linear stability of self-interacting boson stars in the nonrelativistic limit of the Einstein-Klein-Gordon theory. For this purpose, based on a combination of analytic and numerical methods, we determine the behavior of general linear perturbations around the stationary and spherically symmetric solutions of the Gross-Pitaevskii-Poisson system. In particular, we conclude that ground state configurations are linearly stable if the self-interaction is repulsive, whereas there exists a state of maximum mass that divides the stable and the unstable branches in case the self-interaction is attractive. Regarding the excited states, they are in general unstable under generic perturbations, although we identify a stability band in the first excited states of the repulsive theory. This result is independent of the mass of the scalar field and the details of the self-interaction potential, and it is in contrast to the situation of vanishing self-interaction, in which excited states are always unstable.

Flavio C Sánchez, Armando A Roque, Benito Rodríguez and Javier Chagoya

Abstract

The gravitational deflection of light is a critical test of modified theories of gravity. A few years ago, Gibbons and Werner introduced a definition of the deflection angle based on the Gauss–Bonnet theorem. In more recent years, Arakida proposed a related idea for defining the deflection angle in non-asymptotically flat spacetimes. We revisit this idea and use it to compute the angular difference in the Kottler geometry and a non-asymptotically flat solution in Horndeski gravity. Our analytic and numerical calculations show that a triangular array of laser beams can be designed so that the proposed definition of the deflection angle is sensitive to different sources of curvature. Moreover, we find that near the photon sphere, the deflection angle in the Horndeski solution is similar to its Schwarzschild counterpart, and we confirm that the shadows seen by a static observer are identical.

Javier Chagoya, I. Díaz-Saldaña, J. C. López-Domínguez, and C. Martínez-Robles 

Abstract

We apply Wald’s formalism to a Lagrangian within generalised Proca gravity that admits a Schwarzschild black hole with a non-trivial vector field. The resulting entropy differs from that of the same black hole in General Relativity by a logarithmic correction modulated by the only independent charge of the vector field. We find conditions on this charge to guarantee that the entropy is a non-decreasing function of the black hole area, as is the case in GR. If this requirement is extended to black hole mergers, we find that for Planck scale black holes, a non-decreasing entropy is possible only if the area of the final black hole is several times larger than the initial total area of the merger. Finally, we discuss some implications of the vector Galileon entropy from the point of view of entropic gravity.

J. Chagoya, I. Díaz-Saldaña, J.C. López-Domínguez, and M. Sabido

Abstract

In this paper we study the viability of an entropic cosmological model. The effects of entropic gravity are derived from a modified entropy-area relationship with a volumetric entropy term. This model describes a late time limit cosmic acceleration, whose origin is related to a volumetric term in the entropy. Moreover, we analyze the phenomenological implications of the entropic model using the Supernovae Pantheon compilation and the observational Hubble parameter data to find consistency with cosmological observations. Finally, we show the equivalence between the entropic model and a brane world cosmological model, by means of an effective geometrical construction.

Tomás Verdugo, Mario H. Amante, Juan Magaña, Miguel A. García-Aspeitia, Alberto Hernández-Almada, and Verónica Motta 

Abstract

Brane world models have shown to be promising to understand the late cosmic acceleration, in particular because such acceleration can be naturally derived, mimicking the dark energy behaviour just with a five dimensional geometry. In this paper we present a strong lensing joint analysis using a compilation of early-type galaxies acting as a lenses, united with the power of the well studied strong lensing galaxy cluster Abell 1689. We use the strong lensing constraints to investigate a brane model with variable brane tension as a function of the redshift. In our joint analysis we found a value n=7.8+0.9-0.5, for the exponent related to the brane tension, showing that n deviates from a Cosmological Constant (CC) scenario (n=6). We obtain a value for the deceleration parameter, q(z) today, q(0)=-1.2+0.6-0.8, and a transition redshift, zt=0.60\pm0.06 (when the Universe change from an decelerated phase to an accelerated one). These results are in contrast with previous work that favors CC scenario, nevertheless our lensing analysis is in agreement with a formerly reported conclusion suggesting that the variable brane tension model is able to source a late cosmic acceleration without an extra fluid as in the standard one.

