arXiv subjects

Rodrigo Maier

Publications and source records attributed to Rodrigo Maier.

At least 19 recordsLinked to original sources

arXiv2026

Optical Landscapes and High-Energy Collisions in Hairy Horndeski Gravity

We investigate the null geodesic structure, photon sphere dynamics, and high-energy particle collisions within a class of static, spherically symmetric hairy Horndeski black holes. Characterized by an invariant metric root at $r = 2M$ and a scalar hair parameter $Q$, the spacetime maps onto four distinct geometric domains dictated by the surface gravity $\kappa|_{2M}$. We derive exact analytical expressions for the photon sphere radius $r_{\text{ph}}$ and its dynamic stability criterion, showing that external circular null orbits remain dynamically unstable across non-extremal regimes. Crucially, we prove that a stable photon sphere arises exclusively in the extremal configuration ($Q = -2M$), where it coincides precisely with the degenerate horizon ($r = 2M$). We argue that this horizon-bound stable photon orbit acts as an infinitely redshifted bound state for light and ultra-relativistic particles. Finally, we analyze the Ba\~nados-Silk-West (BSW) effect for infalling timelike test particles, demonstrating that the center-of-mass energy $E_{\text{cm}}$ for critical collisions diverges as $E_{\text{cm}} \propto (r - r_h)^{-1/2}$ strictly at the extremal threshold $Q = -2M$.

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arXiv2026

A No-Go Theorem for Topological Bridges with Matter-Vacuum Coupling

Traversable topological bridges traditionally require exotic matter, violating the Null Energy Condition (NEC). This essay investigates whether matter-vacuum coupling can circumvent this necessity. Focusing on zero-tidal-force solutions, we establish a rigorous no-go theorem for static configurations, proving that such coupling cannot bypass the requirement for NEC violation. We demonstrate that the geometric flare-out condition is incompatible with NEC-compliant sources, regardless of the coupling $Q$ or equation of state. Crucially, the vacuum fails to shield the throat; instead, interaction gradients mathematically obstruct the required geometry. This result suggests that causality protection is inherent in the field equations, rendering the vacuum's evolution a regulator rather than a facilitator of topological shortcuts, thereby reinforcing the robustness of classical energy conditions.

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arXiv2026

The Vacuum Displacement Principle: Theoretical Framework and Local Phenomenology

We present a modified gravitational framework in which the standard Einstein field equations are sourced by a classical matter sector coupled to a Higgs-type scalar field $\chi$ modeling a dynamic vacuum substrate. By introducing a phenomenological covariant coupling we implement a physical displacement principle where massive baryonic matter drives the vacuum field away from its vacuum expectation value. We show that this coupling leads to a field-dependent modulation of a particle's inertial rest mass alongside a spatial fifth force, yielding localized violations of the Einstein Equivalence Principle while preserving universal free fall for fundamental point masses. In the weak-field, non-relativistic limit, this interaction manifests as a Yukawa-type correction to the Newtonian potential. We test the viability of this framework against local gravitational constraints, including planetary perihelion precession and E\"otv\"os parameter limits. Finally, we model the steady-state, non-relativistic spherical accretion of dust, demonstrating that the competing effects of vacuum-induced mass modulation and fifth-force acceleration yield distinct density and velocity profiles.

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arXiv2026

Buchdahl Limit and TOV Equations in Interacting Vacuum Scenarios

We investigate the stability of ultra-compact stellar configurations in the context of an interacting vacuum component. By extending the Tolman-Oppenheimer-Volkoff equations to include a covariant energy exchange between the fluid and vacuum sectors, we examine how the classical Buchdahl stability limit is modified. We analyze two phenomenological interaction models: a coupling to the matter energy density gradient and a direct coupling to the spacetime curvature. Numerical integration reveals that while standard General Relativity predicts a central pressure divergence as the compactness approaches the Buchdahl threshold, the interaction term $Q_\nu$ relaxes the pressure gradient and maintains a finite, well-behaved central pressure for proper domains of the coupling parameter. These results demonstrate that an interacting vacuum provides a physical mechanism to bypass classical geometric bounds, potentially supporting ultra-compact objects in regimes previously considered singular.

