arXiv subjects

Reggie C. Pantig

Publications and source records attributed to Reggie C. Pantig.

At least 19 recordsLinked to original sources

arXiv2026

Redshift Spectroscopy as a Probe of Regular Black Holes, Black Bounces, and Scalar-Hair Compact Objects

Motivated by [Phys. Rev. D. 107, 064019 (2023)], we develop a unified and model-independent framework for the spectroscopy of photon frequency shifts in generic static, spherically symmetric spacetimes. Working with a line element characterized by three arbitrary radial metric functions, we derive exact expressions for the conserved quantities of massive and massless probes, the conditions for circular timelike geodesics, the local-emission-angle-dependent photon impact parameter, and the corresponding local redshift and blueshift branches measured by distant static observers. The formalism is further extended to include the line-of-sight peculiar motion of the source and the local propagation of photons in a nonmagnetized cold plasma, thereby identifying the gravitational, orbital, and dispersive factors entering the frequency-shift signal under the stated assumptions. We also show that, in vacuum, the same geometric structures governing orbital spectroscopy determine the photon sphere and the shadow impact parameter whenever an external null critical orbit is present. To make the framework suitable for deformed compact-object models, we construct a perturbative expansion around Schwarzschild geometry up to second order in a dimensionless deformation parameter, obtaining explicit corrections to the orbital energy, angular momentum, emitter four-velocity, photon impact parameter, and the vacuum and plasma frequency shifts. We apply the formalism to regular black holes from nonlinear electrodynamics, the Simpson--Visser black-bounce spacetime, and the Fisher--Janis--Newman--Winicour--Wyman geometry. These examples show that the same local spectroscopic language can be used across regular-black-hole, black-bounce, wormhole, and scalar-supported horizonless sectors.

gr-qc↗

arXiv2026

Josephson interferometry in an Oppenheimer--Snyder-like scale-dependent black-hole spacetime

We develop a covariant framework for Josephson transport, superconducting interference, and shunt noise in the scale-dependent exterior generated by an Oppenheimer--Snyder-like collapse. Static Josephson frequencies and transported currents referred to Killing time acquire one lapse factor, whereas power acquires two. For a junction comoving with the collapsing surface, the coordinate-time phase rate differs from the frequency received at infinity because of null propagation and Doppler effects. We derive the exact radial-null travel-time kernel and show that its local near-extremal logarithmic enhancement crosses over, at fixed emission offset, to pole-controlled extremal behavior. We also obtain the redshifted resistively and capacitively shunted-junction equation and the dc and microwave-driven two-junction interference envelopes. In the negligible-total-inductance limit, static lapse imbalance modifies lobe amplitudes without shifting their centers, whereas microwave-induced translations require dynamical fluxoid closure. In a Hartle--Hawking state, Tolman redshift produces a superconducting exclusion layer and a lapse-independent asymptotic shunt-noise spectrum; its low-frequency limit obeys a parameter-free fluctuation--delay relation. Finally, we derive a shadow--Josephson consistency relation and sensitivity bounds on the running parameter.

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arXiv2026

Fixed ADM reconstruction of extended uncertainty principle black holes

We study a phenomenological fixed-ADM prescription for an extended-uncertainty-principle (EUP) correction to the Schwarzschild exterior. Rather than treat mass constancy as a consequence of the EUP, we hold the charge measured at spatial infinity fixed so that we can compare exteriors at the same physical mass. We impose the EUP-shifted horizon radius and Hawking temperature and select the slowest admissible inverse-power representative. Its Einstein tensor defines an effective anisotropic tensor, but we do not infer an independent matter model, quantum state, or perturbation theory from that definition. For a positive EUP parameter, the effective energy density is negative throughout the exterior, while the transverse null and strong energy conditions fail over an extended radial region. The area entropy and the formal entropy obtained from the reduced relation $\mathrm{d}M=T\,\mathrm{d}S$ disagree at leading order; we interpret this mismatch as evidence that the thermodynamic description lacks work terms or an action-based entropy law, not as a definite EUP entropy correction. An explicit one-parameter family with the same mass, horizon, and temperature shows that the orbit, lensing, and test-field eikonal shifts depend on the chosen representative. Our results therefore characterize the minimal member of a phenomenological family rather than universal consequences of the EUP.