C. Ortiz and F. Ibarra-Castor

Abstract

Redshift is a crucial concept in physics; it has significant implications for our understanding of the dynamics and evolution of the cosmos. In this article, we introduce a generalized formula to determine the redshift parameter. The unified framework, which relates the redshift to the energy of the system, eliminates the need to derive the redshift parameter on a case-by-case basis, uncovering the relationships between different mechanisms. Furthermore, the generalization allows us to extend the redshift to non-considered mechanisms.

C. Ortiz and Raju S. Khatiwada 

Abstract

The least action principle played a central role in the development of modern physics. A major drawback of the principle is that its applicability is limited to holonomic constraints. In the present work, we investigate the energy lost by particles as a result of the gravitational interaction in a homogeneous low-density medium subject to non-holonomic constraints. We perform the calculation for an arbitrary particle and outline the specific result for photons. The energy lost is calculated from first principles based on the principle of virtual work and the d’Alembert principle. Under the formalism mentioned above, the dissipative nature of the effect is established. Furthermore, we show that the results agree with an alternative derivation based on continuum mechanics and the Euler–Cauchy stress principle.

Javier Chagoya, J C López-Domínguez and C Ortiz

Abstract

Rastall gravity is a modified gravity proposal that incorporates a non-conserved energy momentum tensor (EMT). We study the equivalence between Rastall gravity and general relativity, analyzing its consequences for an EMT of dark matter and dark energy. We find that the translation between Rastall and Einstein interpretations modifies the equation of state for each component. For instance, cold dark matter can translate into warm dark matter. If the EMT components are allowed to interact, the translation also changes the type of interaction between the components.

Javier Chagoya, Miguel Sabido and A Silva-García

Abstract

In this paper we present a Yang-Mills type gauge theory of vector-tensor gravity, where the tetrad, the spin connection and vector field are identified with components of the gauge field. This setup leads to a theory that in flat spacetime is contained in Generalized Proca theories, while in curved spacetime is closely related to beyond Generalized Proca. We solve for static and spherically symmetric space-time and show that there are two branches of solutions, one where the metric is asymptotically Schwarzschild even though there is a cosmological constant in the action, and another one where the metric is asymptotically (anti-)de Sitter. Also, we study the effect of the vector field on homogeneous and isotropic spacetimes, finding that it contributes to the accelerated expansion of the spacetime.

Emmanuel Chávez Nambo, Armando A. Roque, and Olivier Sarbach

Abstract

In previous work we analyzed the linear stability of nonrelativistic ℓ-boson stars with respect to radial modes and showed that ground state configurations are stable with respect to these modes, whereas excited states are unstable. In this work we extend the analysis to nonspherical linear mode perturbations. To this purpose, we expand the wave function in terms of tensor spherical harmonics which allows us to decouple the perturbation equations into a family of radial problems. By using a combination of analytic and numerical methods, we show that ground state configurations with ℓ >1 possess exponentially in time growing nonradial modes, whereas only oscillating modes are found for ℓ =0 and ℓ =1. This leads us to conjecture that nonrelativistic ℓ-boson stars in their ground state are stable for ℓ =1 as well as ℓ =0, while ground state and excited configurations with ℓ >1 are unstable.

Armando A. Roque, Emmanuel Chávez Nambo, and Olivier Sarbach

Abstract

We study the linear stability of nonrelativistic ℓ-boson stars, describing static, spherically symmetric configurations of the Schrödinger-Poisson system with multiple wave functions having the same value of the angular momentum ℓ. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the 2⁢ℓ+1 wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each ℓ, the ground state is linearly stable, whereas the 𝑛th excited states possess 2⁢𝑛 unstable (exponentially in time growing) modes. Our results also indicate that all excited states correspond to saddle points of the conserved energy functional of the theory.

