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Marcelo Salgado

Publications and source records attributed to Marcelo Salgado.

At least 19 recordsLinked to original sources
arXiv2026

Black-Hole mimickers in GR and $f(R)$ gravity

Black hole mimickers (BHMs) are horizonless globally regular ultracompact relativistic self-gravitating objects (UCOs) of mass $M$ and radius $R$ with compactness $C = M/R$ higher than that of a neutron star and that produce an effective potential for null geodesics (photons) that possesses a local maximum, which is usually accompanied by an inner local minimum. The presence of a local maximum allows for unstable circular orbits to exist similar to light rings present in actual BH solutions, while it has been conjectured that the presence of a local minimum is symptomatic of potential instabilities. One such candidate for a BHM is a solitonic boson star (SBS) which is a boson star endowed with a sextic potential. In this paper we investigate further solutions of static and spherically symmetric SBSs in general relativity with a larger set of parameter values, and argue that such solutions are very similar to UCOs composed of an incompressible perfect fluid (IPF) with a sufficiently large pressure (the mimicker of a BHM). These IPFUCOs reach the Buchdahl limit $C= 4/9$ for arbitrarily large pressures. We investigate the extent to which the IPFUCOs constructed within a quadratic model in $f(R)$ gravity can overcome this limit or not, and thus pave the way for possibly building SBSs (or other kind of UCO) within this (or other alternative theory of gravity). We further elaborate about the stability properties of SBSs which have been the subject of some controversy recently.

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arXiv2025

Nonlinear Stability of Rotating Hairy Black Holes

Rotating hairy black holes (RHBHs) are axisymmetric equilibrium solutions of the Einstein--Klein--Gordon equations, consisting of a spinning black hole surrounded by a toroidal distribution of complex scalar field. Despite their potential astrophysical relevance, the stability of these configurations -- naturally expected to form through superradiant growth of light bosonic fields -- remains uncertain. In this work, we investigate the stability of RHBHs by performing fully non-linear numerical evolutions of several configurations that differ in the relative mass contribution of the scalar-field torus. We find that configurations in which the scalar field mass is subdominant compared to the black hole mass remain stable throughout the evolution, at least on timescales of order $\mu t > 1600$, where $\mu$ is the scalar field mass. These configurations might therefore be stable, with possible superradiant instabilities developing only on much longer timescales $\mu t \sim 10^{11}$, according to previous linear stability analyses. In contrast, when the scalar-field mass dominates, the system develops an instability on a much shorter timescale around $\mu t \sim \mathcal{O}(100)$, similar to the non-axisymmetric instability observed in rotating boson stars. Given the expected upper limits on scalar-field mass growth achievable through superradiance, our results suggest that rotating hairy black holes formed predominantly via this mechanism are likely to remain stable, at least up to the onset of the superradiant instability.

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arXiv2025

Solar system tests and neutron stars in $f(R)$ gravity revisited

By implementing a full non-linear treatment of $f(R)$ gravity in static and spherically symmetric spacetimes, we analyze two scenarios. The first one within the context of the solar-system tests where we try to recover the chameleon effects without any approximations in the equations (e.g. linearization) from $f(R)$ models that are compatible with cosmology. The second scenario deals with a quadratic $f(R)$ model that is tested in neutron stars. This scenario, which is associated with strong gravity, is completely independent from the first one, but exploits the fact that the equations and formalism are basically the same in both applications. The difference between the two goals lies mainly in the values of the constants involved in the specific $f(R)$ models and the equation of state (EOS) of the central object (Sun or neutron star), but the numerical techniques and the general form of the field equations remain valid in both situations. For the neutron star problem we employ for the first time and in the context of $f(R)$ gravity a multiple algebraic polytropic EOS that mimics accurately realistic EOS in several density ranges. By doing so we avoid the numerical interpolation needed when a realistic EOS is given in tabulated form. Furthermore, we compare our results with the latest data, which includes the most massive neutron star known to date of about $2.35 M_\odot$ from PSRJ0952-0607.

