arXiv subjects

Tibério de Paula Netto

Publications and source records attributed to Tibério de Paula Netto.

At least 19 recordsLinked to original sources

arXiv2026

On the total derivative divergence for a nonminimal vector operator

We report on the calculation of the total derivative $\Box R$ term in the divergence of vacuum effective action for the nonminimal vector field operator in a curved space background. This term led to an interesting discussions in the literature, in particular because it defines the local part of anomaly-induced effective action in conformal quantum gravity and may be decisive for the renormalizability of this theory. The divergent term of our interest was previously derived several times. One of the main results is that the mentioned local term is gauge-fixing dependent in the case of electromagnetic field, that contradicts the general theorems about quantum corrections. We perform the derivation by using Riemann's normal coordinates and confirm the previous results. The discussion includes the possible role of the gauge-dependent IR regulators and the related ambiguity.

hep-th↗

arXiv2025

Effective delta sources and Newtonian limit in nonlocal gravity

We investigate the Newtonian limit of a class of nonlocal gravity models with exponential form factors $f_s (\Box) = \exp [(-\Box/μ_s^2)^{N_s}]$. Our main goal is to identify similarities and differences between models in this family in regard to weak-field solutions. To this end, we use the effective source formalism to compare the related effective delta sources, mass functions, and Newtonian potentials. We obtain a variety of representations for these quantities in terms of series, integrals, and special functions, as well as simple approximations that capture the relevant dependence on the parameters $N_s$ and $μ_s$ - which can be used to explore the weak-field phenomenology of nonlocal gravity. We explain why only for $N_s>1$ the Newtonian potential oscillates and prove that, despite the oscillations, the effective masses are positive. Moreover, we verify that these linearized solutions are regular (without curvature singularities). Finally, we also calculate the form of the leading logarithmic quantum correction to the Newtonian potential in these models. In all our considerations, we assume that $N_s$ is a positive real parameter. The cases of non-integer $N_s$ might be applied beyond nonlocal gravity, in effective approaches to implement quantum corrections in the weak field regime.

gr-qc↗

arXiv2024

On effective models of regular black holes inspired by higher-derivative and nonlocal gravity

In this work we study static spherically symmetric solutions of effective field equations related to local and nonlocal higher-derivative gravity models, based on their associated effective delta sources. This procedure has been applied to generate modifications of the Schwarzschild geometry in several contexts (e.g., modified gravity, string theory, noncommutative geometry, generalized uncertainty principle scenarios), but a general analysis of the possible equations of state and their influence on the solutions was still lacking. Here, we aim to fill this gap in the literature and investigate whether these metrics might be able to reproduce features of the solutions of higher-derivative gravity models. In particular, we present an equation of state such that the solution matches the Newtonian-limit one in both regimes of large and small $r$. A significant part of the work is dedicated to studying the curvature regularity of the solutions and the comparison with the linearized solutions. Explicit metrics are presented for effective sources originating from local and nonlocal models. The results obtained here might be regarded as possible links between the previous research on linearized higher-derivative gravity and the solutions of the nonlinear complete field equations, which remain unknown at the moment.

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arXiv2023

Regular multi-horizon Lee-Wick black holes

In this paper we carry out a detailed analysis of the static spherically symmetric solutions of a sixth-derivative Lee-Wick gravity model in the effective delta source approximation. Previous studies of these solutions have only considered the particular case in which the real and the imaginary part of the Lee-Wick mass $μ=a +i b$ are equal. However, as we show here, the solutions exhibit an interesting structure when the full parameter space is considered, owing to the oscillations of the metric that depend on the ratio $b/a$. Such oscillations can generate a rich structure of horizons, a sequence of mass gaps and the existence of multiple regimes for black hole sizes (horizon position gaps). In what concerns the thermodynamics of these objects, the oscillation of the Hawking temperature determines the presence of multiple mass scales for the remnants of the evaporation process and may permit the existence of cold black holes with zero Hawking temperature $T$ and quasi-stable intermediate configurations with $T \approx 0$ and a long evaporation lifetime. For the sake of generality, we consider two families of solutions, one with a trivial shift function and the other with a non-trivial one (dirty black hole). The latter solution has the advantage of reproducing the modified Newtonian-limit metric of Lee-Wick gravity for small and large values of $r$.

