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H. P. de Oliveira

Publications and source records attributed to H. P. de Oliveira.

At least 19 recordsLinked to original sources
arXiv2025

Distorted black holes: nonextensivity in the gravitational wave emission

We investigate the interaction between a non-rotating black hole and incoming gravitational waves using the characteristic formulation of the Einstein field equations, framed as a Bondi problem. By adopting retarded time as the null coordinate and recognizing that the final state is invariably a black hole, we show that an apparent horizon forms once sufficient mass accretes onto the black hole. We derive the evolution of the Bondi mass and compute its final value, enabling us to quantify the fraction of the incident mass absorbed by the black hole. Additionally, we establish a nonextensive relation for the absorbed mass as a function of initial parameters, such as the amplitude of the gravitational wave data.

gr-qc↗
arXiv2025

Distorted black holes: a characteristic view

We investigate the interaction between a non-rotating black hole and incoming gravitational waves using the characteristic formulation of the Einstein field equations, framed as a Bondi problem. By adopting retarded time as the null coordinate and recognizing that the final state is invariably a black hole, we demonstrate that an apparent horizon forms once sufficient mass accretes onto the black hole. We derive the evolution of the Bondi mass and compute its final value, enabling us to quantify the fraction of the incident mass absorbed by the black hole. Additionally, we establish a scaling law for the absorbed mass as a function of initial parameters, such as the amplitude of the gravitational wave data. Furthermore, we explore the dynamics when a reflecting barrier surrounds the black hole. For low-amplitude initial waves, the barrier reflects the waves, leaving the original black hole as the end state. Conversely, high-amplitude waves lead to the formation of an apparent horizon that engulfs the barrier, producing a new, larger black hole.

gr-qc↗
arXiv2024

Similarity in the Arnowitt-Deser-Misner Mass from Brill and Teukolsky Initial Data Sets Beyond the Linear Approximation

The two most common initial data for vacuum axisymmetric spacetimes are the Brill and Teukolsky gravitational waves. The subsequent numerical evolution of these data exhibits distinct properties mainly associated with the critical gravitational collapse. A possible way of understanding these differences is first to look at the linear level, where the Brill waves have a multipolar structure, while the Teukolsky waves have a quadrupolar structure. Despite being structurally distinct at the linear and nonlinear levels, we show that these gravitational wave initial data share an unexpected similarity related to the distribution of ADM mass as a function of the initial wave's amplitude. More specifically, both configurations satisfy a nonextensive relation, commonly seen in systems governed by long range interactions.

gr-qc↗
arXiv2024

Baumgarte-Shapiro-Shibata-Nakamura formalism in cylindrical coordinates: Brill and Teukolsky waves in both linear and nonlinear regimes

In this article we present a numerical code, based on the collocation or pseudospectal method, which integrates the equations of the BSSN formalism in cylindrical coordinates. In order to validate the code, we carried out a series of tests, using three groups of initial data: i) pure gauge evolution; ii) Teukolsky quadrupole solution for low amplitudes and iii) Brill and Teukolsky solutions with higher amplitudes, which accounts for a deviation from the linear regime when compared to the case of low amplitudes. In practically all cases, violations of the Hamiltonian and momentum constraints were analyzed. We also analyze the behavior of the lapse function, which can characterize the collapse of gravitational waves into black holes. Furthermore, all three groups of tests used different computational mesh resolutions and different gauge choices, thus providing a general scan of most of the numerical solutions adopted.

gr-qc↗
arXiv2023

Dynamical perturbations of black-hole punctures: effects of slicing conditions

While numerous numerical relativity simulations adopt a 1+log slicing condition, shock-avoiding slicing conditions form a viable and sometimes advantageous alternative. Despite both conditions satisfying similar equations, recent numerical experiments point to a qualitative difference in the behavior of the lapse in the vicinity of the black-hole puncture: for 1+log slicing, the lapse appears to decay approximately exponentially, while for shock-avoiding slices it performs approximately harmonic oscillation. Motivated by this observation, we consider dynamical coordinate transformations of the Schwarzschild spacetime to describe small perturbations of static trumpet geometries analytically. We find that the character of the resulting equations depends on the (unperturbed) mean curvature at the black-hole puncture: for 1+log slicing it is positive, predicting exponential decay in the lapse, while for shock-avoiding slices it vanishes, leading to harmonic oscillation. In addition to identifying the value of the mean curvature as the origin of these qualitative differences, our analysis provides insight into the dynamical behavior of black-hole punctures for different slicing conditions.