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arXiv2026

Noether charges and the first law of thermodynamics for multifractional Schwarzschild black hole in the q-derivative theory

In this paper, we investigate black-hole thermodynamics in the multi-fractional theory with $q$-derivatives, focusing on static, spherically symmetric vacuum solutions in the spherical-coordinate approximation. In the geometric frame the solution is exactly Schwarzschild in the areal radius $q$, so that canonical charges can be defined using standard covariant methods. The conserved mass depends only on the Schwarzschild integration constant, and the Iyer--Wald entropy satisfies the usual area law in terms of the geometric horizon radius. When the Hawking temperature is defined in the fractional radial coordinate $r$, however, it acquires an explicit dependence on the multi-fractional profile through the local factor $q'(r_{\rm h})$ at the horizon. As a result, variations of the non-dynamical profile parameters generically obstruct integrability of a naive Clausius relation expressed solely in terms of mass and entropy. We show that this obstruction is resolved by enlarging the thermodynamic state space to include the profile parameters and by constructing an integrable entropy functional obtained from a radial integral of the geometric radius. The corresponding extended first law contains additional work terms conjugate to the multi-fractional couplings. We analyze both binomial and log-oscillating profiles, clarify the role of presentation dependence, and delineate the consistency conditions required for a well-defined exterior branch with a single horizon. Our results make explicit the separation between profile-insensitive canonical charges and profile-sensitive thermal quantities in multi-fractional black-hole thermodynamics.

gr-qc↗

arXiv2026

Time-dependent black hole lensing from ringdown quasinormal mode

Is it possible to find imprints of a black hole ringdown through gravitational lensing? To address this question, we formulate an analytic description of weak-field and strong-deflection lensing of light in a time-dependent, perturbed Schwarzschild spacetime. The spacetime dynamics are modeled by a single, axisymmetric, even-parity quasinormal mode with $\ell=2$, $m=0$ and complex frequency $ω$. Working to first order in a small perturbation amplitude while keeping background null geodesics exact, we derive a time-dependent line-of-sight (Born) expression for the screen-plane deflection measured by a static observer at large radius. From the same integral, an asymptotic expansion yields the familiar weak-field $1/b$ law with a ringdown-frequency correction that drives a harmonic centroid wobble, whereas a near-photon-sphere expansion produces a time-dependent generalization of the logarithmic strong-deflection limit with modulated coefficients, including a small oscillation of the critical impact parameter. An observer tetrad built from the background static frame ensures that all screen-plane quantities, such as centroid motion, multi-image hierarchy, and time delays, as well as photon-ring morphology, are gauge-safe at first order. We provide explicit matching across regimes, showing that the near-critical coefficients governing spacing and ring-radius modulations are encoded in the same Born kernel that controls the weak-field correction. This provides an analytic account of how ringdown-scale perturbations enter imaging observables, without resorting to numerical integration of null geodesics.

