Armando Andrés Roque Estrada

We investigate a representative set of static solitonic solutions of the Einstein–Proca theory in the Newtonian regime, where the field frequency approaches the particle mass, ω → μ , and compare them with the corresponding solutions of the spin-1 Schrödinger–Poisson system, which provides the effective description in this limit. While this correspondence is relatively straightforward in the Einstein–Klein–Gordon case, the vector nature of the Proca field and the emergence of an enhanced U ( 3 ) symmetry in the nonrelativistic spin-1 limit give rise to several nontrivial features that require careful analysis. We establish a mapping between the two descriptions by identifying ℓ = 0 electric Proca stars with radially polarized (hedgehog) configurations and ℓ = 1 electric Proca stars with linearly polarized configurations. We further clarify some aspects of the ground state and resolve several apparent discrepancies between relativistic and Newtonian solutions, particularly concerning their morphology and stability properties. An important conclusion of this work is that the nonrelativistic regime supports a richer spectrum of stable equilibrium configurations than the relativistic theory, including stable excited states.

In this paper, we study the linear stability of self-interacting boson stars in the nonrelativistic limit of the Einstein-Klein-Gordon theory. For this purpose, based on a combination of analytic and numerical methods, we determine the behavior of general linear perturbations around the stationary and spherically symmetric solutions of the Gross-Pitaevskii-Poisson system. In particular, we conclude that ground state configurations are linearly stable if the self-interaction is repulsive, whereas there exists a state of maximum mass that divides the stable and the unstable branches in case the self-interaction is attractive. Regarding the excited states, they are in general unstable under generic perturbations, although we identify a stability band in the first excited states of the repulsive theory. This result is independent of the mass of the scalar field and the details of the self-interaction potential, and it is in contrast to the situation of vanishing self-interaction, in which excited states are always unstable.

The gravitational deflection of light is a critical test of modified theories of gravity. A few years ago, Gibbons and Werner introduced a definition of the deflection angle based on the Gauss–Bonnet theorem. In more recent years, Arakida proposed a related idea for defining the deflection angle in non-asymptotically flat spacetimes. We revisit this idea and use it to compute the angular difference in the Kottler geometry and a non-asymptotically flat solution in Horndeski gravity. Our analytic and numerical calculations show that a triangular array of laser beams can be designed so that the proposed definition of the deflection angle is sensitive to different sources of curvature. Moreover, we find that near the photon sphere, the deflection angle in the Horndeski solution is similar to its Schwarzschild counterpart, and we confirm that the shadows seen by a static observer are identical.

The manuscript proposes some analytical solutions for a Kantowski-Sachs metric in the context of the General-Relativity (GR). In my opinion, the present version must be reviewed in detail by the author (or equivalently not continue as an online versi...