arXiv subjects

Pham Van Ky

Publications and source records attributed to Pham Van Ky.

5 recordsLinked to original sources

arXiv2025

Nonstatic Reissner-Nordström metric in the perturbative $f(R)$ theory: Embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation

This article introduces a nonstatic Reissner-Nordström metric, a metric that does not emit electromagnetic waves but can emit gravitational waves. We first use the GR theory to study a charged spherically symmetric gravitational source (CSSGS), the obtained results are further improved in comparison with the previous studies. In particular, this article considers that the field is not necessarily static. The metric tensors $ g_{μν} $ are considered both outside and inside the gravitational source (the results show that in the first case $ g_{μν} $ are time independent, in the latter case they are time dependent). The gravitational acceleration and the event horizon of a charged black hole are investigated. The results prove that the gravitational field is always attractive. We then use the perturbative $ f(R) $ theory to consider CSSGS. The obtained results not only correct the solution of Einstein's equation in magnitude (this will describe astronomical and cosmological quantities more accurately than Einstein's equation), but also reveal new effects. Outside the gravitational source, the metric tensors can depend on time, this makes it possible for a spherically symmetric gravitational source to emit gravitational waves (Einstein's equation cannot give this effect). However, a spherically symmetric field still does not emit electromagnetic waves. Next we present a new method for embedding the spherically symmetric metrics of a star (or a black hole) in the background of the FLRW cosmological. Finally, we discuss the uniqueness of the solutions of the f(R) theory. The perturbative TOV equation is also found.

gr-qc↗

arXiv2024

Gravitational radiation of a spherically symmetric source in $f(R)$-gravitation

It is shown that Birkhoff's theorem for the general theory of relativity is overcome in the $f(R)$-theory of gravitation. That means, the $f(R)$-theory of gravitation, unlike Einstein's general theory of relativity, does not forbid gravitational radiation from a spherically symmetric source (whether stationary or non-stationary). As a consequence, in the $f(R)$-theory a spherically symmetric gravitational deformation (e.g., collapse/expansion or pulsation) could emit gravitational waves (of tensor- and scalar polarization modes), a phenomenon impossible in the general relativity. A test model is examined and it turns out that the gravitational radiation is strongest when the surface of the deforming object is in the vicinity of the (modified) event horizon, even suddenly flares up just outside the latter. In this letter, within the $f(R)$-theory of gravitation, a gravitational wave equation and a formula for the gravitational emission power are derived. These formulae, along with searching for signals, can be used for the experimental test of the $f(R)$-theory. In general, including the spherically symmetry case, gravitational radiation of both tensor- and scalar polarization modes are allowed, although under some circumstance the contribution of scalar modes is strongly suppressed.

gr-qc↗

arXiv2023

Perturbative approach to $f(R)$-gravitation in FLRW cosmology

The $f(R)$ theory of gravitation developed perturbatively around the general theory of relativity with cosmological constant (the \text{$Λ$}CDM model) in a flat FLWR geometry is considered. As a result, a general explicit cosmological solution that can be used for any model with an arbitrary, but well-defined, $f(R)$ function (just satisfying given perturbation conditions) is derived. This perturbative solution shows how the Hubble parameter $H (t)$ depends on time (along with the cosmological constant and the matter density) to adapt to the evolution of the Universe. To illustrate, this approach is applied to some specific test models. One of these models appears to be more realistic as it could describe three phases of the Universe's evolution. Despite the fact that the perturbation is applied for a flat FLWR geometry (according to the current cosmological observation) indicates that the obtained solution can mainly describe the evolution of the late Universe, it may also work for an early Universe. As a next step, the present method can be applied to the case with a more general FLRW geometry to increase the precision of the description of different stages in the evolution of the Universe. Finally, it is shown that in a desription of the Universe's evolution the perturbative $f(R)$-theory can be considered as an effective GR with the cosmological constant $Λ$ replaced by an effective parameter $ Λ_{eff}[ρ(t)] $. This trick leads to a simpler way of solving an $f(R)$-theory regardless its specific form.

gr-qc↗

arXiv2019

Testing the $f(R)$-theory of gravity

A procedure of testing the $f(R)$-theory of gravity is discussed. The latter is an extension of the general theory of relativity (GR). In order this extended theory (in some variant) to be really confirmed as a more precise theory it must be tested. To do that we first have to solve an equation generalizing Einstein's equation in the GR. However, solving this generalized Einstein's equation is often very hard, even it is impossible in general to find an exact solution. It is why the perturbation method for solving this equation is used. In a recent work \cite{Ky:2018fer} a perturbation method was applied to the $f(R)$-theory of gravity in a central gravitational field which is a good approximation in many circumstances. There, perturbative solutions were found for a general form and some special forms of $f(R)$. These solutions may allow us to test an $f(R)$-theory of gravity by calculating some quantities which can be verified later by the experiment (observation). In \cite{Ky:2018fer} an illustration was made on the case $f(R)=R+λR^2$. For this case, in the present article, the orbital precession of S2 orbiting around Sgr A* is calculated in a higher-order of approximation. The $f(R)$-theory of gravity should be also tested for other variants of $f(R)$ not considered yet in \cite{Ky:2018fer}. Here, several representative variants are considered and in each case the orbital precession is calculated for the Sun--Mercury- and the Sgr A*--S2 gravitational systems so that it can be compared with the value observed by a (future) experiment. Following the same method of \cite{Ky:2018fer} a light bending angle for an $f(R)$ model in a central gravitational field can be also calculated and it could be a useful exercise.

physics.gen-ph↗

arXiv2018

Perturbative solutions of the $f(R)$-theory of gravity in a central gravitational field and some applications

Exact solutions of an $ f(R) $-theory (of gravity) in a static central (gravitational) field have been studied in the literature quite well, but, to find and study exact solutions in the case of a non-static central field are not easy at all. There are, however, approximation methods of finding a solution in a central field which is not necessarily static. It is shown in this article that an approximate solution of an $f(R)$-theory in a general central field, which is not necessary to be static, can be found perturbatively around a solution of the Einstein equation in the general theory of relativity. In particular, vacuum solutions are found for $f(R)$ of general and some special forms. Further, applications to the investigation of a planetary motion and light's propagation in a central field are presented. An effect of an $f(R)$-gravity is also estimated for the SgrA*--S2 system. The latter gravitational system is much stronger than the Sun--Mercury system, thus the effect could be much stronger and, thus, much more measurable.

gr-qc↗