hep-th↗

arXiv2026

Optical-area minimum method for static spherical black hole shadows

We formulate a global optical-area method for shadows of static, spherically symmetric black holes. For the metric $ds^{2}=-A(r)dt^{2}+B(r)dr^{2}+C(r)dΩ^{2}$, spherical sections of the optical geometry have area $\mathcal{A}_{\rm opt}=4πC/A$. A null ray with impact parameter $b$ can cross a spherical section only if $b^{2}\leq C/A$. The capture threshold is fixed by the infimum of $C/A$ on the connected interval between the observer and the black hole horizon. When attained at an interior point, the infimum gives $b_{\rm sh}^{2}=\min(C/A)$, while a static observer outside the controlling minimum, on the inward-sky branch, measures $\sin^{2}α_{\rm sh}=\mathcal{A}_{*}/ \mathcal{A}_{\rm opt}(r_{\rm o})$. The usual photon-sphere equation follows when the minimum occurs at a smooth interior point. Exponential instability additionally requires the minimum to be nondegenerate. The local optical-radius and photon-sphere formulas are established results. Our contribution is to organize them into an observer-to-horizon global selection rule that compares all stationary candidates and relevant endpoint limits. The radial function $B(r)$ does not affect the shadow angle, although it enters the coordinate-time instability rate, whose numerical value also depends on the normalization of the static time coordinate. We derive compact first- and second-order formulas for deformed metrics, demonstrate candidate comparison with a synthetic two-minimum profile, and apply the construction to Reissner--Nordström, Bardeen, charged dilaton, and Kottler black holes. An explicit transformation of the charged-dilaton example from a nonareal to an areal radial coordinate verifies radial-coordinate invariance, while the Kottler example probes a nonasymptotically flat static region.

gr-qc↗

arXiv2026

Chromatic Weak Lensing by Charged Black Holes with Two Lorentz-Violating Kalb-Ramond Couplings

We study weak gravitational lensing and steady spherical test--fluid accretion by a static charged black hole in a Lorentz--violating Kalb--Ramond background with two nonminimal curvature couplings, assuming minimally coupled probe radiation. Using the Gauss--Bonnet theorem with the correct boundary term and perturbed ray boundary, we obtain the complete local deflection angle through second post--Minkowskian order. In a homogeneous cold plasma, the mass and charge sectors acquire different frequency dependences, producing distinct chromatic signatures. The two Lorentz--violating couplings are also separated: one controls the conical geometry and mass normalization, while the other first enters through the effective charge. For neutral adiabatic accretion, we derive the conserved fluxes, Bernoulli relation, Hamiltonian flow, and sonic--point conditions. These results disentangle local, global, dispersive, and accretion effects and establish the calibrations required for phenomenological constraints.

gr-qc↗

arXiv2026

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes

This paper develops a phase-plane formulation of gravitational light deflection by static and spherically symmetric black holes, with Schwarzschild spacetime as the principal case. Instead of perturbing the null trajectory and locating the displaced outgoing asymptote, we represent the orbit through an amplitude and an intrinsic phase. The bending angle then follows from the excess physical azimuth accumulated while the intrinsic phase advances between two fixed asymptotic endpoints. For Schwarzschild spacetime, the exact radial first integral reduces the amplitude evolution to a cubic algebraic relation. Its physical branch generates the local phase factor through a single inverse algebraic map. Lagrange inversion then yields an explicit all-order weak-deflection coefficient formula in powers of the invariant ratio $M/b$. Each coefficient separates into an algebraic phase contribution and a universal trigonometric moment, which explains the alternating rational and $π$-dependent structure of the Schwarzschild series. Independent comparison with the exact radial scattering integral and conventional orbit perturbation reproduces the standard weak-bending coefficients. The same phase framework extends to general static spherical geometries, while the Schwarzschild cubic represents an especially simple member of a broader algebraic class. The branch singularity of the phase map also coincides with the critical photon orbit and governs the convergence of the weak-deflection expansion.

gr-qc↗

arXiv2026

Two-scale magnetically charged regular black holes from nonlinear electrodynamics and a T-duality-inspired zero-point length