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arXiv2024

Slowly Rotating Boson Stars

We present solutions to the Einstein-Klein Gordon system representing boson stars in the slow rotation approximation. By considering slow rotation we are able to reduce the number of equations yielding a system of ordinary differential equations that is conveniently solved numerically without the need of expensive computational resources. We find sequences of solutions and describe some of their physical properties such as, total mass, angular momentum and compactness. We also consider the dynamics of particles (geodesics) in the resulting spacetime. A detailed comparison with fully rotating boson stars (non-linear treatment) is performed by showing the region of validity of the slow-rotation approximation.

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arXiv2024

Dynamical transition to spontaneous scalarization in neutron stars: The massive scalar field scenario

We analyze numerically the dynamical transition to spontaneous scalarization in neutron stars in the framework of a scalar-tensor theory of gravity where the scalar field is free but massive, and it is coupled nonminimally to gravity in the Jordan frame. We show that the quasistatic configuration of the star that settles after the transition can avoid the observational constraints imposed on the amount of scalarization by several observations in binary systems due to the presence of the mass term, which suppresses the range of the scalar field. We also study the impact of the scalar field mass on the total mass of the star relative to the massless scenario.

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arXiv2023

Regular scalar clouds around a Kerr-Newman black hole: subextremal and extremal scenarios

In this work we analyze the existence of electrically charged scalar clouds which are bound states of a complex-valued massive scalar field in the background of subextremal and extremal Kerr-Newman black holes (BH). In particular, we reanalyze neutral (uncharged) clouds in extremal Kerr BH's. For the extremal scenarios we have implemented a novel technique which allows us to obtain regular clouds at the BH horizon ${\cal H}^+$ which turn out to be connected ``continuously'' with the cloud solutions in the subextremal case even if some derivatives of the scalar field are unbounded at the horizon. In particular, for subextremal BH's we have established regularity conditions at ${\cal H}^+$, by demanding that the field and its radial derivatives are bounded there, but in the extremal scenarios we relax this last condition while demanding that some scalar invariants are well behaved at ${\cal H}^+$. Furthermore we have implemented an integral technique to understand and justify in a simple and heuristic way the existence of such cloud configurations in those BH backgrounds.

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arXiv2023

High precision numerical sequences of rotating hairy black holes

We analyze numerically the existence of regular stationary rotating hairy black holes within the framework of general relativity, which are the result of solving the Einstein-Klein-Gordon system for a complex-valued scalar field under suitable boundary (regularity and asymptotically flat) conditions. To that aim we solve the corresponding system of elliptic partial differential equations using spectral methods which are specially suited for such a numerical task. In order to obtain such system of equations we employ a parametrization for the metric that corresponds to quasi-isotropic coordinates (QIC) that have been used in the past for analyzing different kinds of stationary rotating relativistic systems. Our findings are in agreement with those reported originally by Herdeiro \& Radu ite{Herdeiro2014,Herdeiro2015}. The method is submitted to several analytic and numerical tests, which include the recovery of the Kerr solution in QIC and the cloud solutions in the Kerr background. We report different global quantities that allow us to determine the contribution of the boson hair to the spacetime, as well as relevant quantities at the horizon, like the surface gravity. The latter indicates to what extent the hairy solutions approach the extremal limit, noting that for this kind of solutions the ratio of the angular momentum per squared mass $J_\infty/M^2_{\rm ADM}$ can be larger than unity due to the contribution of the scalar hair, a situation which differs from the Kerr metric where this parameter is bounded according to $0\leq |J/M^2| \leq 1$ with the upper bound corresponding to the extremal case.

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arXiv2021

Regular scalar charged clouds around a Reissner-Nordstrom black hole and no-hair theorems

In this work we reanalyze the possibility of finding bound states (scalar clouds) of a test, charged and complex-valued scalar field with mass and charge q in the background of a Reissner-Nordstrom black hole (RNBH). In order to determine the existence of such scalar clouds we impose suitable regularity conditions for the scalar field at the event horizon. We find numerical evidence for the absence of such clouds in the subextremal and extremal RNBH when the field is massive but not self-interacting. More importantly, we put forward a theorem that proves that such clouds cannot exist. On the other hand, when a suitable self-interacting potential is included, the theorem no longer applies, providing a heuristic justification behind the existence of charged clouds (Q-clouds) that were reported recently.

