arXiv subjects

Emmanuel T. Rodulfo

Publications and source records attributed to Emmanuel T. Rodulfo.

9 recordsLinked to original sources

arXiv2026

Two-branch detector response for Dirac infall into a Schwarzschild--MOG black hole

We study a localized spin-$1/2$ detector falling into a Schwarzschild--MOG black hole. The detector interacts with a neutral massless scalar field through a charge-preserving two-level transition, while its translational wave packet obeys the MOG-charged Dirac equation. Near the outer horizon, the separated radial system reduces to an inverse-square equation with index $\Theta_{\rm D}=E_{\rm H}/(2\hbar\kappa_\alpha)$. The gauge-invariant horizon energy satisfies $E_{\rm H}=m_\psi U_{\rm H}>0$ for every future-directed crossing trajectory. We quantize the scalar field in a globally normalized Boulware scattering basis and retain both radial-flux branches of a mode that is outgoing at infinity. This treatment does not identify a local outgoing ansatz with a complete mode. A finite radial gate $\chi_p(x)=(x/L_\chi)^p e^{-x/L_\chi}$ gives closed-form excitation and absorption probability densities that include the ingoing contribution and scattering-phase interference. Within the controlled near-horizon approximation, the full detailed-balance ratio factorizes into a branch-resolved outgoing ratio and a two-branch factor. Only the outgoing ratio approaches $\exp(-2\pi\nu/\kappa_\alpha)$ when the near-horizon, adiabatic, high-gap, and branch-isolation conditions all hold. The leading switching correction is controlled by $(\nu/\kappa_\alpha)/(S_\pm L_\chi)$, not by $(S_\pm L_\chi)^{-1}$ alone. In a weak-MOG expansion, the local correction separates into surface-gravity, trajectory-prefactor, and finite-gate terms. The full response also contains a contribution from global scattering. This separation shows which terms follow from the local horizon geometry and which depend on the detector protocol and scalar propagation outside the horizon region.

gr-qc↗

arXiv2026

Eikonal Quality-Factor Parameterization of Model-Conditional Static Black-Hole Thermodynamics

We study how one complex quasinormal frequency can parameterize the geometry and model-conditional thermodynamics of a prescribed family of static, spherically symmetric black holes. For a minimally coupled massless test scalar in the eikonal limit, the ratio $\chi=\omega_R\tau=\omega_R/\omega_I=2Q$ removes the overall mass scale. If $\chi$ is injective in one dimensionless parameter, that parameter and the geometric scale can be reconstructed within the chosen family. The normalized metric then fixes the horizon and Hawking temperature, whereas Wald entropy requires the gravitational action. For the RN-form family, $\chi$ determines $u=q^2$ but not the sign of charge. The constant-coupling static MOG metric is exactly RN under $\mathcal M=(1+\alpha)m_{\rm MOG}$ and $u=\alpha/(1+\alpha)$; consequently, the complete minimally coupled scalar spectrum is identical on mapped backgrounds for every multipole and overtone. The two assignments have equal temperature but different action-dependent entropy. Chebyshev and WKB--Pad\'e calculations quantify the finite-multipole error, with a maximum eikonal ratio error of $2.1\times10^{-3}$ on the tested $l=2$ RN grid. The construction is therefore a model-dependent inverse, not a theory selector. Applying it to gravitational-wave observations requires the appropriate tensor, vector, and scalar perturbation sectors beyond the test-field eikonal approximation.

