arXiv subjects

David Brizuela

Publications and source records attributed to David Brizuela.

At least 19 recordsLinked to original sources

arXiv2026

How much chaos can be generated by gravitational collapse before reaching the Planck scale?

According to the Belinski-Khalatnikov-Lifshitz (BKL) conjecture the dynamics of general relativity near singularities is highly chaotic. However, since general relativity breaks down at singularities, it is generally expected that a more fundamental theory, such as quantum gravity, is needed to describe the spacetime dynamics in regions with large spacetime curvature. In the absence of a widely accepted theory of quantum gravity, it remains unclear how exactly quantum effects may modify the classical evolution. Taking a conservative point of view, in this paper we study the classical dynamics of a gravitational collapse, starting from a strong-field (though classical) scenario up to the Planck scale to quantify how much chaos is generated during the time the Einstein equations can be trusted. Specifically, we use the Shannon entropy and Kullback-Leibler divergence, as well as Fourier analysis, to find that, when the Planck scale is reached, the chaotic features of the model remain relatively underdeveloped. This suggests that, at least during the classical regime, chaos is not strong enough to erase all information about the initial state of the universe, or about a previous classical universe in the context of bouncing cosmologies. In addition, we also characterize the final invariant phase-space distribution for the chaotic Bianchi IX dynamics in general relativity, which provides a novel description of its invariant repeller.

gr-qc↗

arXiv2025

Dynamical theory for spherical black holes in modified gravity

We provide a general algorithm to construct a Hamiltonian, such that its dynamical flow covariantly defines any given spherically symmetric and static metric. This Hamiltonian is defined as a linear combination of the standard (general relativistic) radial diffeomorphism constraint plus a Hamiltonian constraint that is appropriately deformed as compared to its corresponding form in general relativity though it does not include higher-derivative terms. Therefore, given a static model of spherical gravity, it is possible to obtain its Hamiltonian, and, thus, its canonical (second-order) equations of motion. A particularly relevant application of this construction is the study of regular black holes, where proposed geometries often lack an underlying dynamical theory. The present method provides such a theory. In particular, for a wide class of deformations of the Schwarzschild geometry, we explicitly obtain their corresponding Hamiltonian. This construction can be further used to covariantly couple matter. In this way, one can analyze the backreaction of matter fields on the geometry of interest, and, specifically, whether a particular black-hole model may emerge as the end state of a dynamical collapse.

gr-qc↗

arXiv2025

Gravitational wave propagation in bigravity in the late universe

We carry out a detailed analytical investigation of the propagation of gravitational waves in ghost-free bimetric gravity in a late-time de Sitter epoch. In this regime, the dynamical equations for the massless and massive graviton modes can be decoupled and solved exactly. We provide uniform approximations for the modes in terms of elementary functions, which are valid on all scales and for all viable mass windows. We identify different dynamical regimes for the system, depending on the propagation properties of the massive graviton, and whether the massless and massive components of the signal can be temporally resolved or not. In each regime, we compute the gravitational-wave luminosity distance as a function of redshift and study the propagation of wave packets. This allows for the derivation of a new observational bound for the ghost-free bimetric theory using the event GW170817. Further, by an explicit computation, we show that the massless and massive components of the signal retain their coherence also in the regime where they can be temporally resolved, even when couplings to incoherent matter degrees of freedom are included.

gr-qc↗

arXiv2025

Radiative properties of a nonsingular black hole: Hawking radiation and gray-body factor

We study the radiative properties of a spherical and singularity-free black-hole geometry recently proposed in the literature. Contrary to the Schwarzschild spacetime, this geometry is geodesically complete and regular, and, instead of the singularity, it presents a minimal surface that connects a trapped (black-hole) with an antitrapped (white-hole) region. The geometry is characterized by two parameters: the Schwarzschild radius and another parameter that measures the area of the minimal surface. This parameter is related to certain corrections expected in the context of loop quantum gravity to the classical general-relativistic dynamics. We explicitly compute the spectrum of the Hawking radiation and the gray-body factor. Since the gravitational potential is shallower than in Schwarzschild, the emission spectrum turns out to be colder and purer (less gray). From this, we sketch the evaporation history of this geometry and conclude that, under certain assumptions, instead of completely evaporating, the black hole naturally leads to a remnant, which provides a possible resolution to the information-loss issue.

