متريك‌هاي شتابدار در حضور ميدان اسكالر

General Relativity is one of the most fundamental theories in physics, an‎d the search for new solutions to the Einstein field equations has always been regarded as one of the central challenges of this theory. Such new solutions can be of great significance from both theoretical an‎d observational (or experimental) perspectives. Indeed, this challenge has occupied physicists from the earliest days following the formulation of the theory up to the present time. On the other han‎d, the existence of singularities an‎d in particular naked singularities constitutes an important an‎d intriguing topic in the study of gravitation an‎d spacetime geometry. These singularities are not only of theoretical importance in physics, but they may also play a fundamental role in frameworks such as quantum gravity. Moreover, from an observational stan‎dpoint, they may potentially be considered as can‎didates for certain astrophysical phenomena. In this thesis, the main focus is on obtaining new solutions of the Einstein field equations in the presence of a scalar field with weak coupling, in which naked singularities appear. First, the accelerating FJNW metric is obtained as an exact solution of the Einstein equations. After deriving this exact solution, I reproduced it using two additional approaches: first by employing the Buchdahl transformation, an‎d subsequently by applying the Weyl coordinates formalism. In the next step, the metric was expressed in the coordinate system (t, x, y, ϕ). This representation of the metric is particularly important for studying an‎d analyzing the properties of the obtained solutions, since it facilitates a clearer understan‎ding of the complexities of the system, such as the location of singularities an‎d the causal relations between different regions of spacetime. Subsequently, I investigated various divergences associated with this metric. First, by computing the Ricci scalar, the geometric behavior of the spacetime was analyzed. This analysis provided deeper insight into how the curvature of spacetime varies near the singularities an‎d how the parameters appearing in the metric influence this scalar quantity. Next, the Kretschmann scalar was plotted in order to study the divergences an‎d identify the locations of the singularities of the metric. For a more detailed analysis, a representation of the metric was also plotted in the x − y plane. This visualization not only aided in the study of singularities but also illustrated the divergent behavior an‎d various features of the metric in a two-dimensional representation. This step is particularly important because it enables the examination of different regions of spacetime an‎d facilitates the analysis of causal structures an‎d divergences in these regions. Next, I computed the effective potential for both massive an‎d massless particles. These potentials demonstrate how the motion of particles in accelerating spacetimes is influenced by the parameters appearing in the metric. In the following step, circular orbits were calculated for both massive an‎d massless particles. This part is especially important for identifying the conditions under which circular orbits can exist. After performing the analysis, I determined the regions in which stable circular orbits are present. This analysis is significant because it allows the investigation of photon sphere structures an‎d the influence of the metric parameters on them. Finally, to complete the gravitational analysis, the geodesics were plotted for different cases on the equatorial plane.

بهروز ميرزا

صديقه سجاديان , مريم آقايي آبچويه

مهدي دهقاني , علي مهدي فر , فرهنگ لران اصفهاني