We connect finite-distance Gauss–Bonnet lensing to a boundary wave response in asymptotically anti-de Sitter spacetime. Reference subtraction retains local incidence angles and displacement of the optical-curvature domain. The pure-AdS reference becomes degenerate at conformal infinity, making fixed-endpoint matching nonuniform even for weak deflection. Comparison at fixed conserved impact parameter instead yields a regular scattering characteristic on weak returning branches. For Reissner–Nordström–AdS, we reconstruct this characteristic from the curvature angle and test it against direct ingoing solutions of the conformally coupled scalar equation. An exact boundary relation fixes the first-return amplitude without a fitted normalization. Independent optical Jacobi equations recover both angular focusing directions. Gaussian-filtered boundary profiles from the wave equation agree with optical-phase harmonic sums, with relative complex errors decreasing from [Formula: see text] to [Formula: see text] over a fourfold frequency increase in the reported example. We distinguish this geometric-optics convergence from weak-field phase truncation, whose error grows with frequency.
The pre-big bang scenario describes a dilaton-driven phase emerging from the perturbative string vacuum and preceding the standard hot big bang. Its lowest-order realization is, however, singular and drives the dilaton toward strong coupling. This review summarizes recent progress on two complementary aspects of the scenario. On the phenomenological side, string-phase modifications of scalar and tensor perturbations can generate primordial black holes and a stochastic gravitational-wave background, allowing to probe the structure of the high-curvature epoch. On the theoretical side, the all-order O(d, d) formulation organizes homogeneous α′ corrections and, through a Routhian description, provides simple conditions for regular bouncing solutions. Adding a non-perturbative dilaton potential can then stabilize the string coupling and lead to FLRW or de Sitter attractors, including from anisotropic initial conditions. Together, these results connect the graceful-exit problem with potentially observable relics of the string phase.
We generalize Wilczek’s pre-geometric gravity by incorporating a kinetic mixing term which, upon spontaneous symmetry breaking (SSB), gives rise to the Holst action, thereby providing a dynamical origin for the Barbero-Immirzi parameter. Torsion-mediated four-fermion interactions arise in the Higgsed phase, with their coupling strength controlled by pre-geometric parameters. An attractive channel permits fermion condensation via a gravitational Nambu-Jona-Lasinio (NJL) mechanism akin to BCS superconductivity. The pre-geometric gauge theory inherently supplies a UV completion that may cure unitarity problems plaguing effective four-fermion interactions. The Einstein Equivalence Principle is not automatically recovered, permitting species-dependent cutoffs with phenomenological consequences for neutrino physics, dark matter and dark energy. Our construction furnishes a unified account of the Immirzi parameter, fermion condensation, and early universe cosmology grounded in fundamental pre-geometric principles.
We construct charged anisotropic compact-star models in general relativity coupled to Euler-Heisenberg (EH) nonlinear electrodynamics. The radial metric potential is of Finch-Skea type, the radial pressure obeys the linear relation [Formula: see text], and the electric field is obtained from the EH field equation for an enclosed charge [Formula: see text], solved consistently to first order in the EH coupling [Formula: see text]. The interior is matched to the exterior EH-corrected Reissner-Nordström geometry, and the model constants are fixed by the measured mass [Formula: see text] of PSR J1614−2230 together with a fiducial radius of [Formula: see text] km. All quantities are given in geometrized units with lengths in km; the coupling [Formula: see text], which has dimensions of length squared, is treated as an effective parameter restricted by the perturbative condition [Formula: see text]. The fiducial configuration has a central density of about [Formula: see text], compactness [Formula: see text] and surface redshift [Formula: see text]. The solution is regular, satisfies the energy conditions and causality, and respects both the Buchdahl bound and its charged generalization. Inside the perturbative window the EH terms change the stellar structure only at the level of [Formula: see text], so that the electromagnetic sector acts as a small correction to an anisotropic configuration whose stiffness is controlled by the equation of state. Keeping the equation of state fixed and varying the central density, we construct the mass-radius sequence. Physically admissible configurations reach about [Formula: see text], the Abreu condition holds up to about [Formula: see text]–[Formula: see text], and [Formula: see text] along the admissible branch. A larger charge parameter slightly raises the maximum admissible mass but narrows the range in which the Abreu condition is met.
We investigate the thermodynamic behavior and extremal configurations of magnetically charged black holes in nonminimal Einstein-Yang-Mills theory, focusing on the interplay between nonminimal interactions, local stability, and thermodynamic topology. The derived mass and Hawking temperature recover the Reissner-Nordström-AdS results in the minimally coupled limit. However, integrating the first law leaves an entropy-normalization ambiguity, so conclusions based on entropy positivity remain conditional on the prescription adopted here. Our stability analysis distinguishes the extremal boundary from divergences in the heat capacity, which indicate singular local responses but do not independently establish a first-order phase transition. The topological analysis further shows that the winding number depends on both magnetic charge and pressure. Restricting the thermodynamic domain to positive entropy can alter the endpoint contribution, making a separate evaluation necessary. Regarding extremality, the asymptotically flat solution admits a positive extremal branch throughout the considered nonnegative coupling range, while the AdS case possesses a unique positive extremal radius under the stated conditions. The extremal mass increases with the nonminimal coupling, and its response remains finite at finite positive coupling but grows without bound in the large-coupling limit. These findings clarify the geometric and thermodynamic consequences of the nonminimal interaction without overstating their implications for quantum gravity. In particular, the extremality results alone neither establish nor rule out the magnetic Weak Gravity Conjecture, whose assessment requires a consistently normalized gauge sector and information about the spectrum of charged states.