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arXiv2020

On the formation of "supermassive" neutron stars and dynamical transition to spontaneous scalarization

It is well known that neutron stars can undergo a phase transition under a certain class of Scalar Tensor Theories of gravity (STT's) where a new order parameter, the {\it scalar charge}, appears within the star. This is the well known phenomenon of spontaneous scalarization (SC) discovered by Damour and Esposito-Far\`ese in 1993. Under such mechanism neutron stars can afford in principle a maximum mass larger than in general relativity (GR) for a given equation of state without taking into account additional observational constraints (e.g. binary systems). This opens the possibility that neutron stars might be formed with masses as large as $\sim 2 M_\odot$ without the need of stiff, or more exotic, equations of state for the nuclear matter. Thus, STT's through SC may account for compact objects with large masses observed recently in the sky in the form of pulsars (PSR J0348+0432 with $M= 2.01 M_\pm 0.04\odot$ observed in 2013, PSR J1614-2230 with $M= 1.97\pm 0.04 M_\odot$ observed in 2010 or J0740+6620 $M= 2.14^{+0.10}_{-0.09} M_\odot$ observed in 2019). However, we argue that even if that was possible such maximum mass models within STT cannot be formed solely from the dynamic transition of an initial "isolated" unscalarized neutron star whose mass cannot exceed the maximum mass in GR. This is because SC, being an energetic-preferred configuration, produces a final static star with a mass lower that the initial one with a fixed baryon mass. The mass difference between the initial and final configurations is radiated away in the form of a scalar-field. Thus, maximum mass models of scalarized neutron stars, if present in nature, must have formed by a different process, perhaps of cosmological origin or by the subsequent accretion of additional scalar charge and mass.

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arXiv2020

Solar System tests and chameleon effect in f (R) gravity

Using a novel and self-consistent approach that avoids the scalar-tensor identification in the Einstein frame, we reanalyze the viability of f(R) gravity within the context of solar-system tests. In order to do so, we depart from a simple but fully relativistic system of differential equations that describe a compact object in a static and spherically symmetric spacetime, and then we make suitable linearizations that apply to nonrelativistic objects such as the Sun. We then show clearly under which conditions the emerging chameleonlike mechanism can lead to a post-Newtonian parameter {\gamma} compatible with the observational bounds. To illustrate this method, we use several specific f(R) models proposed to explain the current acceleration of the Universe, and we show which of them are able to satisfy those bounds.

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arXiv2019

On the (non) existence of superregular boson clouds around extremal Kerr black holes and its connection with number theory

