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We show that the Casimir effect should be influenced by variations of the gravitational potential. This could be tested with a satellite in a highly elliptic orbit. Still significant technology development is required to achieve a relative accuracy of $<5\times 10^{-10}$ necessary to detect the effect around Earth. That may be obtained in the future based on recent concepts for giant Casimir forces. Such a space mission could evaluate both the laws of gravitation and quantum mechanics and their interaction. A dedicated mission, Gravity-Probe C (GP-C), is proposed.

Recently, Harko et al. [Phys. Rev. D88, 044032 (2013)] have derived an exact solution of the spherically symmetric field equations in EiBI gravity, describing a compact star with decreasing pressure but increasing energy density. We have explored some features of this solution by restricting the range of the parameter $\kappa$ which satisfies four energy conditions for 10 equation of states (EOSs). Viability and deviations of these features in the light of updated observed properties of neutron stars (NS) have been explored completely. A comparison of those features with recent observations may uncover the future implication of this paper. Analysis of our results indicates that this solution may be used as an alternative EOS.

The redshift of the spectral lines of electromagnetic radiation of a binary star that moves in the vicinity of a supermassive black hole is considered. An approach for the reconstruction of the relative motion of the components of the binary using observational data of redshift is proposed.

General relativity (GR) is an important theory that requires very stringent tests. So far, its supporting evidence comes mainly from measurements of photon gravitational effects, including light bending near the Sun, gravitational lensing in some galaxies and gravitational redshift of light. These previous experiments were designed based on a hidden assumption, namely, the gravitational mass of a photon is zero; thus, light should not be bent in a gravitational field if there is no space-time curving. In this work, we showed that the gravitational mass of a photon is not zero. Instead, it is equal to its quantum mass, which can be determined from its momentum using the de Broglie relation. Based on this understanding, the gravitational effects of light can be explained more simply using quantum physics. Our findings suggest that, in order to fully evaluate the theory of GR, more stringent experimental tests are required. Some examples of future experiments for testing the principle of equivalence are proposed here.

There are discernible and fundamental differences between clocks, waves and physical states in classical physics. These fundamental concepts find a common expression in the context of quantum physics in gravitational fields; matter and light waves, quantum states and oscillator clocks become quantum synonymous through the Planck–Einstein–de Broglie relations and the equivalence principle. With this insight, gravitational effects on quantum systems can be simply and accurately analyzed. Apart from providing a transparent framework for conceptual and quantitative thinking on matter waves and quantum states in a gravitational field, we address and resolve with clarity the recent controversial discussions on the important issue of the relation and the crucial difference between gravimetery using atom interferometers and the measurement of gravitational time dilation.

The properties of the massive neutron star PSR J0348+0432 is calculated in the framework of the relativistic mean field (RMF) theory by choosing the suitable hyperon coupling constants. It is found that the central energy density ϵ_c and the central pressure p_c of the massive neutron star PSR J0348+0432 respectively are 1.5 times larger and 3.6 times larger than those of the canonical mass neutron star. It is also found that in the neutron star PSR J0348+0432 there are five kinds of baryons appearing: n, p, Λ, Ξ^- and Ξ⁰ but in the canonical mass neutron star there are only three kinds of particles appearing: n, p and Λ. In our models, the positive well depth will restrict the production of the hyperons Σ^-, Σ⁰ and Σ⁺ and therefore either in the neutron star PSR J0348+0432 or in the canonical mass neutron star the hyperons Σ^-, Σ⁰ and Σ⁺ all do not appear. In addition, our results also show that the radius R of the massive neutron star PSR J0348+0432 is less than that of the canonical mass neutron star while the gravitational redshift of the former is larger than that of the latter.

The structure of a magnetized quark-hybrid stars (QHS) is modeled using a standard relativistic mean-field equation of state (EoS) for the description of hadronic matter. For quark matter we consider a bag model EoS which is modified perturbatively to account for the presence of a uniform magnetic field. The mass-radius (M-R) relationship, gravitational redshift and rotational Kepler periods of such stars are compared with those of standard neutron stars (NS).

The relativistic Lagrangian in presence of potentials was formulated directly from the metric, with the classical Lagrangian shown embedded within it. Using it we formulated covariant equations of motion, a deformed Euler–Lagrange equation, and relativistic Hamiltonian mechanics. We also formulate a modified local Lorentz transformation, such that the metric at a point is invariant only under the transformation defined at that point, and derive the formulae for time-dilation, length contraction, and gravitational redshift. Then we compare our formulation under non-relativistic approximations to the conventional ad hoc formulation, and we briefly analyze the relativistic Liénard oscillator and the spacetime it implies.

We consider the analytical Bonnor solution for a relativistic neutron star and discuss about the limit in which this solution satisfies Einstein-Maxwell equations. We study the gravitational redshift for Bonnor solution without electric charge. We find that for stars with magnetic fields up to $10^{16}\mathrm{\text{G}}$ in the center, the gravitational redshift for Bonnor metric differs from the Schwarzschild solution on a term that depends on magnetic dipole moment and the polar angle of the emission signal.

The problem of calculating the redshift of electromagnetic spectrum of the star, moving in the vicinity of Schwarzschild black hole is solved within the framework of the General Theory of Relativity. The inverse problem — determination the parameters of the motion of a star from observational data of redshift is considered. The approach that gives possibilities to solve the inverse problem is proposed. The approach is tested on the numerical model that gives possibilities to calculate redshift as function of time of observation for a star moving in the vicinity of Schwarzschild black hole. The parameters of the star in numerical model are close to parameters of the S-stars, moving in the vicinity of the Sgr A*.

A test of a cornerstone of general relativity, the gravitational redshift effect, is currently being conducted with the RadioAstron spacecraft, which is on a highly eccentric orbit around Earth. Using ground radio telescopes to record the spacecraft signal, synchronized to its ultra-stable on-board H-maser, we can probe the varying flow of time on board with unprecedented accuracy. The observations performed so far, currently being analyzed, have already allowed us to measure the effect with a relative accuracy of 4 × 10⁻⁴. We expect to reach 2.5 × 10⁻⁵ with additional observations in 2016, an improvement of almost a magnitude over the 40-year old result of the GP-A mission.