gr-qc↗

arXiv2025

Dipolar perturbations of nonbidiagonal black holes in bigravity

In bimetric gravity, nonbidiagonal solutions describing a static, spherically symmetric, and asymptotically flat black hole are given by a pair of Schwarzschild geometries, one in each metric sector. The two geometries are linked by a nontrivial diffeomorphism, which can be fully determined analytically if the two geometries possess the same isometries. This exact solution depends on four free parameters: the mass parameters of the two black holes, the ratio between the areal radii of the two metrics, and the proportionality constant between their (appropriately normalized) time-translation invariance Killing vector fields. We study the dynamics of axial dipolar perturbations on such a background and obtain general analytical solutions for their evolution. We show that, in general, the characteristic curves followed by dipolar gravitational waves are spacelike with respect to both metrics, and thus the propagation is superluminal. In fact, the velocity of a pulse, as measured by a static observer, turns out to increase with the distance to the black hole. The only exception to this general behavior corresponds to the special case where the two proportionality constants linking the areal radii and the Killing vectors coincide, for which waves travel at the speed of light. Therefore, we conclude that this is the only physically reasonable background, and thus our results restrict the class of viable black-hole solutions in bimetric gravity.

gr-qc↗

arXiv2024

Asymptotics of Bianchi IX under the presence of matter: approximate Kasner map

The goal of this paper is to analyze the effects of the matter fields in the evolution of the Bianchi IX cosmology close to the singularity. Although the dynamics of this model is very involved, asymptotically, as the singularity is approached, it can be well approximated as a succession of Bianchi I periods connected by quick bounces against potential walls. Moreover, in such limit, matter fields (excluding stiff matter) are known to be subdominant with respect to the anisotropies. Therefore, by performing an expansion around small volumes, and assuming that the dominant matter contribution in this regime can be described as a barotropic perfect fluid with a linear equation of state, we obtain an approximate analytic solution of the dynamics. Then, we explicitly compute the form of the transition (Kasner) map that relates the pre- and post-bounce Bianchi I periods including the leading matter effects. As an important conclusion, we observe that generically the presence of matter leads to a post-bounce velocity with a lower deflection angle than in the vacuum case, and thus effectively increases the convex curvature of the potential walls. This effect may have important consequences in the chaotic nature of general relativity near spacelike singularities.

gr-qc↗

arXiv2024

Analytic solutions for the Bianchi I universe coupled to several barotropic perfect fluids

We consider the Bianchi I geometry coupled to several species of comoving barotropic perfect fluids with a linear equation of state in the context of general relativity. The solution of the dynamics can be reduced to a quadrature, which can be explicitly performed in certain cases. In particular, we obtain the explicit solution for one species, as well as for two species, given their barotropic indices obey a certain relation. These solutions include and generalize different models studied in the literature. For completeness, we analyze all the different possible signs of the matter energy densities, and we obtain a particularly interesting model in which an exotic species produces a bounce of the scale factor, providing a singularity-free cosmology, and then decays to leave a nonexotic component as the dominant fluid for large volumes.

gr-qc↗

arXiv2024

Perturbations of bimetric gravity on most general spherically symmetric spacetimes

We present a formalism to study linear perturbations of bimetric gravity on any spherically symmetric background, including dynamical spacetimes. The setup is based on the Gerlach-Sengupta formalism for general relativity. Each of the two background metrics is written as a warped product between a two-dimensional Lorentzian metric and the round metric of the two-sphere. The different perturbations are then decomposed in terms of tensor spherical harmonics, which makes the two polarity (axial and polar) sectors decouple. In addition, a covariant notation on the Lorentzian manifold is used so that all expressions are valid for any coordinates. In this theory, there are seven physical propagating degrees of freedom, which, as compared to the two degrees of freedom of general relativity, makes the dynamics much more intricate. In particular, we discuss the amount of gauge and physical degrees of freedom for different polarities and multipoles. Finally, as an interesting application, we analyze static nonbidiagonal backgrounds and derive the corresponding perturbative equations.

gr-qc↗

arXiv2023

Nonsingular collapse of a spherical dust cloud

We provide a covariant framework to study singularity-free Lema\^itre-Tolman-Bondi spacetimes with effective corrections motivated by loop quantum gravity. We show that, as in general relativity, physically reasonable energy distributions lead to a contraction of the dust shells. However, quantum-gravity effects eventually stop the collapse, the dust smoothly bounces back, and no gravitational singularity is generated. This model is constructed by deforming the Hamiltonian constraint of general relativity with the condition that the hypersurface deformation algebra is closed. In addition, under the gauge transformations generated by the deformed constraints, the structure function of the algebra changes adequately, so that it can be interpreted as the inverse spatial metric. Therefore, the model is completely covariant in the sense that gauge transformations in phase space simply correspond to coordinate changes in spacetime. However, in the construction of the metric, we point out a specific freedom of considering a conformal factor, which we use to obtain a family of singularity-free spacetimes associated to the modified model.

