Abstract
Formulation of the Lagrangian approach is presented for studying features of motions of stellar bodies with non-zero rest mass in the vicinity of fast-spinning black holes. The structure of Lagrangian is discussed. The general method is applied to description of body motion in the Kerr model of space–time to transition to the problem of tidal disruption of elastic bodies by a strong gravitational field.
Highlights
In contrast to the well-known ray-method for describing motion of both photon and “test body”—an idealized conceptualization of a material object with non-zero but small mass—we formulate a step-by-step Lagrangian approach that describes the motion of the test body with non-zero rest mass, and describes interactions of test-like bodies in a multi-body system, for example, a system of interacting bodies moving in a given strong gravitational field
One vivid example of its importance comes from the astronomical observations showing that at the center of our galaxy a super-massive black hole significantly affects the dynamics of nearby stars
The geometry of space–time in the vicinity of mass M rotating with angular momentum Jh is described by the Kerr metric
Summary
In contrast to the well-known ray-method for describing (in non-flat space–time) motion of both photon and “test body”—an idealized conceptualization of a material object with non-zero but small mass (not perturbing space–time around it)—we formulate a step-by-step Lagrangian approach that describes the motion of the test body with non-zero rest mass (obviously, it must move along a geodesic), and describes interactions of test-like bodies in a multi-body system, for example, a system of interacting bodies moving in a given strong gravitational field. One vivid example of its importance comes from the astronomical observations showing that at the center of our galaxy a super-massive black hole significantly affects the dynamics of nearby stars (see Figure 1). This black hole is apparently one of the closest such objects to us. The importance of the task of formulating the proper procedure for describing motions of bodies, both non-deformable and such that can be torn apart by tidal forces, is apparent.
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