Ahdab K. Althukair | Searcharxiv

arXiv2026

C-infinity Compact-Support Wormholes with Exact Schwarzschild Exterior in Trace-Coupled Gravity

We study static, spherically symmetric traversable wormholes in trace-coupled gravity with action density f(R,T) = R + lambda T^2. The spacetime is built from C-infinity deformations of Schwarzschild that vanish identically outside a finite core, so the exterior is exactly Schwarzschild and no thin shell or junction surface is needed. Because f_R = 1, the metric equations remain second order and the matter problem reduces to a local algebraic reconstruction. For an anisotropic source, we derive unified inversion formulas for (rho, p_r, p_t) in terms of the effective source and the dimensionless trace variable chi = lambda T/(4 pi), and show that the admissible matter branch is the vacuum-connected real root of a cubic equation. The resulting parameter space contains regular positive-density and negative-density throat regimes, a critical boundary where the reconstruction degenerates, and a nonadmissible branch-failure sector. The geometry itself is branch-independent, but the reconstructed matter depends on the matter-Lagrangian prescription. On the admissible branch the radial NEC still fails at the throat, so the model localizes exoticity rather than removing it. The Ricci support and reconstructed matter remain confined to a finite interval, while the exterior tidal field is exactly Schwarzschild with ADM mass M. The results should be read as controlled existence and viability statements within the displayed ansatz families, not as a stability proof.

gr-qc↗

arXiv2026

Odd-parity perturbations of trace-quadratic $f(R,T)$ black holes with anisotropic matter: admissible branches, axial ringdown, and a coupled-PINN benchmark

We study odd-parity gravitational perturbations of static black holes in trace-quadratic $f(R,T)=R+αT^2$ gravity supported by an anisotropic effective fluid with constant closure parameters $(w_r,w_t)$. From the unreduced axial system and its principal symbol, we identify the sector of parameter space that supports a regular horizon, asymptotic flatness, and hyperbolic odd-sector evolution. Within this closure the admissible branch lies at negative $w_r$, while the commonly used positive-$w_r$ family fails the background regularity test and is kept only as a numerical comparison branch. On static admissible backgrounds the odd sector is exactly equivalent to Einstein gravity coupled to a frozen effective anisotropic fluid, so the physical axial spectrum is governed by a single gauge-invariant master equation. For the anchored branch $(w_r,w_t)=(-0.2,0.15)$ we compute the fundamental axial $\ell=2$ quasinormal mode with an exact Chebyshev solve. The mass-normalized spectrum differs from Schwarzschild by about $22\%$, whereas no statistically resolved direct $α$-dependence appears within the conservative spectral envelope over $0\le α/M^2\le 0.3$. We also construct a coupled physics-informed neural network for the unreduced two-field eigenproblem and use it to benchmark the inadmissible comparison branch. A closure-level audit of the anchored family shows positive diagnostic combinations associated with the null, weak, and dominant energy conditions, denominator safety in the modified balance law, and an effective exterior mass fraction of about $20\%$, while indicating that the constant-$(w_r,w_t)$ model should be read as an effective anisotropic stress rather than as a microphysical fluid. Within this closure, the main observable imprint in axial ringdown comes from the existence of the matter-supported branch itself, not from direct variation of the trace coupling.

gr-qc↗