We construct a two-scale, static, spherically symmetric regular black hole in Einstein gravity sourced by magnetic nonlinear electrodynamics (NED). The zero-point length $\ell$ regularizes the mass and charge profiles, whereas $q$ is the asymptotic magnetic charge. The geometry approaches Reissner-Nordström at large radius, reduces to the neutral zero-point-length solution for $q=0$, and coincides geometrically with the Ayón-Beato-García solution for $\ell=|q|$. For $q\neq0$, inverse reconstruction gives a single-valued magnetic Lagrangian with Maxwell asymptotics and a finite strong-field limit. The center is regular and is de Sitter, locally Minkowski, or anti-de Sitter according to the sign of $2M\ell-q^2$; the weak energy condition holds globally if and only if $3M\ell\geq2q^2$. We derive the extremality curve, the exact heat capacity, and homogeneous horizon-variation and Smarr identities while retaining the Wald area entropy. We also prove that every charged black hole in this family has a nondegenerate extraordinary NED optical metric throughout the domain of outer communication. The associated capture shadow is selected by the global minimum of the optical impact-parameter function and generally differs from the background-geodesic shadow. Weak-field calculations yield the periapsis, bending, time-delay, and redshift corrections; in particular, $\ell$ first appears beyond the standard first-post-Newtonian parameters. Finally, for minimally coupled test radiation in a cold transparent plasma, we obtain exact parametric shadow relations for power-law density profiles and combine Hamiltonian ray tracing with a Novikov-Thorne disk model. A separate extraordinary NED-plasma continuation is displayed only as a phenomenological prescription because a material plasma breaks the conformal ambiguity of the vacuum characteristic metric.

gr-qc↗

arXiv2026

Density-preserving core-Einasto black holes with Event Horizon Telescope bounds

A Newtonian halo density does not uniquely determine a relativistic spacetime, and the resulting completion ambiguity can dominate predicted horizon-scale signals. We make this dependence explicit for the feedback-cored Einasto profile calibrated on FIRE-2 simulations. In Schwarzschild gauge, the Einstein equations give an asymptotically flat, density-preserving geometry supported by an effective anisotropic fluid; no microscopic description of collisionless dark matter is assumed. By contrast, a commonly used rotation-curve completion replaces the finite seed core by an inverse-square source cusp. For the density-preserving solution we derive the enclosed mass in closed form, obtain a sharp one-horizon criterion and the extremal boundaries of a three-horizon phase, and establish the fixed-halo first law. More generally, the leading fractional shift of a spherical black-hole shadow is the environmental mass enclosed within the vacuum photon sphere divided by the central black-hole mass. Applying this result to published Event Horizon Telescope shadow-deviation summaries gives illustrative one-sided 95\% credible limits of $4.8\times10^{23}\,\Msun\,{\rm pc}^{-3}$ for $\sgr$ and $4.1\times10^{17}\,\Msun\,{\rm pc}^{-3}$ for $\mseven$, far above realistic smooth-halo densities. A Milky-Way calibration predicts a fractional shadow shift of $1.7\times10^{-25}$, whereas the rotation-curve completion gives a shift 19 orders of magnitude larger for the same galactic inputs. A covariant polarized thin-disk calculation shows the same weak-core suppression. Thus current horizon-scale images do not constrain a smooth kiloparsec-scale core-Einasto halo; an observable environmental signal would instead require a compact inner component or a physically different relativistic source.

gr-qc↗

arXiv2026

An obstruction and residual-completion theory for Newman--Janis deformations

We formulate an obstruction and residual-completion theory for Newman-Janis-type deformations of black hole seeds, where Newman-Janis-type includes both the original complex-coordinate Newman-Janis algorithm and modified prescriptions such as non-complexification variants. The Newman-Janis algorithm is treated as an off-shell map from a static seed to a stationary-axisymmetric trial geometry, rather than as a solution-generating theorem. Its failure is encoded in a Newman-Janis obstruction tensor, defined as the residual obtained after substituting the trial configuration into the intended field equations. We decompose this residual into dynamical, geometrical/coordinate-admissibility, and source-preservation channels, separating field-equation failure from circularity, Boyer-Lindquist integrability, stress-tensor type, equation-of-state preservation, and matter-model realizability. When the obstruction is nonzero, residual completion asks whether a minimal correction of the metric and matter fields can cancel it. At leading nonzero order in the rotation parameter, this becomes a linear solvability problem: the obstruction must lie in the image of a gauge-fixed completion operator subject to boundary and source-sector constraints, while the cokernel condition gives a no-go criterion in the chosen ansatz class. We illustrate the framework with a Schwarzschild example in vacuum GR. Using an ONJA-type complexification different from the Kerr-generating one, we obtain a non-Kerr rotating trial metric and compute its obstruction. The example gives $n_\star=2$ and $\ell_\star=0$, with an additional quadrupolar component at the same order, and shows how the leading residual is removed by the minimal even-parity correction restoring the Kerr complexification. The framework replaces the search for the correct complexification rule with computable criteria for success, completion, or obstruction.