gr-qc↗
arXiv2023

Bona-Massó slices of Reissner-Nordström spacetimes

Motivated by recent numerical relativity simulations of charged black holes and their interactions, we explore the properties of common slicing conditions in Reissner-Nordström spacetimes. Specifically, we consider different choices for the so-called Bona-Massó function, and construct static and spherically symmetric slices of the Reissner-Nordström spacetime satisfying the corresponding slicing conditions. For some of these functions the construction is entirely analytical, while for others we use numerical root-finding to solve quartic equations. Our solutions are parameterized by the charge-to-mass ratio $λ= Q/M$ and approach a unique slice, independent of the Bona-Massó functions considered here, in the extremal limit $λ\to 1$.

gr-qc↗
arXiv2022

Spherical collapse of non-top-hat profiles in the presence of dark energy with arbitrary sound speed

We study the spherical collapse of non-top-hat matter fluctuations in the presence of dark energy with arbitrary sound speed. The model is described by a system of partial differential equations solved using a pseudo-spectral method with collocation points. This method can reproduce the known analytical solutions in the linear regime with an accuracy better than $10^{-6}\%$ and better than $10^{-2}\%$ for the virialization threshold given by the usual spherical collapse model. We show the impact of nonlinear dark energy fluctuations on matter profiles, matter peculiar velocity and gravitational potential. We also show that phantom dark energy models with low sound speed can develop a pathological behaviour around matter halos, namely negative energy density. The dependence of the virialization threshold density for collapse on the dark energy sound speed is also computed, confirming and extending previous results in the limit for homogeneous and clustering dark energy.

astro-ph.CO↗
arXiv2022

Quest for eternal oscillons

Nonlinear field theories produce unstable but long-lived configurations known as oscillons. These structures have been studied with asymmetric and symmetric double-well potentials and extended to other forms of potentials. In the present work, we examine the consequences of considering higher-order field theories, where we have used a generalization of the symmetric double-well potential and a $ϕ^6$ potential. Consequently, we have found $3+1$ spherically symmetric oscillons with significantly large lifetimes without parameter fine-tuning.

gr-qc↗
arXiv2021

The Bondi problem revisited: a spectral domain decomposition code

We present a simple domain decomposition code based on the Galerkin-Collocation method to integrate the field equations of the Bondi problem. The algorithm is stable, exhibits exponential convergence when considering the Bondi formula as an error measure, and is computationally economical. We have incorporated features of both Galerkin and Collocation methods along with the establishment of two non-overlapping subdomains. We have further applied the code to show the decay of the Bondi mass in the nonlinear regime and its power-law late time decay. Another application is the determination of the wave-forms at the future null infinity connected with distinct initial data.

gr-qc↗
arXiv2021

Multidomain Galerkin-Collocation method: spherical collapse of scalar fields II

We follow the strategy initiated in Ref. [1] and proceed with the implementation of the Galerkin-Collocation domain decomposition (GCDD) applied to the dynamics of a spherical self-gravitating scalar field with the field equation in the Cauchy formulation. We have adopted the areal slicing gauge. We have presented a detailed implementation for an arbitrary number of subdomains and adopted the simplest form of the transmission conditions. Further, by an appropriated choice of the basis functions in the inner subdomain, we eliminated exactly the 1/r terms near the origin present in the field equations. The code is validated using two error measures: the conservation of the ADM mass and the Hamiltonian constraint that must be satisfied during the spacetime dynamics. In general, both error measures converge exponentially in all subdomains. As a useful illustration of placing more subdomains near the strong-field region, meaning an efficient concentrating of collocation points near the origin, we exhibited the formation of an apparent horizon even though the numerical integration diverges.

gr-qc↗
arXiv2021

New numerical framework for the generalized Baumgarte-Shapiro-Shibata-Nakamura formulation: The vacuum case for spherical symmetry

Here we report a developed high performance and simplified version of the code denominated RIO, which can be easily extended, for the generalized BSSN formulation. We implement a code which is regular at the center of symmetry, without use a special procedure for regularization, as usual. We get exponential convergence for constraints. The numerical algorithm is based on the Galerkin-Collocation method developed successfully for diverse physical scenarios by the Numerical Relativity Group at UERJ. For the sake of clarity in presentation, we consider here the most simple case to display the most salient features of the procedure. Thus, we focus on the definite tests of the new numerical framework. The timing and performance of the code show that we can reach a better accuracy close to the machine precision, for the Hamiltonian and momentum constraints. RIO will be an open source code; currently is under continuous development to consider more general and realistic problems.

gr-qc↗
arXiv2021

Multidomain Galerkin-Collocation method: characteristic spherical collapse of scalar fields

We initiate a systematic implementation of the spectral domain decomposition technique with the Galerkin-Collocation (GC) method in situations of interest such as the spherical collapse of a scalar field in the characteristic formulation. We discuss the transmission conditions at the interface of contiguous subdomains that are crucial for the domain decomposition technique for hyperbolic problems. We implemented codes with an arbitrary number of subdomains, and after validating them, we applied to the problem of critical collapse. With a modest resolution, we obtain the Choptuik's scaling law and its oscillatory component due to the discrete self-similarity of the critical solution.

