Generalized deviation equation and determination of the curvature in General Relativity
arXiv:1511.08465 · doi:10.1103/PhysRevD.93.044073
Abstract
We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation equation. We show how the standard as well as a generalized deviation equation can be used to measure the curvature of spacetime by means of a set of test bodies. In particular, we provide exact solutions for the curvature by using the standard deviation equation as well as its next order generalization.
16 pages, 5 figures, RevTex format
References in corpus (6)
- Geodesic deviation at higher orders via covariant bitensors
- Spin-geodesic deviations in the Schwarzschild spacetime
- Equations of motion in metric-affine gravity: A covariant unified framework
- On the generalized Jacobi equation
- Multipolar test body equations of motion in generalized gravity theories
- World-line deviation and spinning particles
Cited by in corpus (15)
- Geometric optics in general relativity using bilocal operators
- Phantom singularities and their quantum fate: general relativity and beyond
- Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals
- Motion of localized sources in general relativity: gravitational self-force from quasilocal conservation laws
- On the Applicability of the Geodesic Deviation Equation in General Relativity
- Deviation equation in Riemann-Cartan spacetime
- Gravitational clock compass in General Relativity
- Measuring the gravitational field in General Relativity: From deviation equations and the gravitational compass to relativistic clock gradiometry
- Generalized geodesic deviation in de Sitter spacetime
- Gravitational Plane Waves in a Non-Riemannian Description of Brans-Dicke Gravity
- Gravitational clock compass and the detection of gravitational waves
- Extended gravitational clock compass: new exact solutions and simulations
- Geodesic deviation to all orders via a tangent bundle formalism
- Operational significance of the deviation equation in relativistic geodesy
- Spin-induced motion in black hole spacetime