gr-qc↗

arXiv2026

Spinning particle dynamics, epicyclic frequencies, and transient QPO signatures in Schwarzschild spacetime

We study the motion of spinning test particles in Schwarzschild spacetime within the Mathisson--Papapetrou--Dixon pole--dipole approximation, imposing the Tulczyjew--Dixon spin supplementary condition. Restricting to equatorial orbits with the particle spin aligned with the orbital angular momentum, and retaining terms through linear order in the specific spin $s$, we derive the spin-corrected radial potential, circular-orbit conditions, bound periodic trajectories, epicyclic frequencies, and Lyapunov exponents of unstable circular orbits. The spin--curvature coupling shifts the circular-orbit energy and angular momentum and moves the innermost stable circular orbit to $r_{\rm ISCO}=6M-2\sqrt{2/3}\,s+\mathcal{O}(s^2)$ in the sign convention adopted here. We construct bound periodic orbits using the Levin--Perez-Giz zoom--whirl taxonomy and show how the particle spin deforms the corresponding energy--angular-momentum map. We then obtain the coordinate-time azimuthal and radial epicyclic frequencies and use them as kinematical inputs for relativistic-precession and resonance prescriptions for quasi-periodic oscillations. Finally, we relate the Lyapunov exponent of unstable circular orbits to the local separatrix structure governing near-homoclinic zoom--whirl motion. The resulting formulation provides a compact analytic connection between linear-in-spin MPD dynamics, periodic-orbit taxonomy, epicyclic-frequency shifts, and transient strong-field phenomenology in a nonrotating black-hole background. Also, we study the gravitational waveforms from the periodic orbits of a massive spinning particle around a black hole, presenting those associated with extreme mass-ratio inspirals involving a stellar-mass compact spinning object orbiting a supermassive black hole.

gr-qc↗

arXiv2026

Ringdown modulation of acceleration radiation in the Schwarzschild background

We derive an analytic first-order description of how Schwarzschild ringdown affects a detector-based detailed-balance diagnostic in a near-horizon, single-mode setting. A freely falling two-level system couples to a cavity-filtered outgoing mode of fixed asymptotic frequency, whose static Schwarzschild response gives geometric photon statistics and a detailed-balance ratio governed by the surface gravity. We perturb this baseline by an even-parity, axisymmetric quadrupolar quasinormal mode and work in ingoing Eddington-Finkelstein coordinates, regular at the future horizon. The perturbation shifts the outgoing eikonal through the double-null contraction of the metric perturbation along the outgoing congruence. After fixing the residual endpoint phase calibration on the cavity worldtube, this redshift-map deformation induces a first-order decaying-oscillatory correction to the detector detailed-balance exponent at the quasinormal frequency. We express the geometric response through a closed boundary formula at the sampling radius and state the adiabatic, narrowband, and linear-response conditions under which the result applies. Detector details, including the gap, switching, and wavepacket profile, enter only through a smooth prefactor, while the ringdown dependence is carried by the quasinormal frequency and calibrated response coefficient. The modulation vanishes in the zero-amplitude, late-time, and stationary quadrupolar limits. The result is not a modification of the Hawking temperature, global Hawking flux, or dynamical horizon thermality, but a controlled correction to an operational detector/cavity detailed-balance observable.