We argue about the (non) existence of {\it superregular} scalar clouds (i.e., bound states of a massive and complex-valued scalar field $\Psi$) around exact {\it extremal} ($a = M$) Kerr black holes (BH's) possessing {\it bounded radial derivatives at the horizon} (in Boyer-Lindquist coordinates) as opposed to similar cloud solutions that exist but with unbounded derivatives in the same coordinate system. The latter solutions have been reported recently both analytically and numerically. The superregular clouds cannot be obtained from the regular clouds around subextremal Kerr BH's ($|a|< M$) in the limit of extremality $(a\rightarrow M)$ as in this limit the radial derivatives of $\Psi$ at the horizon $r_H$ diverge when $r_H\rightarrow r_H^{\rm ext}:=M=a$, thus, such superregular clouds must be analyzed separately. We conclude that the superregular clouds, which are found in the {\it exact} extremal scenario ($a = M$), are not continuously connected with the regular ones in the limit of extremality $(a\rightarrow M)$. Remarkably, the spectrum leading to the existence of the radial part of the full solution of these superregular clouds (which obeys a Teukolsky equation) is given by the exact formula $M=a=\frac{1}{2\mu}\sqrt{m^2 + \left[-\kappa+\sqrt{\kappa^2+m^2}\,\right]^2}$, which depends on three (positive) integers: the principal number $n$, the {\it magnetic number} $m$, and an integer $j$, related with the {\it type} of regularity at the horizon. Here $\kappa= j +n$, and $\mu$ is the mass associated with $\Psi$. This spectrum depends implicitly on the {\it orbital} number $l$, an integer number that determines the existence of well behaved spheroidal harmonics which are associated with the angular part of the cloud solution. Since the separation constants that are obtained from the superregularity conditions in the radial part of the solution do {\it not} coincide in general with the standard separation constants required for the spheroidal harmonics to be well behaved on the axis of symmetry, we conclude that non-trivial boson clouds having such superregularity conditions cannot exist in the background of an exact extremal Kerr BH. The only exception to this conclusion is in the limit $n\rightarrow \infty$ and $m\ll n$. In such a large $n$ limit consistency in the separation constants leads to a quadratic Diophantine equation of Pell's type for the integer numbers $(l,m)$. Such Pell's equation can be readily solved using standard techniques. In that instance well behaved spheroidal harmonics are obtained, and thus, well behaved non-trivial superregular clouds can be computed. Of course, this situation, does not preclude the existence of other kind of smooth cloud solutions for any other $n$, not necessarily large (e.g. clouds with a non-integer $\kappa$) when using a better behaved coordinate system at the horizon (e.g. Wheeler's tortoise coordinate or proper radial distance).

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arXiv2019

Thick shell regime in the chameleon two-body problem

In a previous paper [Phys. Rev. D 97, 104044 (2018)] we pointed out some shortcomings of the standard approach to chameleon theories consisting in treating the small bodies used to test the weak equivalence principle (WEP) as test particles, whose presence do not modify the chameleon field configuration. In that paper we developed an alternative method to determine the relevant field configuration which takes into account the influence of both test and source bodies, and computed the chamaleon mediated force. Relying on that analysis we showed that the effective acceleration of test bodies is composition dependent even when the model is based on universal couplings. In this paper, we improve our method by using a more suitable approximation for the effective chameleon potential in situations where the bodies are in the so-called "thick shell regime". We then find new and more restrictive bounds on the model' s parametres by confronting the new theoretical predictions with the empirical bounds on E\"otv\"os parameter comming from the lunar laser ranging experiments.

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arXiv2018

Obstructions towards a generalization of no-hair theorems: I. Scalar clouds around Kerr black holes

We show that the integral method used to prove the no-hair theorem for Black Holes (BH's) in spherically symmetric and static spacetimes within the framework of general relativity with matter composed by a complex-valued scalar-field does not lead to a straightforward conclusion about the absence of hair in the stationary and rotating (axisymmetric) scenario. We argue that such a failure can be used to justify in a simple and heuristic way the existence of non-trivial boson clouds or hair found numerically by Herdeiro and Radu [1,2] and analytically by Hod in the test field limit [3-5]. This is due to the presence of a contribution that is negative when rotation exists which allows for an integral to vanish even when a non-trivial boson hair is present. The presence of such a negative contribution that depends on the rotation properties of the BH is perfectly correlated with the eigenvalue problem associated with the boson-field equation. Conversely, when the rotation is absent the integral turns to be composed only by non negative (i.e. positive semidefinite) terms and thus the only way it can vanish is when the hair is completely absent. This analysis poses serious challenges and obstructions towards the elaboration of no-hair theorems for more general spacetimes endowed with a BH region even when including matter fields that obey the energy conditions. Thus rotating boson stars, if collapsed, may lead indeed to a new type of rotating BH, like the ones found in [1,2]. In order to achieve this analysis we solve numerically the eigenvalue problem for the boson field in the Kerr-BH background by imposing rigorous regularity conditions at the BH horizon for the non-extremal case ($0<a<M$) which include the near extremal one in the limit $M\rightarrow a$, as well as the small BH limit $M\rightarrow a\rightarrow 0$.

