Universe

The classical Erlangen Program sought to classify metric spaces entirely in terms of their symmetries. In physical spacetimes, these symmetries define transformations between classical reference frames, yielding a one-to-one correspondence between frame transformations and the underlying geometry. More recently, the classical notion of an ideal frame has been extended to the quantum regime, by considering observers as embodied physical systems, subject to the laws of quantum mechanics. Here, we build on this approach, but outline an alternative definition of the term ‘quantum reference frame’, which differs somewhat from the mainstream view. We then show how the new definition can be used to construct a simple model of Planck-scale spacetime, which makes contact with existing quantum gravity phenomenology. Finally, we show how classical spacetime symmetries can be ‘mathematically preserved but operationally broken’ using the new model, suggesting that quantum spacetime may be classified, at least locally, in terms of transformations between quantised frames of reference. This work is based on a talk given at the 13th Bolyai–Gauss–Lobachevsky Conference on Non-Euclidean Geometry in Oujda, Morocco, in May 2025.

We investigate the spin-charge-induced scalarization of Kerr–Newman (KN) black holes in the Einstein–Maxwell-scalar (EMS) theory with a scalar potential and positive coupling parameter. In the linearized theory, there exists a bound of with onset spin $a_c$ for the negative region signaling instability by analyzing the effective scalar mass term in the $\theta$-direction. Solving the (2 + 1)-dimensional evolution equation numerically, we find the region where the KN black hole becomes unstable, giving rise to scalarized KN black holes. The threshold curve for representing the boundary between stable and unstable KN black holes depends on charge Q, scalar mass $m_{\varphi }$, coupling parameter $\alpha$, and spin parameter a with upper bound .

The Atomic Clock Ensemble in Space (ACES) mission, currently operating aboard the International Space Station (ISS), is designed to provide high-precision time and frequency measurements and to test fundamental aspects of relativistic physics. Gravitational redshift (GRS), a fundamental prediction of General Relativity (GR), implies that clocks positioned at different gravitational potentials experience relative time dilation. Previous GRS experiments have focused primarily on microwave technologies, with negligible experimental coverage in the optical domain, particularly for ground-to-space links. Motivated by the European Laser Timing (ELT) experiment and the high-precision laser-cooled cesium clock aboard ACES, we introduce and evaluate an optical time-transfer method designed to achieve high-accuracy measurements of GRS. In the absence of actual ELT/ACES optical data, a high-fidelity numerical simulation framework was developed to assess the performance of this method. The framework incorporates representative ELT/ACES mission parameters, including the space-based cesium clock and the H-MASER clock located at the reference ground station, both providing frequency stability at the level of ${10}^{-15}$ for 1000 s averaging time. Applying a $\pm 1\sigma$ filtering criterion, we obtain a simulated dataset comprising 33 ELT/ACES passes, representing a total observation time of 4.38 h over a single week. Analysis of this high-fidelity dataset reveals a GRS deviation from GR of $(-7.19\pm 0.63)\times {10}^{-5}$, achieving a 3.4 orders of magnitude improvement over the best previous laser-ranging experiment conducted at the University of Maryland (UMD), USA, 51 years ago. These simulation results demonstrate that the optical time-transfer link constitutes a powerful tool for testing fundamental physics and, when combined with next-generation optical atomic clocks, enables unprecedented capabilities in space-based timekeeping and geoscience applications.