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arXiv2025

General Boosted Black Holes: A First Approximation

In this paper we obtain an approximate solution of Einstein field equations which describes a general boosted Kerr-Newman black hole relative to a Lorentz frame at future null infinity. The boosted black hole is obtained from a general twisting metric whose boost emerges from the BMS group. Employing a standard procedure we build the electromagnetic energy-momentum tensor with the Kerr boosted metric together with its timelike Killing vector as the electromagnetic potential. We demonstrate that our solution satisfies Einstein field equations up to a fourth-order expansion in $1/r$, indicating that the spacetime closely resembles a Kerr-Newman black hole whose boost points in a arbitrary direction. Spacetime structures of the general black hole -- namely the event horizon and ergosphere -- are examined in Bondi-Sachs coordinates. For a proper timelike observer we show that the electric field generated by the boosted black hole exhibits a purely radial behavior, whereas the magnetic field develops a complex structure characterized by two pronounced lobes oriented opposite to the boost direction.

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arXiv2024

Relativistic Einstein Rings of Reissner-Nordstr\"om metric Black Holes Nonminimally Coupled to Electrodynamics

In this paper we examine the relativistic Einstein rings assuming a nonminimal coupling between gravitation and electromagnetism in a Reissner-Norstr\"om background. Starting from a general action of a nonminimal coupled electrodynamics we show that an unstable effective photon sphere may be obtained in the regime of eikonal approximation. Restricting ourselves to the unstable photon sphere domain we examine the expected angular positions of the first and second relativistic Einstein rings. To compare our results with previous studies in the literature we model the lens as a Galactic supermassive black hole. For fixed coupling parameters we show that such angular positions decrease as the charge parameter increases. The angular separation between the first and second rings is also evaluated. We show that such separation increases as the charge parameter increases. These patterns are not followed by nearly extremal configurations. In this case we show that there is an overlap domain so that the angular position and the corresponding coupling parameter do not allow one to differ extremal cases from complementary configurations which satisfy the cosmic censorship hypothesis.

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arXiv2024

Boosted Kerr-Newman Black Holes

In this paper we obtain a new solution of Einstein field equations which describes a boosted Kerr-Newman black hole relative to a Lorentz frame at future null infinity. To simplify our analysis we consider a particular configuration in which the boost is aligned with the black hole angular momentum. The boosted Kerr-Newman black hole is obtained considering the complete asymptotic Lorentz transformations of Robinson-Trautman coordinates to Bondi-Sachs, including the perturbation term of the boosted Robinson-Trautman metric. To verify that the final form of the metric is indeed a solution of Einstein field equations, we evaluate the corresponding energy-momentum tensor the boosted Kerr-Newman solution. To this end, we consider the electromagnetic energy-momentum tensor built with the Kerr boosted metric together with its timelike killing vector. We show that the Papapetrou field thus obtained engender an energy-momentum tensor which satisfies Einstein field equations up to 4th order for the Kerr-Newman metric. To proceed, we examine the causal structure of the boosted Kerr-Newman black hole in Bondi-Sachs coordinates as in a preferred timelike foliation. We show that the ultimate effect of a nonvanishing charge is to shrink the overall size of the event horizon and ergosphere areas when compared to the neutral boosted Kerr black holes. Considering the preferred timelike foliation we obtain the electromagnetic fields for a proper nonrotating frame of reference. We show that while the electric field displays a pure radial behaviour, the magnetic counterpart develops an involved structure with two intense lobes of the magnetic field observed in the direction opposite to the boost.

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arXiv2024

Charged Black Holes from Interacting Vacuum

In this paper charged black holes are obtained assuming that a Born-Infeld electrodynamics may arise from an interaction between the electromagnetic field and a vacuum component. In this context Cauchy horizons do not appear in the maximal analytical extension once an event horizon is formed so that the interior spacetime does not suffer from any sort of instabilities which are well known in the literature. On the contrary, the causal structure exhibits an event horizon -- encapsulating a spacelike singularity -- and a cosmological horizon. We show that the strong cosmic censorship is then restored for a wide range of the parameters including configurations in which the black hole charge is much larger than its mass. We also show that the black hole thus formed described by our solution exhibits an unstable photon sphere analogous to that of the Schwarzschild metric.

