Interpreting spacetimes of any dimension using geodesic deviation
Podolský, J.; Švarc, R.
We present a general method that 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 the local effect of the gravitational field on particles, as described by the 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 generic higher-dimensional gravitational waves observed in such physical subspace need not be trace-free.
type: | article |
journal: | Phys. Rev. D |
volume: | 85 |
nr: | 4 |
pages: | 044057 |
year: | 2012 |
month: | 2 |
eprint: | arXiv:1201.4790 |
grants: | Spacetimes and Fields in Higher Dimensional and Classical Gravity, GAČR 203/12/0118 ; 2012-2016; hlavní řešitel: Jiří PodolskýGeneral relativity and its applications in astrophysics and cosmology, GAČR 205/09/H033; 2009-2012; hlavní řešitel: Oldřich Semerák, doktorandský grantFyzikální studium objektů a procesů ve sluneční soustavě a v astro-fyzikálních systémech, výzkumný záměr MSM0021620860; 2007-2013; hlavní řešitel: Jiří BičákAktuální problémy teoretické fyziky, astronomie a astrofyziky; 2013; řešitel: Oldřich Semerák |