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arXiv2023

Renormalizability of nonlocal quantum gravity coupled to matter

We extensively study the ultraviolet quantum properties of a nonlocal action for gravity nonminimally coupled to matter. The theory unifies matter and gravity in an action principle such that all the classical solutions of Einstein's theory coupled to matter are also solutions of the nonlocal theory. At the quantum level, we show that the theory is power-counting super-renormalizable in even dimensions and finite in odd dimensions. A simple extension of the model compatible with the above properties is finite also in even dimensions.

hep-th↗

arXiv2023

Regular black holes from higher-derivative effective delta sources

Certain approaches to quantum gravity and classical modified gravity theories result in effective field equations in which the original source is substituted by an effective one. In these cases, the occurrence of regular spacetime configurations may be related to the regularity of the effective source, regardless of the specific mechanism behind the regularization. In this chapter, we make an introduction to the effective source formalism applied to higher-derivative gravity. The results presented here, however, can be easily transposed to other frameworks that use similar sources. The generality obtained is also because we consider a general higher-derivative gravity model instead of restricting the analysis to some specific theories. In the first part, we discuss the model in the Newtonian limit, which offers a natural context for introducing effective sources. We show how the regularity properties of the effective sources depend on the behavior of the action's form factor in the ultraviolet regime, which leads to results valid for large families of models (or for families of modified delta sources). Subsequently, we use the general results on the effective sources to construct regular black hole metrics. One of our concerns is the higher-order regularity of the solutions, i.e., the possibility that not only the invariants built with curvature tensors but also the ones with covariant derivatives are regular. In this regard, we present some theorems relating the regularity of sets of curvature-derivative invariants with the regularity properties of the effective sources.

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arXiv2022

Black holes in non-local gravity

In this chapter we present a status report of black hole-like solutions in non-local theories of gravity in which the Lagrangians are at least quadratic in curvature and contain specific non-polynomial (i.e., non-local) operators. In the absence of exact black hole solutions valid in the whole spacetime, most of the literature on this topic focus on approximate and simplified equations of motion, which could provide insights on the full non-linear solutions. Therefore, the largest part of this chapter is devoted to the linear approximation. We present results on stationary metric solutions (including both static and rotating cases) and dynamical spacetimes describing the formation of non-rotating mini black holes by the collapse of null shells. Non-local effects can regularize the curvature singularities in both scenarios and, in the dynamical case, there exists a mass gap below which the formation of an apparent horizon can be avoided. In the final part we discuss interesting attempts towards finding non-linear black hole solutions in non-local gravity. Throughout this chapter, instead of focusing on a particular non-local model, we present results valid for large classes of theories (to a feasible extent). This more general approach allows the comparison of similarities and differences of the various types of non-local gravity models.

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arXiv2022

Stringballs and Planckballs for Dark Matter

As a follow up of the seminal work by Guiot, Borquez, Deur, and Werner on "Graviballs and Dark Matter", we explicitly show that contrary to Einstein's gravity, in string theory, local and nonlocal higher derivative theories, as well as general asymptotically-free or finite theories, gravitationally interacting bound states can form when the energy is larger than the Planck energy. On the other hand, in higher derivative or nonlocal theories with interaction governed by a dimensionless or a dimensionful coupling constant, the bound states form when the energy is smaller than the Planck energy. Such bound states are allowed because of the softness of the scattering amplitudes in the ultraviolet region. Indeed, in such theories, the potential is finite while the force is zero or constant in $r=0$. Finally, since the bound states that form in the early Universe may have an energy that ranges from the Planck mass to any arbitrarily large or small value, we argue that they can serve as dark matter candidates and/or as the seeds for the structure's formation at large scale in the Cosmos.

hep-th↗

arXiv2022

Effective quantum gravity, cosmological constant and the Standard Model of particle physics

The renormalization group in effective quantum gravity can be consistently formulated using the Vilkovisky and DeWitt version of effective action and assuming a non-zero cosmological constant. Taking into account that the vacuum counterpart of the cosmological constant is dramatically different from the observed energy density of vacuum, the running of the last quantity in the late cosmology indicates strong constraints on the physics beyond the minimal Standard Model of particle physics.

hep-th↗

arXiv2022

Universal leading quantum correction to the Newton potential

The derivation of effective quantum gravity corrections to Newton's potential is an important step in the whole effective quantum field theory approach. We hereby add new strong arguments in favor of omitting all the diagrams with internal lines of the massive sources, and we also recalculate the corrections to the Newtonian potential using functional methods in an arbitrary parametrization of the quantum fluctuations of the metric. The general proof of the gauge- and parametrization-independence within this approach is also explicitly given. On top of that, we argue that the universality of the result holds regardless of the details of the ultraviolet completion of quantum gravity theory. Indeed, it turns out that the logarithm quantum correction depends only on the low energy spectrum of the theory that is responsible for the analytic properties of loop's amplitudes.