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arXiv2024

Scalar Perturbations in Nonsingular Universes from Interacting Vacuum

In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange between a nonrelativistic fluid and a vacuum component. In both scenarios it can be shown that closed models may furnish nonsingular orbits of physical interest in phase space once a decelerated past era is connected to a graceful exit to late-time acceleration. Regarding such configurations as background spacetimes we introduce scalar perturbations in order to examine the stability of these models in a high energy domain. We explicitly show that the vacuum perturbation is not an independent variable and diverges as dynamics approaches the bounce. This feature assigns a rather unstable signature to the dynamics making the choices for the energy transfer ill defined at least for nonsingular configurations at the bounce scale.

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arXiv2023

Particle Dynamics on Test Papapetrou Fields of Vacuum Spacetimes

In this paper we examine the dynamics of particles subjected to test Papapetrou fields of vacuum spacetimes. The staring point of our analysis is based on fundamental electrodynamics which emerge from spacetime isometries of a Kerr and Schwarzschild black holes. Taking into account Killing vectors which satisfy Maxwell equations we evaluate the corresponding electric and magnetic fields -- Papapetrou fields -- by fixing proper frames of reference in each spacetime. A timelike observer is considered for the case of a Schwarzschild spacetime while a locally non-rotating (LNR) frame of reference is fixed for a Kerr black hole. In order to probe for the effect of such electromagnetic fields we study the motion of charged test particles in the equatorial plane of both spacetimes. For the case of a Schwarzschild black hole we show that massive/charged test particles may populate the unstable photon sphere for a given domain of the parametric space. Restricting ourselves to orbits with LNR initial conditions for the case of a Kerr black hole we show that there is an explicit deviation between orbits of neutral and charged particles in the case of repulsive configurations. For critical charge-mass ratios $\zeta_*$ test particles can be found in the Kerr retrograde photon sphere thus assigning a physical signature to Papapetrou fields.

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arXiv2023

Stellar Instability from Parametric Resonance

In this paper we examine the stability of stellar configurations in which the interior solution is described by a closed FLRW geometry sourced with a charged pressureless fluid and radiation. An interacting vacuum component and a conformally coupled massive scalar field are also included. Given a simple factor for the energy transfer between the pressureless fluid and the vacuum component we obtain bounded interior oscillatory solutions. We show that in proper domains of the parameter space the interior dynamics is highly unstable so that the break of the KAM tori leads to a disruptive ejection of mass. For such configurations the interior solution asymptotically matches an exterior Reissner-Nordstr\"om-de Sitter spacetime.

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arXiv2022

General Boosted Kerr Black Holes and Papapetrou Electrodynamics

In this paper the spacetime of a general boosted Kerr black hole relative to a Lorentz frame at future null infinity is regarded as a background to examine its respective Papapetrou fields. Taking into account its sole Killing vector we evaluate the electric and magnetic components -- in Bondi-Sachs (BS) and Kerr-Schild (KS) coordinates -- of the Maxwell field which comes from spacetime isometries. To this end we consider a general timelike observer in KS coordinates. Satisfying sufficient conditions for horizon and ergosphere formation it is shown that nonsingular magnetic field configurations are formed around the boosted Kerr black hole while the electric counterpart vanishes. Different magnetic field patterns are discussed in the case of variations of the boost parameter $\gamma$ and direction $\boldsymbol{\hat{n}}$.

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arXiv2021

Nonsingular Cosmology from an Interacting Vacuum

We examine the dynamics of FLRW cosmologies in which the vacuum interacts with a perfect fluid through an energy exchange, focusing on the exploration of nonsingular configurations, including cyclic and bouncing models. We consider two specific choices for the energy transfer. In the first case, the energy transfer is proportional to a linear combination of the vacuum and fluid energy densities which makes the conservation equations exactly integrable. The resulting Friedmann equation can be interpreted as an energy constraint equation with an effective potential for the scale factor that may include an infinite barrier forcing a bounce at small values of the scale factor, as well as a potential well allowing for cycling solutions. In the second case, the energy transfer is a nonlinear combination of the vacuum and fluid energy densities. Nonetheless even in this case the dynamics can be partially integrated, leading to a first integral, reducing the number of degrees of freedom. We show that also in this nonlinear case bouncing and cycling cosmologies may arise. In both cases the structure of the resulting phase space allows for nonsingular orbits with an early accelerated phase around a single bounce, connected via a decelerated matter-dominated era to a late-time accelerated phase dominated by an effective cosmological constant.

