SPACE, TIME AND FUNDAMENTAL INTERACTIONS

SPHERICALLY SYMMETRIC SOLUTIONS OF THE CHIRAL SELF-GRAVITATING \(f(R, (\nabla R)^2)\) MODEL OF GRAVITY IN QUASI-GLOBAL COORDINATES

Chaadaev A.A.

We study spherically symmetric solutions of the chiral self-gravitating model \(f(R, (\nabla R)^2)\) of gravity in quasiglobal coordinates. The paper presents the action of the model and the metric of the chiral space. For this model,the equations of Einstein and fields are presented in a spherically symmetric metric of a general form with a selfaction potential \(W\), the equations of the model are presented in quasi-global coordinates. The special case \(W = 0\) is considered in the paper. Within the framework of this case, it is shown that the Einstein equations are reduced to a second-order differential equation that allows a change of variables for a combination of metric functions. Exact solutions are obtained for all metric functions. The possibility of solving field equations for determining the dependence of fields on the radial coordinate ?? is investigated. A non-linear second-order differential equation is obtained, which makes it possible to determine the field function \(\chi(u)\).