gr-qc↗

arXiv2026

Shadow dependent phenomenology framework for rotating black hole metric

We establish a formal thermodynamic-optical duality that bridges the semiclassical quantum evaporation of black holes with their classical macroscopic geometry. The physical viability of this framework is anchored by a stable multivariate coordinate transformation and a non-vanishing Jacobian determinant, which allows for a diffeomorphic inversion mapping that decouples intrinsic physical quantities such as bare mass from the unobservable spacetime interior. By re-parameterizing black hole properties entirely in terms of the analytical shadow radius ($R_{sh}$), we derive explicit, observable-based expressions for the weak deflection angle, Hawking temperature, and integrated semiclassical luminosity. We demonstrate the framework's predictive utility by applying it to standard Kerr, Kerr-MOG (Scalar-Tensor-Vector Gravity), and rotating Horndeski spacetimes. Our results provide a definitive mathematical solution to parameter degeneracy, revealing that distinct fundamental fields (vector vs. scalar) leave unique observational fingerprints on far-field astrometry and horizon-scale quantum thermodynamics. By confronting these models with Event Horizon Telescope (EHT) M87* data, we show that this formalism successfully breaks mass-parameter degeneracies, offering a robust and computationally efficient operational tool for testing the Kerr hypothesis and probing modified gravity theories with next-generation very-long-baseline interferometry (VLBI).

gr-qc↗

arXiv2026

Dynamical Black Hole Thermodynamics in Modified Gravity

We investigate the dynamical and thermodynamic evolution of a Schwarzschild black hole in Modified Gravity (MOG) perturbed by a scalar gravitational wave breathing mode. By evaluating the linearized modified Einstein equations at the near-horizon boundary, we reduce the spatial wave operator to a closed-form temporal ordinary differential equation, thereby explicitly deriving the damped-oscillatory kinematics of the scalar strain. Using a quasi-adiabatic approximation, we show that the effective surface gravity and dynamical temperature are linearly modulated by the perturbation amplitude and velocity. These rapid geometric fluctuations break the semiclassical adiabatic regime, triggering explicitly non-thermal particle creation analogous to the dynamical Casimir effect. Furthermore, we resolve a local thermodynamic paradox concerning apparent horizon area fluctuations. We prove that first-order geometric perturbations $\mathcal{O}(h_b)$ are fully reversible kinematic artifacts, whereas irreversible entropy generation is a strictly second-order $\mathcal{O}(h_b^2)$ effect driven by the Raychaudhuri expansion, thereby preserving the Generalized Second Law. Finally, we apply these mechanisms to the black hole information paradox. We show that treating the MOG deformation parameter as a quantum-scale running coupling, $\alpha(M)$, mathematically decouples the effective gravitational charge from linear mass scaling. This dynamically forces the evaporating black hole toward the extremal limit ($M_G \to Q_G$), smoothly quenching the Hawking temperature to zero and yielding a thermodynamically stable, information-preserving remnant.

gr-qc↗

arXiv2026

Breathing Black Hole Shadows in Modified Gravity (MOG)

In this paper, we investigate the dynamic phenomenological signatures of a Schwarzschild-MOG black hole shadow perturbed by passing gravitational waves. By perturbing the Hamilton-Jacobi equation for photon null geodesics, we demonstrate that the unique field content of MOG breaks the observational degeneracy with standard General Relativity. We mathematically prove two distinct, time-dependent signatures. First, the massless MOG scalar field induces a volumetric ``breathing mode'' polarization, causing the total apparent area of the shadow to rhythmically expand and contract. Second, the massive MOG vector field undergoes quantum vacuum dispersion, arriving at the observer with a predictable time delay. This delayed massive wave sources secondary longitudinal metric perturbations that manifest as a sudden, asymmetric translational wobble of the shadow on the celestial screen. These dynamic geometric shifts offer a robust observational template for next-generation interferometry to strictly test the existence of massive force carriers and scalar fields in gravity.

gr-qc↗

arXiv2021

Shadow and weak deflection angle of extended uncertainty principle black hole surrounded with dark matter