gr-qc↗

arXiv2026

Near extremal RN-AdS control of holographic Josephson transport

We formulate a holographic weak-link construction in which Josephson transport is controlled by the charge sector of a Reissner--Nordstrom-AdS black brane. The model is an Einstein-Maxwell-charged-scalar theory in asymptotically AdS$_4$, with a spatially inhomogeneous boundary chemical potential that creates two superconducting banks separated by a normal or weakly superconducting barrier. The Josephson phase difference is defined from gauge-invariant boundary observable of the charged condensate, rather than from the black hole charge itself, allowing a controlled extension of the standard holographic SNS junction to charged AdS backgrounds. We identify the current-phase relation, critical current, coherence length, and small-phase stiffness as the main observables. In the SNS regime, the critical current and midpoint condensate probe the same proximity scale, while higher harmonics in the current-phase relation diagnose enhanced transparency or departure from the opaque weak-link limit. The new mechanism is the near-extremal RN-AdS throat: as extremality is approached, the emergent AdS$_2\times\mathbb{R}^2$ region can radially modify the Josephson coupling before it reaches the ultraviolet boundary. After removing the ordinary spatial suppression due to the junction width, the residual critical current and phase stiffness are expected to exhibit scaling governed by the infrared dimension of the charged scalar in AdS$_2$. This separates ordinary proximity suppression, smooth finite-density corrections, and genuinely near-extremal throat control, providing a framework for phase-sensitive transport in charged holographic matter.

hep-th↗

arXiv2026

Breaking Parameter Degeneracies in a Magnetically Charged Black Hole Embedded in a Hernquist Dark-Matter Halo: A Multi-Observable Analysis

We study the degeneracy of intrinsic and environmental parameters for BH observables in a static spacetime sourced by a nonlinear magnetic monopole immersed in a Hernquist dark-matter halo. We explore four complementary probes; the shadow radius $R_{sh}$, eikonal quasinormal-mode frequencies $Mω_R$, weak gravitational lensing $\hatθ_\infty$, and neutrino-antineutrino annihilation $\dot{Q}/\dot{Q}_{Newt}$, and map their degeneracy contours in the $(g/\mathcal{M},α/\mathcal{M})$ plane at fixed $β/\mathcal{M}$. Different parameter combinations yield signatures nearly indistinguishable from a Schwarzschild black hole single-observable diagnostics cannot uniquely constrain the magnetic charge and halo amplitude. The degeneracy contours are, however, mutually non-parallel: the slopes $dα/dg$ along constant-$R_{sh}$ and constant-$Mω_R$ contours differ by a factor $\sim 5$, so their combination breaks the remaining degeneracy and constrains both parameters simultaneously. We compute the QNMs spectra using a high-order WKB method with Padé resummation. The magnetic charge raises the real oscillation frequency while the halo lowers it; the cancellation is observable-dependent and does not persist across all four channels. An expansion around an asymptotically renormalized Schwarzschild background of mass $\mathcal{M}=M+α$ shows that at fixed $\mathcal{M}$ both sectors reduce $R_{sh}$ at first perturbative order. For weak lensing, $\mathcal{M}$ alone determines the leading deflection, first subleading correction depends on $\mathcal{Q}=g^2+4αβ$, separating total halo mass from halo concentration. For neutrino-pair annihilation, the magnetic charge suppresses the deposition rate by raising the lapse, while the halo enhances it through the reverse mechanism.

gr-qc↗

arXiv2026

Josephson's effect in the Schwarzschild background

We develop a fully covariant, analytic framework for Josephson phenomena in static curved spacetimes and specialize it to the Schwarzschild exterior. The formulation rests on two invariant elements: the gauge-invariant condensate momentum that governs phase dynamics and the conserved current whose hypersurface flux encodes transport for an observer at infinity. Using the timelike Killing field to relate proper and asymptotic quantities, we derive a redshifted AC Josephson law in which the asymptotic phase-evolution rate is proportional to the difference of redshifted voltage drops, i.e. to $V_i^\infty \equiv α_i V_i^{\rm proper}$; equivalently, it depends on $α_i V_i^{\rm proper}$ for local control. Under RF drive specified at infinity, the Shapiro-step loci are invariant (expressed in asymptotic voltages) while propagation phases set any apparent lobe translation. For DC transport, a short-junction solution on a static slice yields the proper current-phase relation; mapping to asymptotic observables gives a single-power redshift scaling of critical currents, $I_{c,\infty}\propto αI_c^{\rm proper}$, whereas power scales as $P_\infty\propto α^2 P_{\rm proper}$. In a "vertical" dc-SQUID with junctions at different radii, gravity does not shift the DC interference pattern at linear order; it produces a small envelope deformation and an amplitude rescaling. Gravity does not alter the local Josephson microphysics; it reshapes the clocks and energy accounting that define measurements at infinity. The resulting predictions are gauge- and coordinate-invariant, operationally stated in terms of an experimenter who can control (proper vs. asymptotic bias), and remain analytic from the weak-field regime to the near-horizon limit.