gr-qc↗
arXiv2019

Scattering of compactlike structures

We investigate the collision of a new class of topological defects that tends to become compact as a control parameter increases to larger and larger values These new compactlike defects have, in general, more than one internal discrete mode depending on the value of the control parameter and, as usual, there is a critical velocity above which the defects escape after the collision. We noticed that below the critical velocity there are the windows of escape presenting fractal structure. An interesting novelty is the appearance of metastable structures with the formation of compactlike defects, maintaining a fixed distance from each other. Another new feature is the formation of boosted localized distributions of the scalar field which we called moving oscillons. These oscillons carry away almost all scalar field energy producing a complete disruption of the compactlike defects. The pattern of the moving oscillons depends on the control parameter, and becomes more complex as we increase its value. We conjecture that the new effects may be connected with the presence of more than one vibrational mode in the spectrum of the stability potential of the model under investigation.

hep-th↗
arXiv2019

The affine-null formulation of the gravitational equations: spherical case

A new evolution algorithm for the characteristic initial value problem based upon an affine parameter rather than the areal radial coordinate used in the Bondi-Sachs formulation is applied in the spherically symmetric case to the gravitational collapse of a massless scalar field. The advantages over the Bondi-Sachs version are discussed, with particular emphasis on the application to critical collapse. Unexpected quadratures lead to a simple evolution algorithm based upon ordinary differential equations which can be integrated along the null rays. For collapse to a black hole in a Penrose compactified spacetime, these equations are regularized throughout the exterior and interior of the horizon up to the final singularity. They are implemented as a global numerical evolution code based upon the Galerkin method. New results regarding the global properties of critical collapse are presented.

gr-qc↗
arXiv2019

A Galerkin-Collocation domain decomposition method: application to the evolution of cylindrical gravitational waves

We present a Galerkin-Collocation domain decomposition algorithm applied to the evolution of cylindrical unpolarized gravitational waves. We show the effectiveness of the algorithm in reproducing initial data with high localized gradients and in providing highly accurate dynamics. We characterize the gravitational radiation with the standard Newman-Penrose Weyl scalar $Ψ_4$. We generate wave templates for both polarization modes, $\times$ and $+$, outgoing and ingoing, to show how they exchange energy nonlinearly. In particular, considering an initially ingoing $\times$ wave, we were able to trace a possible imprint of the gravitational analog of the Faraday effect in the generated templates.

gr-qc↗
arXiv2019

Aspects of wave turbulence in preheating III: The case of the two-fields models

The present work is the continuation of the investigation of aspects of wave turbulence in preheating we have started in Refs. [1, 2] but considering several classes of inflationary two-fields models. We exhibit the main elements of the wave turbulence phase imprinted in the power spectra of relevant quantities in the time and space domains. As a general feature, the power spectra resemble in their structure to those obtained using the single nonminimally coupled scalar field of the previous work. As a consequence, we obtained an estimate of the temperature corresponding to the thermalized phase from the power spectrum of the total energy density. Another feature allowed by the simulations was the determination of the effective equation of state after taking into account the backreaction of the produced particles.

gr-qc↗
arXiv2019

Aspects of wave turbulence in preheating II: Rebirth of the nonminimal coupled models

We study the nonlinear stage of preheating in a model consisting of a single inflaton field $ϕ$ nonminimally coupled to the spacetime curvature and considering a self-coupling quartic potential V ($ϕ$) = $λϕ^4/4$. As the first motivation, we mention that this nonminimally coupled model agrees with the observational data. The second and the central issue of the present work is to exhibit aspects of wave turbulence associated with the mechanism of energy transfer from the inflaton field to the inhomogeneous fluctuations towards a state of thermalization. The imprints of the turbulence phase are mainly shown in the power spectra in time and wavenumber of relevant quantities such as the variance and the energy density of the inflaton field. We performed the simulations for several values of the nonminimally coupled models and taking into account the backreaction of the inflaton fluctuations in the dynamics of the Universe, and that allowed to determine the effective equation of state.

gr-qc↗
arXiv2018

The collision of two-kinks revisited: the creation of kinks and lump-like defects as metastable states

We present a more detailed numerical investigation of the head-on collision of a two-kink/two-antikink system. We identified the escape of oscillon-like configurations as a pair of kinks of the standard $ϕ^4$ model moving apart from each other. New pieces of evidence support that the lump-like defects can emerge from the two-kinks interaction to form metastable configurations. Moreover, these configurations signalize the windows of escape that have a fractal structure similar to the $n$-bounce sequence when the kinks of $ϕ^4$ interact. As the last piece of the numerical experiment, we show that by perturbing conveniently a lump-like defect it is possible to recover another lump-like configuration as a metastable configuration.

hep-th↗