Elham Nazari

In General Relativity (GR), both branches of the conservation law ∇μTμν = 0 involve the samecombination, the inertial mass density (IMD) I = ρ+p. In cosmology, it can be probed only through the energy-conservation branch, where its parametrization underlies dynamical dark-energy models, whereas in the momentum-conservation branch it is the quantity multiplying the acceleration. Motivated by this consideration, we develop a relativistic generalized-inertia (RGI) framework to the first post-Newtonian (PN) order, in which the inertial response of matter is generalized but the gravitational dynamics of GR remain unchanged. The contributions of pressure and gravitational self-energy to the PN inertial mass density are weighted by two phenomenological parameters, α and β. It is shown that this generalization results in a difference between the inertial, passive, and activegravitational masses and gives rise to a kinematic Nordtvedt effect and momentum non-conservation. We place limits on these parameters by means of Lunar Laser Ranging and by using observations of binary and triple millisecond pulsars, along with constraints derived from linear-momentum conservation. We then investigate the implications of the framework for galactic dynamics.

We present the structure of a low angular momentum accretion flows around rotating compact objects incorporating relativistic corrections up to the leading post-Newtonian order. To begin with, we formulate the governing post-Newtonian hydrodynamic equations for the mass and energy-momentum flux without imposing any symmetries. However, for the sake of simplicity, we consider the flow to be stationary, axisymmetric, and inviscid. Toward this, we adapt the polytropic equation of state (EoS) and analyze the vertically integrated accretion flow confined to the equatorial plane. It is shown that the spin-orbit effects manifest themselves in the accretion dynamics. In the present analysis, we focus on global transonic accretion solutions, where a subsonic flow enters far away from the compact object and gradually gains radial velocity as it moves inwards. Thus, the flow becomes supersonic after reaching a certain radius, known as the critical point. To better understand the transonic solutions and examine the effect of post-Newtonian corrections, we classify the post-Newtonian equations into semi-relativistic (SR), semi-Newtonian (SN), and non-relativistic (NR) limits and compare the accretion solutions and their corresponding flow variables. With these, we find that SR and SN flow are in good agreement all throughout, although they deviate largely from the NR ones. Interestingly, the density profile seems to follow the profile ρ ∝ r ^-3/2 in the post-Newtonian regime. The present study has the potential to connect Newtonian and GR descriptions of accretion dynamics.

In this paper, we study the gravitational-wave (GW) radiation and radiative behavior of relativistic compact binary systems in the scale-independent energy-momentum squared gravity (EMSG). The field equations of this theory are solved approximately. The gravitational potential of a gravitational source is then obtained by considering two matter Lagrangian densities that both describe a perfect fluid in general relativity (GR). We derive the GW signals emitted from a compact binary system. The results are different from those obtained in general relativity (GR). It is shown that the relevant non-GR corrections modify the wave amplitude and leave the GW polarizations unchanged. Interestingly, this modification depends on the choice of the matter Lagrangian density. This means that for different Lagrangian densities, this theory presents different predictions for the GW radiation. In this case, the system loses energy to modified GWs. This leads to a change in the secular variation of the Keplerian parameters of the binary system. In this work, we investigate the non-GR effects on the radiative parameter, i.e., the first time derivative of the orbital period. Next, applying these results together with GW observations from the relativistic binary systems, we constrain/test the scale-independent EMSG theory in the strong-field regime. After assuming that GR is the valid gravity theory, as a priori expectation, we find that the free parameter of the theory is of the order 10⁻⁵ from the direct GW observation, the GW events GW190425 and GW170817, as well as the indirect GW observation, the double pulsar PSR J0737−3039A/B experiment.