gr-qc↗

arXiv2023

Hybrid classical-quantum systems in terms of moments

We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution function and the quantum density matrix, is described in terms of its corresponding moments. We then define a hybrid Poisson bracket, such that the dynamics of the moments is ruled by an effective Hamiltonian. In particular, a closed formula for the Poisson brackets between any two moments for an arbitrary number of degrees of freedom is presented, which corrects previous expressions derived in the literature for the purely quantum case. This formula is of special relevance for practical applications of the formalism. Finally, we study the dynamics of a particular hybrid system given by two coupled oscillators, one being quantum and the other classical. Due to the coupling, specific quantum and classical properties are transferred between different sectors. In particular, the quantum sector is allowed to violate the uncertainty relation, though we explicitly show that there exists a minimum positive bound of the total uncertainty of the hybrid system.

quant-ph↗

arXiv2023

Spacetime geometry from canonical spherical gravity

We study covariant models for vacuum spherical gravity within a canonical setting. Starting from a general ansatz, we derive the most general family of Hamiltonian constraints that are quadratic in first-order and linear in second-order spatial derivatives of the triad variables, and obey certain specific covariance conditions. These conditions ensure that the dynamics generated by such family univocally defines a spacetime geometry, independently of gauge or coordinates choices. This analysis generalizes the Hamiltonian constraint of general relativity, though keeping intact the covariance of the theory, and leads to a rich variety of new geometries. We find that the resulting geometries depend on seven free functions of one scalar variable, and we study their generic features. By construction, there are no propagating degrees of freedom in the theory. However, we also show that it is possible to add matter to the system by simply following the usual minimal-coupling prescription, which leads to novel models to describe dynamical scenarios.

gr-qc↗

arXiv2023

Gravitational wave oscillations in bimetric cosmology

Unlike general relativity, in bimetric gravity linear gravitational waves do not evolve as free fields. In this theory there are two types of tensor perturbations, whose interactions are inherited from non-trivial couplings between two dynamical metric tensor fields in the Hassan-Rosen action, and are responsible for the phenomenon of bigravity oscillations. In this work, we analyze the dynamics of cosmological tensor modes in bimetric gravity on sub-horizon scales and close to the general relativity limit. In this limit, the system has a characteristic length scale $L$ that is strictly contained within the comoving Hubble radius. Thus, depending on the magnitude of the comoving wavelength $\lambda$ relative to $L$, we identify two regimes of interest where the system can be studied analytically: (i) deep sub-horizon modes with $\lambda\ll L$, whose dynamics can be studied using multiple scale analysis and are characterized by small and slowly evolving super-imposed perturbations; (ii) sub-horizon modes with $\lambda\gg L$, where the dynamics is characterized by fast super-imposed oscillations that can be studied using asymptotic techniques for highly oscillatory problems. Furthermore, our analysis represents a substantial improvement compared to previous analyses based on a generalization of the WKB method, which, as we show, is ill-suited to study the system at hand.

gr-qc↗

arXiv2023

Reduction of primordial chaos by generic quantum effects

According to general relativity, the generic early-universe dynamics is chaotic. Various quantum-gravity effects have been suggested that may change this behavior in different ways. Here, it is shown how key mathematical properties of the classical dynamics can be extended to evolving quantum states using quasiclassical methods, making it possible to apply the established dynamical-systems approach to chaos even to quantum evolution. As a result, it is found that quantum fluctuations contribute to the reduction of the primordial chaos in early-universe models.

gr-qc↗

arXiv2023

The chaotic behavior of the Bianchi IX model under the influence of quantum effects

A quantum analysis of the vacuum Bianchi IX model is performed, focusing in particular on the chaotic nature of the system. The framework constructed here is general enough for the results to apply in the context of any theory of quantum gravity, since it includes only minimal approximations that make it possible to encode the information of all quantum degrees of freedom in the fluctuations of the usual anisotropy parameters. These fluctuations are described as canonical variables that extend the classical phase space. In this way, standard methods for dynamical systems can be applied to study the chaos of the model. Two specific methods are applied that are suitable for time-reparameterization invariant systems. First, a generalized version of the Misner-Chitre variables is constructed, which provides an isomorphism between the quantum Bianchi IX dynamics and the geodesic flow on a suitable Riemannian manifold, extending, in this way, the usual billiard picture. Secondly, the fractal dimension of the boundary between points with different outcomes in the space of initial data is numerically analyzed. While the quantum system remains chaotic, the main conclusion is that its strength is considerably diminished by quantum effects as compared to its classical counterpart.

