Interpreting spacetimes of any dimension using geodesic deviation

Abstract

We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test particles. We demonstrate that local effect of the gravitational field on particles, as described by equation of geodesic deviation with respect to a natural orthonormal frame, can always be decomposed into a canonical set of transverse, longitudinal and Newton-Coulomb-type components, isotropic influence of a cosmological constant, and contributions arising from specific matter content of the universe. In particular, exact gravitational waves in Einstein's theory always exhibit themselves via purely transverse effects with D(D-3)/2 independent polarization states. To illustrate the utility of this approach we study the family of pp-wave spacetimes in higher dimensions and discuss specific measurable effects on a detector located in four spacetime dimensions. For example, the corresponding deformations caused by a generic higher-dimensional gravitational waves observed in such physical subspace, need not be tracefree.

19 pages, 2 figures. To appear in Phys. Rev. D. The reference [125] added

References in corpus (42)

• General Kerr-NUT-AdS Metrics in All Dimensions
• Instabilities of Black Strings and Branes
• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Kundt Spacetimes
• Robinson-Trautman spacetimes in higher dimensions
• Generalization of the Geroch-Held-Penrose formalism to higher dimensions
• Type D Einstein spacetimes in higher dimensions
• Higher dimensional VSI spacetimes
• General Kundt spacetimes in higher dimensions
• New nonuniform black string solutions
• Higher dimensional Kerr-Schild spacetimes
• Global solutions of the Einstein-Maxwell equations in higher dimensions
• Black string solutions with negative cosmological constant
• Black Holes in Higher-Dimensional Gravity
• Stationary axisymmetric solutions of five dimensional gravity
• Kerr-Schild spacetimes with (A)dS background
• Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
• Gravity Dual of Gauge Theory on S^2 x S^1 x R
• On the smoothness of static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory
• Tidal Dynamics in Kerr Spacetime
• Perturbations of higher-dimensional spacetimes
• Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction
• Cosmological Black Holes on Taub-NUT space in Five-Dimensional Einstein-Maxwell Theory
• Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions
• Radiation Beyond Four Space-Time Dimensions
• Black strings with negative cosmological constant: inclusion of electric charge and rotation
• The Linet-Tian solution with a positive cosmological constant in four and higher dimensions
• From black strings to black holes: nuttier and squashed AdS${}_5$ solutions
• Supersymmetric gyratons in five dimensions
• String Gyratons in Supergravity
• On higher dimensional Einstein spacetimes with a warped extra dimension
• Higher Dimensional Bondi Energy with a Globally Specified Background Structure
• Charged-rotating black holes and black strings in higher dimensional Einstein-Maxwell theory with a positive cosmological constant
• Asymptotic structure of radiation in higher dimensions
• A thin disk in higher dimensional space-time and dark matter interpretation
• Photon rockets moving arbitrarily in any dimension
• A note on cosmological Levi-Civita spacetimes in higher dimensions
• Algebraic classification of the Weyl tensor in higher dimensions based on its "superenergy" tensor
• Comment on the new AdS universe
• Type II Einstein spacetimes in higher dimensions
• The asymptotics of stationary electro-vacuum metrics in odd space-time dimensions
• Non-uniform Black Strings with Schwarzschild-(Anti-)de Sitter Foliation

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• Spinning particles in vacuum spacetimes of different curvature types
• Explicit algebraic classification of Kundt geometries in any dimension
• Black holes and other spherical solutions in quadratic gravity with a cosmological constant
• Physical interpretation of Kundt spacetimes using geodesic deviation
• Algebraic structure of Robinson-Trautman and Kundt geometries in arbitrary dimension
• Interpretation of the Weyl tensor
• Exact Parallel Waves in General Relativity
• The local and global geometrical aspects of the twin paradox in static spacetimes: I. Three spherically symmetric spacetimes
• Classification of Gravitational Waves in Higher-dimensional Space-time and Possibility of Observation
• Kundt spacetimes in the Einstein-Gauss-Bonnet theory
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• Penrose junction conditions extended: impulsive waves with gyratons
• On Integrability of the Geodesic Deviation Equation
• Jacobi fields, conjugate points and cut points on timelike geodesics in special spacetimes
• Weyl type N solutions with null electromagnetic fields in the Einstein-Maxwell $p$-form theory
• Twisted Gravitational Waves in the Presence of a Cosmological Constant
• Cosmology on a cosmic ring
• New results on the physical interpretation of black-brane gravitational perturbations
• General Relativistic Gravity Gradiometry
• Geodesic deviation in Kundt spacetimes of any dimension
• Exact Bachian singularity in quadratic gravity
• Gravitational waves in Cubic Metric-Affine Gravity
• Interpreting gravitational fields of Topologically Massive Gravity using geodesic deviation