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arXiv2017

Cosmic acceleration in asymptotically Ricci flat Universe

We analyze the evolution of a Friedmann-Robertson-Walker spacetime within the framework of $f(R)$ metric gravity using an exponential model. We show that $f(R)$ gravity may lead to a vanishing effective cosmological constant in the far future (i.e. $R\rightarrow 0$) and yet produce a transient accelerated expansion at present time with a potentially viable cosmological history. This is in contrast with several $f(R)$ models which, while viable, produce in general a non-vanishing effective cosmological constant asymptotically in time ($R\rightarrow 4\Lambda_{\rm eff}$). We also show that relativistic {stars in asymptotically flat spacetimes can be supported within this framework without encountering any singularity, notably in the Ricci scalar $R$.

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arXiv2016

Equivalence Principle in Chameleon Models: first approach

Most theories that predict time and/or space variation of fundamental constants also predict violations of the Weak Equivalence Principle (WEP). Khoury and Weltmann proposed the chameleon model in 2004 and claimed that this model avoids experimental bounds on WEP. We present a contrasting view based on an approximate calculation of the two body problem for the chameleon field and show that the force depends on the test body composition. Furthermore, we compare the prediction of the force on a test body with Eötvös type experiments and find that the chameleon field effect cannot account for current bounds.

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arXiv2015

Equivalence Principle in Chameleon Models

Most theories that predict time and/or space variation of fundamental constants also predict violations of the Weak Equivalence Principle. In 2004 Khoury and Weltman proposed the so called chameleon field arguing that it could help avoiding experimental bounds on the WEP while having a non-trivial cosmological impact. In this paper we revisit the extent to which these expectations continue to hold as we enter the regime of high precision tests. The basis of the study is the development of a new method for computing the force between two massive bodies induced by the chameleon field which takes into account the influence on the field by both, the large and the test bodies. We confirm that in the thin shell regime the force does depend non-trivially on the test body\' s composition, even when the chameleon coupling constants are universal. We also propose a simple criterion based on energy minimization, that we use to determine which of the approximations used in computing the scalar field in a two body problem is better in each specific regime. As an application of our analysis we then compare the resulting differential acceleration of two test bodies with the corresponding bounds obtained from E\"otv\"os type experiments. We consider two setups: 1) an Earth based experiment where the test bodies are made of Be and Al; 2) the Lunar Laser Ranging experiment. We find that for some choices of the free parameters of the chameleon model the predictions of the E\"otv\"os parameter are larger than some of the previous estimates. As a consequence, we put new constrains on these free parameters. An important result of our analysis is that our approach leads to new constraints on the parameter space of the chameleon models.

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arXiv2015

Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?

We discuss with a rather critical eye the current situation of black hole (BH) solutions in $f(R)$ gravity and shed light about its geometrical and physical significance. We also argue about the meaning, existence or lack thereof of a Birkhoff's theorem in this kind of modified gravity. We focus then on the analysis and quest of $non-trivial$ (i.e. hairy) $asymptotically\,\,flat$ (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does $not$ vanish identically in the domain of outer communication. To do so, we provide and enforce the $regularity\,\,conditions$ at the horizon in order to prevent the presence of singular solutions there. Specifically, we consider several classes of $f(R)$ models like those proposed recently for explaining the accelerated expansion in the universe and which have been thoroughly tested in several physical scenarios. Finally, we report analytical and numerical evidence about the $absence$ of $geometric\,\,hair$ in AFSSSBH solutions in those $f(R)$ models. First, we submit the models to the available no-hair theorems, and in the cases where the theorems apply, the absence of hair is demonstrated analytically. In the cases where the theorems do not apply, we resort to a numerical analysis due to the complexity of the non-linear differential equations. Within that aim, a code to solve the equations numerically was built and tested using well know exact solutions. In a future investigation we plan to analyze the problem of hair in De Sitter and Anti-De Sitter backgrounds.

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