We propose a mechanism for symmetry breaking or restoration that can occur in the middle of inflation, due to the coupling of the Gauss–Bonnet term to a charged scalar. The Gauss–Bonnet coupling results in an inflaton-dependent effective squared mass of the charged scalar, which can change its sign (around the symmetric point) during inflation. This can lead to spontaneous breaking of the symmetry, or to its restoration, if it is initially broken. We show the conditions under which the backreaction of the Gauss–Bonnet coupling on the inflationary background is negligible, such that the predictions of a given inflationary model are unaffected by the symmetry breaking/restoration process.

A straightforward and fully analytic approach is introduced to examine how polytropic fluids influence arbitrary gravitational sources in static, spherically symmetric spacetimes. As a concrete application, we explore the internal mechanism of energy transfer between gravitational sources embedded within a self-gravitating system.

We here investigate the consequences of an exotic fluid, exhibiting negative radial and tangential pressures, \emph{de facto} violating the Zel'dovich limit, on a regular solution that easily generalizes the Schwarzschild black hole. More precisely, we focus on the regular Fan-Wang spacetime, computing how the black hole shadow images, surrounded by the quoted fluid, is modified through the presence of \emph{negative} equations of state for the two pressure components. Even though quite different from quintessence, we consider constant radial and tangential equations of state with the aim of emulating, but not reproducing, dark energy effects. Moreover, we explore the main properties of infalling spherical accretion flows and, accordingly, the influence of the equations of state on the horizons, photosphere, and impact parameter of the Fan-Wang black hole. Afterwards, we examine the luminosities of the shadow and the photon ring in two distinct spherically accretion flows, as well as the observed specific intensity of the shadow itself. Last but not least, we physically interpret the impact of negative pressures on our findings and discuss possible extensions to the isotropic case.

We consider a model problem of polarization-dependent light bending and time delays in the vicinity of neutron stars endowed with magnetar-strength magnetic fields (B∼${10}^{15}\mathrm{G}$), combining an effective-metric formulation of Heisenberg–Euler nonlinear electrodynamics with general-relativistic ray tracing. The spacetime geometry is analyzed using both the Kerr metric and a quadrupole-deformed q-metric, characterized by a quadrupole parameter varying in the range $q\in [{10}^{-3},0.5]$. In addition, the impact of complex magnetic-field topologies is examined by introducing a magnetic quadrupole component alongside the dipole configuration. The simulations performed in this study demonstrate that the inclusion of the quadrupole deformation parameter significantly modifies photon trajectory deflections compared to the standard Kerr solution. We further quantify the geometric dilution of the photon beam, finding a cross-section expansion ratio of approximately $4.7\times {10}^{13}$ for rays reaching Earth. This strong dilution imposes stringent constraints on the detectability of polarization-dependent signatures and time-delay echoes. Finally, characteristic illustrations are presented for trajectory distortions, bending-angle distributions, and intensity valleys produced by the combined gravitational and magnetic lensing effects.