gr-qc↗

arXiv2023

Generalized boundary conditions in closed cosmologies

Considering a generalization of the Gibbons-Hawking-York covariant boundary action that depends on both the extrinsic and the intrinsic geometry of the boundary, we derive boundary conditions for the cosmological background and tensor perturbations in a closed universe with space-like boundaries. We also give a general method to reconstruct the covariant boundary action starting from a given set of boundary conditions for the cosmological background. These results may be of special relevance in the context of the path-integral formulation of quantum cosmology, where boundary terms contain essential physical information of the system.

gr-qc↗

arXiv2023

Singularity resolution by holonomy corrections: Spherical charged black holes in cosmological backgrounds

We study spherical charged black holes in the presence of a cosmological constant with corrections motivated by the theory of loop quantum gravity. The effective theory is constructed at the Hamiltonian level by introducing certain correction terms under the condition that the modified constraints form a closed algebra. The corresponding metric tensor is then carefully constructed ensuring that the covariance of the theory is respected, that is, in such a way that different gauge choices on phase space simply correspond to different charts of the same spacetime solution. The resulting geometry is characterized by four parameters: the three usual ones that appear in the general relativistic limit (describing the mass, the charge, and the cosmological constant), as well as a polymerization parameter, which encodes the quantum-gravity corrections. Contrary to general relativity, where this family of solutions is generically singular, in this effective model the presence of the singularity depends on the values of the parameters. The specific ranges of values that define the family of singularity-free spacetimes are explicitly found, and their global structure is analyzed. In particular, the mass and the cosmological constant need to be nonnegative to provide a nonsingular geometry, while there can only be a bounded, relatively small, amount of charge. These conditions are suited for any known spherical astrophysical black hole in the de Sitter cosmological background, and thus this model provides a globally regular description for them.

gr-qc↗

arXiv2022

Relativistic effects on the Schr\"odinger-Newton equation

The Schr\"odinger-Newton model describes self-gravitating quantum particles, and it is often cited to explain the gravitational collapse of the wave function and the localization of macroscopic objects. However, this model is completely nonrelativistic. Thus, in order to study whether the relativistic effects may spoil the properties of this system, we derive a modification of the Schr\"odinger-Newton equation by considering certain relativistic corrections up to the first post-Newtonian order. The construction of the model begins by considering the Hamiltonian of a relativistic particle propagating on a curved background. For simplicity, the background metric is assumed to be spherically symmetric and it is then expanded up to the first post-Newtonian order. After performing the canonical quantization of the system, and following the usual interpretation, the square of the module of the wave function defines a mass distribution, which in turn is the source of the Poisson equation for the gravitational potential. As in the nonrelativistic case, this construction couples the Poisson and the Schr\"odinger equations and leads to a complicated nonlinear system. Hence, the dynamics of an initial Gaussian wave packet is then numerically analyzed. We observe that the natural dispersion of the wave function is slower than in the nonrelativistic case. Furthermore, for those cases that reach a final localized stationary state, the peak of the wave function happens to be located at a smaller radius. Therefore, the relativistic corrections effectively contribute to increase the self-gravitation of the particle and strengthen the validity of this model as an explanation for the gravitational localization of the wave function.

gr-qc↗

arXiv2022

Semiclassical study of the Mixmaster model: the quantum Kasner map

According to the Belinski-Khalatnikov-Lifshitz conjecture, close to a spacelike singularity different spatial points decouple, and the dynamics can be described in terms of the Mixmaster (vacuum Bianchi IX) model. In order to understand the role played by quantum-gravity effects in this context, in the present work we consider the semiclassical behavior of this model. Classically, this system undergoes a series of transitions between Kasner epochs, which are described by a specific transition law. This law is derived based on the conservation of certain physical quantities and the rotational symmetry of the system. In a quantum scenario, however, fluctuations and higher-order moments modify these quantities, and consequently also the transition rule. In particular, we perform a canonical quantization of the model and then analytically obtain the modifications of this transition law for semiclassical states peaked around classical trajectories. The transition rules for the quantum moments are also obtained, and a number of interesting properties are derived concerning the coupling between the different degrees of freedom. More importantly, we show that, due to the presence of quantum-gravity effects and contrary to the classical model, there appear certain finite ranges of the Kasner parameters for which the system will not undergo further transitions and will follow a Kasner regime until the singularity. Even if a more detailed analysis is still needed, this feature points toward a possible resolution of the classical chaotic behavior of the model. Finally, a numerical integration of the equations of motion is also performed in order to verify the obtained analytical results.

gr-qc↗