hep-th↗

arXiv2026

Semi-Analytic Trajectory Analysis of Light in Generic Static Spacetimes

We study a unified semi-analytical framework to study null geodesics and weak-field light deflection in generic static, spherically symmetric spacetimes of the form $ds^2 = -α(r,δ)\,dt^2 + γ(r,δ)\,dr^2 + β(r,δ)\,dΩ_2^2,$ where $α$, $β$, and $γ$ encode model-dependent deviations from Schwarzschild gravity inspired from [Phys.Rev.D 112 (2025) 12, 124072]. Starting from the exact first-order orbit equation, we derive a compact master equation for the impact-parameter-dependent trajectory $u(φ)\equiv 1/r(φ)$ and obtain a model-independent expression for the bending angle $α(b)$ in terms of generic metric functions and their derivatives. This master equation is then solved semi-analytically by three complementary techniques: (i) the homotopy perturbation method (HPM), (ii) the variational iteration method (VIM), and (iii) a calibrated impulse (single-kick) approximation expressed directly in terms of the effective gravitational potential. As nontrivial test beds we consider a scalar-hairy Reissner-Nordström-like black hole where the scalar hair enters as $Q_s$ in an effective charge parameter. Then we derive closed-form expressions for the deflection angle, identify the leading scalar-hair, and compare the accuracy and convergence properties of HPM, VIM, and the impulse method against the standard Schwarzschild limits. Our results show that the generic formulation in $(α,β,γ)$ can efficiently accommodate a broad class of modified gravity black hole solutions. We further supplement the analytic treatment with a compact numerical results against the exact null-geodesic integral near the photon sphere in order to delineate the practical range of validity of the three approximation schemes.

gr-qc↗

arXiv2026

Boundary-only weak deflection angles from isothermal optical geometry

We develop a boundary only method for computing weak gravitational deflection angles at finite source and receiver distances within the Gauss-Bonnet theorem formulation of optical geometry. Exploiting the fact that the relevant equatorial optical manifold is two dimensional, we introduce isothermal (conformal) coordinates in which the optical metric is locally conformal to a flat reference metric and the Gaussian curvature reduces to a Laplacian of the conformal factor. Such an identity converts the curvature area term in the Gauss-Bonnet theorem into a pure boundary contribution via Green/Stokes-type relations, yielding a deflection formula that depends only on boundary data and controlled closure terms. The residual normalization freedom of the isothermal radius is isolated as an additive freedom in the conformal factor and is shown to leave physical observables invariant, eliminating the need for orbit dependent calibration prescriptions. We explicitly implement the boundary only formalism in weak deflection, where the leading bending reduces to elementary one-dimensional integrals evaluated on a flat reference ray in the conformal plane, with finite distance dependence entering solely through endpoint data. We validate the construction by reproducing finite distance weak deflection for Schwarzschild, deriving the leading finite distance charge correction for Reissner-Nordström, and applying the same boundary only framework to the Kottler (Schwarzschild-de Sitter) geometry as a representative non-asymptotically flat test case, recovering the standard finite distance expansion including the explicit $\mathcal{O}(Λ)$ and mixed $\mathcal{O}(ΛM)$ contributions to the total deflection angle.

gr-qc↗