The Intrinsic Derivative and Centrifugal Forces in General Relativity: II. Applications to Circular Orbits in Some Familiar Stationary Axisymmetric Spacetimes

Abstract

The tools developed in a preceding article for interpreting spacetime geometry in terms of all possible space-plus-time splitting approaches are applied to circular orbits in some familiar stationary axisymmetric spacetimes. This helps give a more intuitive picture of their rotational features including spin precession effects, and puts related work of Abramowicz, de Felice, and others on circular orbits in black hole spacetimes into a more general context.

Poynting-Robertson effect as a dissipative system in general relativity

“…Robertson [20,21], we write the equations of motion first in the test particle rest frame and then in the static observer frame located at infinity. To this aim, we exploit the relativity of observer splitting formalism, which represents a powerful method in GR to distinguish the gravitational effects from the fictitious forces arising from the relative motion of two noninertial observers [27,[29][30][31]. Such formalism allows us to derive the test particle equations of motion in the reference frame of the static observer located at infinity as a set of coupled first order differential equations [22][23][24][25].…”

Position determination and strong field parallax effects for photon emitters in the Schwarzschild spacetime

“…(24) Recalling that ℓ 1 = r 0 cos β 1 , ℓ 1 = r 0 cos β 2 , one obtains r * = cos 2 β 1 + cos 2 β 2 − 2 cos β 1 cos β 2 cos δ 12 | sin δ 12 | .…”

“…Note that the intrinsic curvature of this circular orbit in the curved Schwarzschild spacetime can be described in terms of the associated Lie relative curvature and radius of curvature defined in [11,12] …”

Scattering by a Schwarzschild black hole of particles undergoing drag force effects

“…to form a spacetime orthonormal tetrad. The observers n can be used to decompose the particle's 4-velocity as [14,15,16]…”