Inertial forces in General Relativity

Spanish Relativity Meeting: almost 100 years after Einstein's revolution

Costa, L. Filipe O.^1 ; Natário, José^1

CAMGSD, Instituto Superior Técnico, Universidade de Lisboa, Portugal^1

关键词: General Relativity;    Gravitomagnetic field;    Inertial forces;    Newtonians;    Orthonormal frames;    Reference frame;    Spacetime;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/600/1/012053/pdf
DOI  :  10.1088/1742-6596/600/1/012053

来源: IOP

【 摘 要 】

An exact equation describing the inertial forces for arbitrary orthonormal frames on arbitrary spacetimes is presented. It manifests that the so-called gravitomagnetic field consists of a combination of two effects of independent origin: the vorticity of the observer congruence, plus the angular velocity of rotation, relative to Fermi-Walker transport, of the triad of spatial axes that each observer "carries" with it. Such formulation encompasses different gravitomagnetic fields in the literature. The formalism is applied to notable reference frames in Kerr spacetime, and their inertial forces shown to have familiar Newtonian analogues.