arXiv subjects

Gustavo Melgarejo

Publications and source records attributed to Gustavo Melgarejo.

3 recordsLinked to original sources

arXiv2026

Perturbative vacuum constraints in higher-curvature gravity: Schwarzschild deformations and strong-field observables

Higher-curvature terms modify the action but do not necessarily generate new vacuum geometries on the branch perturbatively connected to GR. We develop a first-order framework for static, spherical vacuum black holes in 4D metric theories with $\mathcal L_{\mathrm{grav}}=R/2+λΨ(R,X,Y)$, $X=R_{μν}R^{μν}$, and $Y=R_{μνρσ}R^{μνρσ}$. On the coupling-analytic branch, purely Ricci-based terms $Ψ(R,X)$, analytic in curvature with $Ψ(0,0)=0$, do not deform a Ricci-flat background under adopted regularity and boundary assumptions. Riemann-dependent terms can, since Kretschmann scalar is nonzero. In areal-radius gauge, we derive model-independent first-order expressions for the horizon shift, ISCO, epicyclic frequencies, periapsis advance, photon sphere, critical shadow impact parameter, Wald entropy, and Hawking temperature. For $Ψ_η=\ell_λ^{-2+4η}\mathcal G^η$, treating noninteger powers as phenomenological parametrizations of nonlinear curvature, we obtain a closed first-order Schwarzschild-connected solution. Perturbations decay for $η>1/2$, while fixed-ADM interpretation requires $η>2/3$; at $η=2/3$, sourced $1/r$ term mixes with asymptotic mass mode. For positive effective coupling, the horizon, ISCO, photon sphere, and critical shadow impact parameter increase for $2/3<η<1$ and decrease for $η>1$. On the fixed-ADM branch, mass, Wald entropy, and Hawking temperature satisfy $dM=T_H,dS_{\rm W}$ to first order at fixed couplings. At $η=1$, the linear 4D Gauss--Bonnet term leaves local geometry and geodesic observables unchanged but adds a constant topological entropy shift. Finally, an Event Horizon Telescope-inspired shadow-size criterion gives a conservative first-order sensitivity estimate for the effective dimensionless coupling, a geometric consistency test rather than a complete observational constraint.

gr-qc↗

arXiv2026

On the Metric Propagator and Affine Modes of Extended Hybrid Metric--Palatini Gravity with Ricci--Squared Invariants

We investigate an extended hybrid metric--Palatini theory defined by an arbitrary function $f(R,\mathcal{R},\hat{Q},Q,\mathcal{Q})$, where $R$ and $\mathcal{R}$ are the metric and Palatini scalar curvatures, and $Q=R_{μν}R^{μν}$, $\mathcal{Q}=\mathcal{R}_{(μν)}\mathcal{R}^{(μν)}$, and $\hat{Q}=R_{μν}\mathcal{R}^{(μν)}$ are the metric, Palatini, and mixed quadratic Ricci invariants, respectively. We derive the field equations and analyze the Minkowski weak--field limit. We obtain the metric propagator and identify the additional spin--$2$ and spin--$0$ poles that couple to the metric source. When these poles are finite, real, and simple, the spin-2 sector of the metric propagator contains two additional poles, at least one of which has a negative residue. Once the spin-2 sector is restricted to contain at most one additional pole, the absence of ghostlike metric-coupled excitations in the generic two-scalar branch requires eliminating the remaining spin--$2$ pole, whereas one healthy metric-coupled spin--$2$ pole may coexist with at most one healthy scalar pole when the scalar denominator becomes linear in $k^2$. We derive the corresponding algebraic conditions on the Minkowski-background derivatives of $f$ and specialize them to hybrid $f(R,\mathcal{R})$, mixed $f(R,\mathcal{Q})$, and purely Palatini $f(\mathcal{R},\mathcal{Q})$ theories, including the metric $f(R)$ and Palatini $f(\mathcal{R})$ limits. We further show that the complete linearized system can admit modes carried entirely by the independent connection that are absent from the metric propagator. These results therefore provide necessary flat-space stability criteria for the metric-coupled sector on the branches analyzed, supplemented by the analysis of purely affine modes.

gr-qc↗

arXiv2026

Another Look at the Weak-Field Limit of Generalized Hybrid Metric-Palatini Gravity

We investigate the weak-field regime of generalized hybrid metric-Palatini theories, described by a generic function $f(R,\mathcal{R})$, where $R$ is the metric Ricci scalar and $\mathcal{R}$ is constructed from an independent torsionless connection. Linearizing the field equations about Minkowski spacetime, we show, without using the scalar-tensor representation, that the theory propagates the usual massless spin-2 mode and two massive scalar modes, with an effective gravitational coupling. The absence of tachyonic and ghostlike instabilities at the linearized level, together with the nondegeneracy of the scalar sector, is shown to impose algebraic restrictions on the derivatives of $f(R,\mathcal R)$ evaluated on the Minkowski background, which generalize previously obtained conditions. The Newtonian limit for an extended static source is derived, yielding a gravitational potential with two Yukawa corrections whose amplitudes are fixed by the scalar residues, while finite-size effects are encoded in source-dependent form factors. We determine the conditions under which the usual Newtonian limit is recovered and derive the effective post-Newtonian parameter $γ_Σ$ governing light propagation. Finally, we compute the radial epicyclic frequency and the corresponding anomalous periapsis advance, and compare it with planetary precession data to constrain the parameters of a viable hierarchical scalar-mass regime.

gr-qc↗