Andrés Lizardo, Javier Chagoya, and C. Ortiz

Abstract

The propagation of gravitational waves offers new possibilities for testing the theory of gravity. Amongst these possibilities there is the luminosity distance of gravitational waves, dgw. A few phenomenological parametrizations for this property have been proposed in the literature, but their generality is still under study. In this work, we contribute to this study by confronting these parametrizations to the predictions of quadratic and degenerate higher order gravity. Furthermore, we propose a novel parametrization that unifies some of the existing proposals. We expect our findings to be relevant for future constraints on modified gravity based on the properties of standard sirens.

Rafael Hernández-Jiménez, Claudia Moreno, Mauricio Bellini, and C. Ortiz

Juan Barranco, Javier Chagoya, Alberto Diez-Tejedor, Gustavo Niz and Armando A. Roque

Abstract

We establish the existence of time-dependent solitons in a modified gravity framework, which is defined by the low energy limit of theories with a weakly broken galileon symmetry and a mass term. These are regular vacuum configurations of finite energy characterized by a single continuous parameter representing the amplitude of the scalar degree of freedom at the origin. When the central field amplitude is small the objects are indistinguishable from boson stars. In contrast, increasing the central value of the amplitude triggers the effect of higher derivative operators in the effective theory, leading to departures from the previous solutions, until the theory becomes strongly coupled and model-dependent. The higher order operators are part of the (beyond) Horndeski theory, hence the name of the compact objects. Moreover, a remnant of the galileon non-renormalization theorem guarantees that the existence and properties of these solutions are not affected by quantum corrections. Finally, we discuss the linear stability under small radial perturbations, the mass-radius relation, the compactness, the appearance of innermost stable circular orbits and photon spheres, and some astrophysical signatures (accretion disks, gravitational radiation and lensing) that may be relevant to falsify the model.

Javier Chagoya, Graciela Reyes-Ahumada, and M. Sabido

Abstract

By determining the relation between topological M-theory and the Chern-Simons actions for a gauge field constructed from the Lie algebra of either 𝑆⁢𝐿⁡(2,ℝ)×𝑆⁢𝐿⁡(2,ℝ) or 𝑆⁢𝐿⁡(2,ℂ) ×𝑆⁢𝐿⁡(2,ℂ), depending on the sign of the space-time curvature, we show that the standard and exotic actions of three-dimensional gravity can be recovered from topological M-theory. With this result, we provide a concrete realization of a conjecture by Dijkgraaf et al. stating that the partition function of topological M-theory is equivalent to the partition function of a black hole in a related theory. We do this for the standard and exotic BTZ black holes in three-dimensional gravity.

Javier Chagoya, C Ortiz, Benito Rodríguez and Armando A Roque

Abstract

The gravitational deflection of light in the strong field limit is an important test for alternative theories of gravity. However, solutions for the metric that allow for analytic computations are not always available. We implement a hybrid analytic-numerical approximation to determine the deflection angle in static, spherically symmetric spacetimes. We apply this to a set of numerical black hole solutions within the class of modified gravity theories known as degenerate higher order scalar–tensor theories (DHOST). Comparing our results to a more time consuming full numerical integration, we find that we can accurately describe the deflection angle for light rays passing at arbitrary distances from the photon sphere with a combination of two analytic-numerical approximations. Furthermore, we find a range of parameters where our DHOST black holes predict strong lensing effects whose size is comparable with the uncertainty in the properties of the supermassive black hole in M87 reported by the event horizon telescope, showing that strong lensing is a viable alternative to put constraints on these models of modified gravity.

I. Díaz-Saldaña, M. Sabido, J. C. López-Domínguez, and J. E. Rosales-Quintero

Abstract

In this work, we study the symmetry breaking conditions, given by a (anti)de Sitter-valued vector field, of a full (anti)de Sitter-invariant MacDowell–Mansouri inspired action. We show that under these conditions, the action breaks down to General Relativity with a cosmological constant, the four-dimensional topological invariants, as well as the Holst term. We obtain the equations of motion of this action, and analyze the symmetry breaking conditions.