2014

Properties of an affine transport equation and its holonomy

Vines, Justin, Nichols, David A.

Understand

An affine transport equation was used recently to study properties of angular momentum and gravitational-wave memory effects in general relativity.

In this paper, we investigate local properties of this transport equation in greater detail.
Associated with this transport equation is a map between the tangent spaces at two points on a curve.
This map consists of a homogeneous (linear) part given by the parallel transport map along the curve plus an inhomogeneous part, which is related to the development of a curve in a manifold into an affine tangent space.

DOI 10.1007/s10714-015-1901-9
Original
J. Vines, Gen. Relativ. Gravit. 47 · 1901
Earlier work this paper cites.
DOI 10.1112/plms/s2-32.1.241
J. Synge, Proc. Lond. Math. Soc. 32 · 1931
Earlier work this paper cites.
M. Mathisson, Acta Phys. Polon. 6
1937
Earlier work this paper cites.
DOI 10.1098/rspa.1951.0200
A. Papapetrou, Proc. R. Soc. Lond. 209 · 1951
Earlier work this paper cites.
Series in physics (North-Holland Pub. Co., Amsterdam, 1960)
J.L. Synge, Relativity: the general theory · 1960
Earlier work this paper cites.
DOI 10.1016/0003-4916(60)90030-0
B.S. DeWitt, R.W. Brehme, Annals of Physics 9 · 1960
Earlier work this paper cites.
DOI 10.1098/rspa.1962.0161
H. Bondi, M.G.J. van der Burg, A.W.K. Metzner, Proc. R. Soc. Lond. 269 · 1962
Earlier work this paper cites.
DOI 10.1098/rspa.1962.0206
R.K. Sachs, Proc. R. Soc. Lond. 270 · 1962
Earlier work this paper cites.

S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Volume I (Interscience Publishers, New York, 1963)
1963
Cited alongside, same era.
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W. H. Freeman and Co., San Francisco, 1973)
1973
Cited alongside, same era.
DOI 10.1007/BF00770462
R.J. Petti, Gen. Relativ. Gravit. 18 · 1986
Cited alongside, same era.
DOI 10.1088/0264-9381/4/1/004
J.A.G. Vickers, Class. Quantum Gravity 4 · 1987
Cited alongside, same era.
DOI 10.1088/0264-9381/11/5/019
K.P. Tod, Class. Quantum Gravity 11 · 1994
Cited alongside, same era.
R.W. Sharpe, Differential Geometry: Cartan’s Generalization of Klein’s Erlangen Program (Springer-Verlag, New York, 1997)
1997
Cited alongside, same era.
É. Cartan, Riemannian Geometry in an Orthogonal Frame (World Scientific, New Jersey, 2001)
2001
Cited alongside, same era.

M. Nakahara, Geometry, Topology and Physics , 2nd edn. (Taylor and Francis Group, New York, 2003)
2003
Later among the works it cites.
DOI 10.1088/0264-9381/25/20/205008
A.I. Harte, Class. Quantum Grav. 25 · 2008
Later among the works it cites.
DOI 10.12942/lrr-2011-7
E. Poisson, A. Pound, I. Vega, Living Reviews Relativ. 14 · 2011
Later among the works it cites.
DOI 10.1103/PhysRevD.84.104039
A.C. Ottewill, B. Wardell, Phys. Rev. D 84 · 2011
Later among the works it cites.
Y. Chitour, P. Kokkonen, Annales L’Institute Henri Poincaré (C) 29
2012
Later among the works it cites.
DOI 10.1103/PhysRevD.90.044005
A.D. Helfer, Phys. Rev. D 90 · 2014
Closest in time.
DOI 10.1103/PhysRevD.92.084057
É.É. Flanagan, D.A. Nichols, Phys. Rev. D 92 · 2015
Closest in time.

alphaXiv searches the wider corpus for related work and actual follow-ups.

alphaXiv is searching for related work…

Reading the bibliography…