Universe

We investigated an exact solution in a conformal invariant Randall-Sundrum 5D warped brane world model on a time dependent Kerr-like spacetime. The singular points are determined by a quintic polynomial in the complex plane and fulfills Cauchy’s theorem on holomorphic functions. The solution, which is determined by a first-degree differential equation, shows many similarities with an instanton. In order to describe the quantum mechanical aspects of the black hole solution, we apply the antipodal boundary condition. The solution is invariant under time reversal and also valid in Riemannian space. Moreover, CPT invariance in maintained. The vacuum instanton solution follows from the 5D as well as the effective 4D brane equations, only when we allow the contribution of the projected 5D Weyl tensor on the brane (the KK-‘particles’). The topology of the effective 4D space of the brane is the projective $\mathbb{R}{P}^3$ (elliptic space) by identifying antipodal points on $S^3$. The 5D is completed by applying the Klein bottle embedding and the ${\mathbb{Z}}_2$ symmetry of the RS model. This model fits very well with the description of the Hawking radiation, which remains pure. We have also indicated a possible way to include fermions. Our 5D space admits a double cover of $S^3$ and after fibering to the $S^2$, we obtain the effective black hole horizon. The connection with the icosahedron discrete symmetry group is investigated. It seem that Bekenstein’s conjecture that the area of a black hole is quantized, could be applied to our model.

In this paper, we investigate the running vacuum energy (RVE) model within the framework of $f\left(Q\right)$ gravity ($f\left(Q\right)$-RVE). In this context, the modified Friedmann equation can be used to establish a formal analogy with the structure of the RVE. A key feature is that the vacuum equation of state is no longer fixed but receives a dynamical correction proportional to $\dot{H}$ and $\ddot{H}/H$. We consider two cases of $f\left(Q\right)$-RVE, denoted as Model I (parametrized by $\nu$) and Model II (parametrized by $\nu$ and $\alpha$), corresponding to the first and second derivatives of H, respectively. The models are constrained using recent DESI BAO data in combination with ${\mathrm{Pantheon}}^{+}$, cosmic chronometer (CC), and CMB observations. Our analysis shows a deviation of $\nu$ from zero at a significance level of ∼$1.4\sigma$ for Model I, while in Model II, $\nu$ and $\alpha$ deviate from zero at $0.7\sigma$ and $1.3\sigma$, respectively, relative to $\mathrm{\Lambda }$CDM. Furthermore, the statistical comparison based on the Akaike, Bayesian, and Deviance Information Criteria (AIC, BIC, DIC) indicates that Model I remains competitive with $\mathrm{\Lambda }$CDM, while Model II is penalized due to its higher complexity and the sensitivity associated with the additional parameter $\alpha$.

Black hole jets represent one of the most extreme manifestations of astrophysical processes, linking accretion physics, relativistic magnetohydrodynamics, and large-scale feedback in galaxies and clusters. Despite decades of observational and theoretical work, the mechanisms governing jet launching, collimation, and energy dissipation remain open questions. In this article, we discuss how upcoming facilities such as the Event Horizon Telescope (EHT), the Cherenkov Telescope Array (CTA), the Vera C. Rubin Observatory (LSST), and the Whole Earth Blazar Telescope (WEBT) will provide unprecedented constraints on jet dynamics, variability, and multi-wavelength signatures. Furthermore, we highlight theoretical challenges, including the role of magnetically arrested disks (MADs), plasma microphysics, and general relativistic magnetohydrodynamic (GRMHD) simulations in shaping our understanding of jet formation. By combining high-resolution imaging, time-domain surveys, and advanced simulations, the next decade promises transformative progress in unveiling the physics of black hole jets.