Angular diameter distances reconsidered in the Newman and Penrose formalism. (English) Zbl 1334.83025
Summary: Using the Newman and Penrose spin coefficient (NP) formalism, we provide a derivation of the Dyer-Roeder equation for the angular diameter distance in cosmological space-times. We show that the geodesic deviation equation written in NP formalism is precisely the Dyer-Roeder equation for a general Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular diameter distance to redshift relation in the case that a flat FRW metric is perturbed by a gravitational potential. We examine the perturbation in the case that the gravitational potential exhibits the properties of a thin gravitational lens, demonstrating how the weak lensing shear and convergence act as source terms for the perturbed Dyer-Roeder equation.
MSC:
83C10 | Equations of motion in general relativity and gravitational theory |
83C60 | Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism |
83F05 | Relativistic cosmology |
53Z05 | Applications of differential geometry to physics |
Keywords:
Dyer-Roeder equation; Newman-Penrose spin coefficient formalism; gravitational lensing; geodesic deviation equation; Friedman-Robertson-Walker (FRW) space-timeReferences:
[1] | Newman, ET; Penrose, R., No article title, J. Math. Phys., 3, 566-578 (1962) · Zbl 0108.40905 · doi:10.1063/1.1724257 |
[2] | Kling, TP; Bianchini, L., No article title, Gen. Relativ. Gravit., 43, 2575 (2011) · Zbl 1228.83079 · doi:10.1007/s10714-011-1181-y |
[3] | Kling, TP; Campbell, B., No article title, Phys. Rev. D, 77, 123012 (2008) · doi:10.1103/PhysRevD.77.123012 |
[4] | Dyer, CC; Roeder, RC, No article title, Astrophys. J., 180, l31 (1973) · doi:10.1086/181146 |
[5] | Giovi, F.; Occhionero, F.; Anendola, L., No article title, Mon. Not. R. Astron. Soc., 325, 1097 (2001) · doi:10.1046/j.1365-8711.2001.04531.x |
[6] | Lewis, GF; Ibata, R., No article title, Mon. Not. R. Astron. Soc., 337, 26 (2002) · doi:10.1046/j.1365-8711.2002.05797.x |
[7] | Clarkson, C.; etal., No article title, Mon. Not. R. Astron. Soc., 426, 1121 (2012) · doi:10.1111/j.1365-2966.2012.21750.x |
[8] | Clarkson, C.; etal., No article title, J. Cosmol. Astropart. Phys., 1411, 036 (2014) · doi:10.1088/1475-7516/2014/11/036 |
[9] | Kaiser, N., Peacock, J.: Retrieved from arXiv:1503.08506v1 |
[10] | Bonvin, C.; etal., No article title, J. Cosmol. Astropart. Phys., 1506, 050 (2015) · doi:10.1088/1475-7516/2015/06/050 |
[11] | Perlick, V.: Living Rev. Relativity 7, 9. http://www.livingreviews.org/lrr-2004-9 cited on January 8, 2016 |
[12] | Kling, TP; Keith, B., No article title, Class. Quantum Gravity, 22, 2921-2932 (2005) · Zbl 1076.83002 · doi:10.1088/0264-9381/22/14/005 |
[13] | Peacock, J.: Cosmological Physics. Cambridge University Press, Cambridge (1999) · Zbl 0952.83002 |
[14] | Penrose, R., Rindler, W.: Spinors and Space-Time, vol. 2. Cambridge University Press, Cambridge (1986) · Zbl 0591.53002 · doi:10.1017/CBO9780511524486 |
[15] | Schneider, P., Ehlers, J., Falco, E.E.: Gravitational Lenses. Springer, Berlin (1992) |
[16] | Ryden, B.: Introduction to Cosmology. Addison Wesley, New York (2003) |
[17] | Seitz, S., Schneider, P.: Astron. Astrophys. 374, 740 (2001) |
[18] | Baltz, E. et al.: from arXiv:0705.0682v2 [astro-ph] (2007) |
[19] | Seitz, S., No article title, LIACo, 93, 579s (1993) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.