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arXiv2021

The running vacuum in effective quantum gravity

We briefly review the previous works on the renormalization group in quantum general relativity with the cosmological constant, based on the Vilkovisky and DeWitt version of effective action. On top of that, we discuss the prospects of the applications of this version of renormalization group to the cosmological models with a running Newton constant and vacuum energy density.

gr-qc↗

arXiv2021

Action principle selection of regular black holes

We elaborate on the role of higher-derivative curvature invariants as a quantum selection mechanism of regular spacetimes in the framework of the Lorentzian path integral approach to quantum gravity. We show that for a large class of black hole metrics prominently regular there are higher-derivative curvature invariants which are singular. If such terms are included in the action, according to the finite action principle applied to a higher-derivative gravity model, not only singular spacetimes but also some of the regular ones do not seem to contribute to the path integral.

gr-qc↗

arXiv2021

Higher-order regularity in local and nonlocal quantum gravity

In the present work we investigate the Newtonian limit of higher-derivative gravity theories with more than four derivatives in the action, including the non-analytic logarithmic terms resulting from one-loop quantum corrections. The first part of the paper deals with the occurrence of curvature singularities of the metric in the classical models. It is shown that in the case of local theories, even though the curvature scalars of the metric are regular, invariants involving derivatives of curvatures can still diverge. Indeed, we prove that if the action contains $2n+6$ derivatives of the metric in both the scalar and the spin-2 sectors, then all the curvature-derivative invariants with at most $2n$ covariant derivatives of the curvatures are regular, while there exist scalars with $2n+2$ derivatives that are singular. The regularity of all these invariants can be achieved in some classes of nonlocal gravity theories. In the second part of the paper, we show that the leading logarithmic quantum corrections do not change the regularity of the Newtonian limit. Finally, we also consider the infrared limit of these solutions and verify the universality of the leading quantum correction to the potential in all the theories investigated in the paper.

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arXiv2021

Newtonian potential in higher-derivative quantum gravity

We hereby derive the Newtonian metric potentials for the fourth-derivative gravity including the one-loop logarithm quantum corrections. It is explicitly shown that the behavior of the modified Newtonian potential near the origin is improved respect to the classical one, but this is not enough to remove the curvature singularity in $r=0$. Our result is grounded on a rigorous proof based on numerical and analytic computations.

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arXiv2020

Vilkovisky unique effective action in quantum gravity

The divergent part of the one-loop Vilkovisky unique effective action for quantum Einstein gravity is evaluated in the general parametrization of the quantum field, including the separated conformal factor. The output of this calculation explicitly demonstrates the parametrization and conformal gauge independence of the unique effective action with the configuration space metric chosen following Vilkovisky's prescription.

hep-th↗

arXiv2020

Primordial universe with the running cosmological constant

Theoretically, the running of the cosmological constant in the IR region is not ruled out. On the other hand, from the QFT viewpoint, the energy released due to the variation of the cosmological constant in the late universe cannot go to the matter sector. For this reason, the phenomenological bounds on such a running are not sufficiently restrictive. The situation can be different in the early universe when the gravitational field was sufficiently strong to provide an efficient creation of particles from the vacuum. We develop a framework for systematically exploring this ossibility. It is supposed that the running occurs in the epoch when the Dark Matter already decoupled and is expanding adiabatically, while baryons are approximately massless and can be abundantly created from vacuum due to the decay of vacuum energy. By using the handy model of Reduced Relativistic Gas for describing the Dark Matter, we consider the dynamics of both cosmic background and linear perturbations and evaluate the impact of the vacuum decay on the matter power spectrum and to the first CMB peak. Additionally, using the combined data of CMB+BAO+SNIa we find the best fit values for the free parameters of our model.

gr-qc↗

arXiv2020

On the Vilkovisky-DeWitt approach and renormalization group in effective quantum gravity

The effective action in quantum general relativity is strongly dependent on the gauge-fixing and parametrization of the quantum metric. As a consequence, in the effective approach to quantum gravity, there is no possibility to introduce the renormalization-group framework in a consistent way. On the other hand, the version of effective action proposed by Vilkovisky and DeWitt does not depend on the gauge-fixing and parametrization off-shell, opening the way to explore the running of the cosmological and Newton constants as well as the coefficients of the higher-derivative terms of the total action. We argue that in the effective framework the one-loop beta functions for the zero-, two- and four-derivative terms can be regarded as exact, that means, free from corrections coming from the higher loops. In this perspective, the running describes the renormalization group flow between the present-day Hubble scale in the IR and the Planck scale in the UV.

hep-th↗

arXiv2020

Functional renormalization group approach and gauge dependence in gravity theories

We investigate the gauge symmetry and gauge fixing dependence properties of the effective average action for quantum gravity models of general form. Using the background field formalism and the standard BRST-based arguments, one can establish the special class of regulator functions that preserves the background field symmetry of the effective average action. Unfortunately, regardless the gauge symmetry is preserved at the quantum level, the non-invariance of the regulator action under the global BRST transformations leads to the gauge fixing dependence even under the use of the on-shell conditions.

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