We propose a non-metastable de-Sitter infinitesimal patch as a replacement for the theoretical singularity that occurs during the description of maximally extended Schwarzschild Anti-de Sitter spacetimes. This corresponds to a highly non-perturbative modification of the entangled sector or a dual thermofield double state. We speculate that the de-Sitter core may alter late-time correlators, regulate divergences, and appear as a deformation in the growth of holographic complexity. The description involves a copy of the conformal field theory associated with Israel Junction conditions and an entangled state. We also discuss a version of the possible solution of the Page Curve via. The evaporation of non-metastable space its range of impact in its solution.

The radio detection of very inclined air showers offers a promising avenue for studying ultra-high-energy cosmic rays (UHECRs) and neutrinos. Accurate reconstruction methods are essential for investigating the properties of primary particles. Recently, we developed an analytical least-squares method to reconstruct the electric field using three polarization components. The reconstruction yields no bias, with a 68\% confidence interval of [-0.02, 0.02], and a standard deviation of 0.04. Using this reconstructed electric field, we perform a realistic reconstruction of the the properties of primary particles. We employ a spherical wave model combined with an angular distribution function (ADF) for arrival direction reconstruction, achieving an angular resolution of 0.04$^\circ$. This paper also presents an energy reconstruction in which we account for the effects of geosynchrotron radiation in inclined air showers, we implement an air density correction in the energy reconstruction, resulting in a 10\% resolution in energy estimation. These findings demonstrate the reliability and effectiveness of our reconstruction methodology, paving the way for future detection experiments using sparse antenna arrays.

First-principles density functional theory (DFT) is used to investigate the electronic and magnetic properties of Sr$_4$Rh$_3$O$_{10}$, a member of the Ruddlesden-Popper series. Based on the DFT calculations taking into account the co-operative effect of Coulomb interaction ($U$) and spin-orbit couplings (SOC), Sr$_4$Rh$_3$O$_{10}$ is found to be a half metallic ferromagnet (HMF) with total angular moment $\mu_{\rm {tot}}$=12$\mu_B$ per unit cell. The material has almost 100$\%$ spin-polarization at the Fermi level despite of sizable SOC. Replacement of Rh atom by the isovalent Co atom is considered. Upon full-replacement of Co, a low-spin to intermediate spin transition happens resulting in a HMF state with the total angular moment three-time larger (i.e. $\mu_{\rm {tot}}$=36$\mu_B$ per unit cell), compared to Sr$_4$Rh$_3$O$_{10}$. We propose Sr$_4$Rh$_3$O$_{10}$ and Sr$_4$Co$_3$O$_{10}$ as candidates of half metals.