In this paper, we discuss the possible effects of dark matter on a Schwarzschild black hole with the correction of extended uncertainty principle (EUP), such as the parameter $α$ and the large fundamental length scale $L_*$. In particular, we surround the EUP black hole of mass $m$ with a static spherical shell of dark matter described by the parameters mass $M$, inner radius $r_s$, and thickness $Δr_s$. In this study, we find that there is no deviation in the event horizon, which readily implies that the black hole temperature due to the Hawking radiation is independent of any dark matter concentration. In addition, we show some effects of the EUP parameter on the innermost stable circular orbit (ISCO) radius of time-like particles, photon sphere, shadow radius, and weak deflection angle. It is found that time-like orbits are affected by deviation of low values of mass $M$. A greater dark matter density is needed to have remarkable effects on the null orbits. Using the analytic expression for the shadow radius and the approximation $Δr_s>>r_s$, it is revealed that $L_*$ should not be lower than $2m$. To broaden the scope of this study, we also calculate the analytic expression for the weak deflection angle using the Ishihara et al. method \cite{Ishihara_2016}. As a result, we show that $Δr_s$ is improved by a factor of $(1+4αm^2/L_*^2)$ due to the EUP correction parameters. The calculated shadow radius and weak deflection angle are then compared using the estimated values of the galactic mass from Sgr A*, M87, and UGC 7232, as well as the mass of the supermassive black hole at their center.

gr-qc↗

arXiv2020

Rotating dirty black hole and its shadow

In this paper, we examine the effect of dark matter to a Kerr black hole of mass $m$. The metric is derived using the Newman-Janis algorithm, where the seed metric originates from the Schwarzschild black hole surrounded by a spherical shell of dark matter with mass $M$ and thickness $Δr_{s}$. The seed metric is also described in terms of a piecewise mass function with three different conditions. Specializing in the non-trivial case where the observer resides inside the dark matter shell, we analyzed how the effective mass of the black hole environment affects the basic black hole properties. A high concentration of dark matter near the rotating black hole is needed to have considerable deviations on the horizons, ergosphere, and photonsphere radius. The time-like geodesic, however, shows more sensitivity to deviation even at very low dark matter density. Further, the location of energy extraction via the Penrose process is also shown to remain unchanged. With how the dark matter distribution is described in the mass function, and the complexity of how the shadow radius is defined for a Kerr black hole, deriving an analytic expression for $Δr_{s}$ as a condition for notable dark matter effects to occur remains inconvenient.

gr-qc↗

arXiv2020

Weak deflection angle of a dirty black hole

In this paper, we present the weak deflection angle in a Schwarzschild black hole of mass $m$ surrounded by the dark matter of mass $M$ and thickness $Δr_{s}$. The Gauss-Bonnet theorem, formulated for asymptotic spacetimes, is found to be ill-behaved in the third-order of $1/Δr_{s}$ for very large $Δr_{s}$. Using the finite-distance for the radial locations of the source and the receiver, we derived the expression for the weak deflection angle up to the third-order of $1/Δr_{s}$ using Ishihara (\textit{et al.}) method. The result showed that the required dark matter thickness is $\sim2\sqrt{3mM}$ for the deviations in the weak deflection angle to occur. Such thickness requirement is better by a factor of 2 as compared to the deviations in the shadow radius ($\sim\sqrt{3mM}$). It implies that the use of the weak deflection angle in detecting dark matter effects in one's galaxy is better than using any deviations in the shadow radius.

gr-qc↗

arXiv2002

A Closed Integral Form for the Background Gauge Connection

By the appropriate use of the Fock-Schwinger gauge properties, we derive the closed integral form of the `point-split' non-local background gauge connection originally expressed as a finite sum. This is achieved in the limit when the finite sum becomes infinite. With this closed integral form of the connection, we obtain the same exact results in the calculation of one-loop effective Lagrangian accommodating arbitrary orders of covariant field derivatives in quantum field theory of arbitrary spacetime dimensions and of arbitrary gauge group. Particularly, we display the one-loop effective Lagrangian for real boson fields up to 8 mass dimensions-the same result obtained when the connection was yet in the finite sum form.

hep-th↗