This paper describes steady-state ensembles of thermally excited electromagnetic radiation in nano-scale layered media with a constant non-vanishing heat flux across the layers. It is shown that Planck's law of thermal radiation, the principle of equivalence, and the laws of wave propagation in layered media, imply that in order for the ensemble of thermally excited electromagnetic fields to exist in a medium consisting of a stack of layers between two half-space, the net heat flux across the layers must exceed a certain threshold that is determined by the temperatures of the half spaces and by the reflective properties of the entire structure. The obtained results provide a way for estimating the radiative heat transfer coefficient of nano-scale layered structures.

Superallowed β-decay strengths or corrected values provide some of the most stringent limits for physics beyond the standard three-quark model. For this reason, the -value ¹⁰C has been measured and found to be 3468.31(51) keV with the TITAN Penning trap mass spectrometer. The facility is unique in coupling such an online spectrometer to a charge breeder, permitting a mass measurement of another superallowed β-emitter, ⁷⁴Rb, in the 8+ charge state. An overview of the TITAN facility and recent highlights are presented alongside the new -value determination of ¹⁰C.

Microwave and submillimeter molecular transition frequencies between nearly degenerated rotational levels, tunneling transitions, and mixed tunneling-rotational transitions show an extremely high sensitivity to the values of the fine-structure constant, α, and the electron-to-proton mass ratio, μ. This review summarizes the theoretical background on quantum-mechanical calculations of the sensitivity coefficients of such transitions to tiny changes in α and μ for a number of molecules which are usually observed in Galactic and extragalactic sources, and discusses the possibility of testing the space- and time-invariance of fundamental constants through comparison between precise laboratory measurements of the molecular rest frequencies and their astronomical counterparts. In particular, diatomic radicals CH, OH, NH⁺, and a linear polyatomic radical C₃H in Π electronic ground state, polyatomic molecules NH₃, ND₃, NH₂D, NHD₂, H₂O₂, H₃O⁺, CH₃OH, and CH₃NH₂ in their tunneling and tunneling-rotational modes are considered. It is shown that sensitivity coefficients strongly depend on the quantum numbers of the corresponding transitions. This can be used for astrophysical tests of Einstein's Equivalence Principle all over the Universe at an unprecedented level of sensitivity of , which is a limit three to two orders of magnitude lower as compared to the current constraints on cosmological variations of α and μ: , .

The status of quantum cosmologies as testable models of the early universe is assessed in the context of inflation. While traditional Wheeler–DeWitt quantization is unable to produce sizable effects in the cosmic microwave background, the more recent loop quantum cosmology can generate potentially detectable departures from the standard cosmic spectrum. Thus, present observations constrain the parameter space of the model, which could be made falsifiable by near-future experiments.

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to alternative insights into the theory. The equivalence with the standard formulation in terms of the metric and curvature tensors takes place at the level of field equations. The review starts with a brief account of the history of teleparallel theories of gravity. Then the ordinary interpretation of the tetrad fields as reference frames adapted to arbitrary observers in space–time is discussed, and the tensor of inertial accelerations on frames is obtained. It is shown that the Lagrangian and Hamiltonian field equations allow us to define the energy, momentum and angular momentum of the gravitational field, as surface integrals of the field quantities. In the phase space of the theory, these quantities satisfy the algebra of the Poincaré group.

The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short-range behavior of the integrands around the sources. The Hamiltonian of a test-spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post-Newtonian approximate) Poincaré algebra are applied. Along the way a self-contained overview for the computation of the 3PN ADM point-mass Hamiltonian is provided, too.