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arXiv2021

Yukawa Black Holes from Interacting Vacuum

In this paper we obtain an exact solution of Einstein field equations assuming an interaction between a vacuum component and the Maxwell field. The key feature of such interaction refers to a simple stress exchange so that the electromagnetic field naturally incorporates the Yukawa potential. It is shown that the resulting spacetime thus obtained can either be a naked singularity or a black hole with an inner Cauchy horizon $R_-$ and an exterior event horizon $R_+$. For this latter configuration we examine the group velocity of test photons in the region $R>R_+$. Beyond a lower bound for the frequency we show that superluminal velocities arise in a neighbourhood of the event horizon and that the coupling parameter of the interaction is actually connected to a nonvanishing rest mass for the photon.

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arXiv2021

Hairy Black Holes from Horndeski Theory

We present an exact static black hole solution of Einstein field equations in the framework of Horndeski Theory by imposing spherical symmetry and choosing the coupling constants in the Lagrangian so that the only singularity in the solution is at $r=0$. The analytical extension is built in two particular domains of the parametric space. In the first domain we obtain a solution exhibiting an event horizon analogous to that of the Schwarzschild geometry. For the second domain, we show that the metric displays an exterior event horizon and a Cauchy horizon which encloses a singularity. For both branches we obtain the corresponding Hawking temperature which, when compared to that of the Schwarzschild black hole, acquires a correction proportional to a combination of the coupling constants. Such a correction also modifies the definition of the entropy of the black hole.

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arXiv2021

Maxwell Fields in Boosted Kerr Black Holes

The spacetime of a boosted Bondi-Sachs rotating black hole is considered as a proper background to examine electromagnetic configurations connected to analytic solutions of Maxwell equations. In our analysis, we first use the Bondi-Sachs transformations in order to bring the boosted rotating black hole metric into the Kerr-Schild form, from which zero angular momentum observers (ZAMOs) are constructed via the ADM formalism. In Kerr-Schild coordinates we obtain the Killing fields as sources of Maxwell electrodynamics, and we fix a ZAMO in order to evaluate the components of the electric and magnetic fields, from which we obtain nonsingular patterns of an eventual momentum-energy emission of a boosted Kerr-Schild black hole. Distinct patterns are examined and discussed in the case of variations of the boost parameter $\gamma$. We extend our analysis by considering the nonsingular electromagnetic emission in the framework of a boosted Bondi-Sachs rotating black hole, as it moves at relativistic speeds. We also discuss possible mechanisms that may resemble magnetospheres of rotating boosted black holes and give rise to hydromagnetic flows from accretion discs and to the production of jets.

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arXiv2020

Strong Lensing and Nonminimally Coupled Electromagnetism

The lensing at large deflection angles caused by a Schwarzschild black hole for the case of a nonminimal coupling between gravitation and electromagnetism is examined. We show that photons follow an effective geometry, which displays an effective photon sphere. For the case in which the source, lens and observer are aligned, so that relativistic Einstein rings are formed, the dependence of the angular separation $\delta\theta$ between the first and second ring with the relevant coupling parameter is calculated. We argue that such a separation, which may be measured by telescopes that will be operative in the near future, may set an upper and a lower limit for the coupling parameter.

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arXiv2020

Nonsingular Black Holes From Charged Dust Collapse: A Concrete Mechanism to Evade Interior Singularities in General Relativity

In this essay we examine the gravitational collapse of a nonrelativistic charged perfect fluid interacting with a dark energy component. Given a simple factor for the energy transfer, we obtain a nonsingular interior solution which naturally matches the Reissner-Nordstr\"om-de Sitter exterior geometry. We also show that the interacting parameter is proportional to the overall charge of the final black hole thus formed. For the case of quasi-extremal configurations, we propose a statistical model for the entropy of the collapsed matter. This entropy extends Bekenstein's geometrical entropy by an additive constant proportional to the area of the extremal black hole.

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