TY - JOUR AU - Ky, Nguyen Anh AU - Ky, Pham Van AU - Van, Nguyen Thi Hong PY - 2019/02/05 Y2 - 2024/03/29 TI - Testing the \(f(R)\)-theory of Gravity JF - Communications in Physics JA - Comm. Phys. VL - 29 IS - 1 SE - Papers DO - 10.15625/0868-3166/29/1/13192 UR - https://vjs.ac.vn/index.php/cip/article/view/13192 SP - 35 AB - <pre>A procedure of testing the \(f(R)\)-theory of gravity is discussed. </pre><pre>The latter is an extension of the general theory of relativity (GR). </pre><pre>In order this extended theory (in some variant) to be really confirmed </pre><pre>as a more precise theory it must be tested. To do that we first have </pre><pre>to solve an equation generalizing Einstein's equation in the GR. </pre><pre>However, solving this generalized Einstein's equation is often very </pre><pre>hard, even it is impossible in general to find an exact solution. </pre><pre>It is why the perturbation method for solving this equation is used. </pre><pre>In a recent work <span>\cite</span>{Ky:2018fer} a perturbation method was applied </pre><pre>to the <span>$f(R)$</span>-theory of gravity in a central gravitational field which </pre><pre>is a good approximation in many circumstances. There, perturbative </pre><pre>solutions were found for a general form and some special forms of \(f(R)\). </pre><pre>These solutions may allow us to test an \(f(R)\)-theory of gravity by </pre><pre>calculating some quantities which can be verified later by the experiment </pre><pre>(observation). In <span>\cite</span>{Ky:2018fer} an illustration was made on the case </pre><pre><span>\(f(R)=R+\lambda R^2\)</span>. For this case, in the present article, the orbital </pre><pre>precession of S2 orbiting around Sgr A* is calculated in a higher-order </pre><pre>of approximation. The <span>$f(R)$</span>-theory of gravity should be also tested for </pre><pre>other variants of <span>$f(R)$</span> not considered yet in <span>\cite</span>{Ky:2018fer}. Here, </pre><pre>several representative variants are considered and in each case the </pre><pre>orbital precession is calculated for the Sun--Mercury- and the Sgr A*--S2 </pre><pre>gravitational systems so that it can be compared with the value observed </pre><pre>by a (future) experiment. Following the same method of <span>\cite</span>{Ky:2018fer} </pre><pre>a light bending angle for an <span>$f(R)$</span> model in a central gravitational field </pre><pre>can be also calculated and it could be a useful exercise.</pre> ER -