# Imprints from the global cosmological expansion to the local spacetime dynamics

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## Abstract

We study the general relativistic spacetime metrics surrounding massive cosmological objects, such as suns, stars, galaxies or galaxy clusters. The question addressed here is the transition of local, object-related spacetime metrics into the global, cosmological Robertson–Walker metrics. We demonstrate that the answer often quoted for this problem from the literature, the so-called Einstein–Straus vacuole, which connects a static outer Schwarzschild solution with the time-dependent Robertson–Walker universe, is inadequate to describe the local spacetime of a gravitationally bound system. Thus, we derive here an alternative model describing such bound systems by a metrics more closely tied to the fundamental problem of structure formation in the early universe and obtain a multitude of solutions characterising the time-dependence of a local scale parameter. As we can show, a specific solution out of this multitude is able to, as a by-product, surprisingly enough, explain the presently much discussed phenomenon of the PIONEER anomaly.

## Keywords

Cosmology: theory Early universe Relativity## References

- Anderson JD, Laing PA, Lau EL, Liu AS, Nieto MM, Turyshev SG (1998) Indication, from pioneer 10/11, galileo, and ulysses data, of an apparent anomalous, weak, long-range acceleration. Phys Rev Lett 81:2858CrossRefGoogle Scholar
- Anderson JD, Laing PA, Lau EL, Liu AS, Nieto MM, Turyshev SG (2002) Study of the anomalous acceleration of pioneer 10 and 11. Phys Rev D 65:082004 (for an updated version, see www.arxiv.org/abs/gr-qc/0104064)CrossRefGoogle Scholar
- Bennet CL, Halpern M, Hinshaw G, Jarosik N, Kogut A, Limon M, Meyer SS, Page L et al (2003) First-year wilkinson microwave anisotropic probe (wmap) observations: preliminary maps and basic results. Astrophys J Suppl Ser 148:1–27CrossRefGoogle Scholar
- Bertolami O, Paramos J (2006) Current tests of alternative gravity theories: the modified newtonian dynamics case. www.arxiv.org/abs/gr-qc/0611025
- Bertolami O, Paramos J (2007) A mission to test the pioneer anomaly: estimating the main systematic effects. www.arxiv.org/abs/gr-qc/0702149
- Bertolami O, Pedro FG, Delliou ML (2007) Dark energy-dark matter interaction and the violation of the equivalence principle from the abell cluster a586. www.arxiv.org/abs/astro-ph/0703462
- Blome HJ, Hoell J, Priester W (2001) Kosmologie. vol. 8 of Lehrbuch der Experimentalphysik. W. de Gruyter, BerlinGoogle Scholar
- Bonnor WB (1957) Jeans formula for gravitational instability. Mon Not R Astron Soc 117:104–117Google Scholar
- Bonnor WB, Vickers PA (1981) Junction conditions in general relativity. Gen Relativ Gravit 13:29–36Google Scholar
- Carrera M, Giulini D (2006) On the influence of the global cosmological expansion on the local dynamics of the solar system. www.arxiv.org/abs/gr-qc/0602098
- Cooperstock FI, Faraoni V, Vollick DN (1999) The influence of the cosmological expansion on local systems. Astrophys J 501:61–66Google Scholar
- Einstein A, Straus EG (1945) The influence of the expansion of space on the gravitation fields surrounding individual stars. Rev Mod Phys 17(2):120–124CrossRefGoogle Scholar
- Einstein A, Straus EG (1946) Corrections and additional remarks to our paper: the influence of the expansion of space on the gravitation fields surrounding individual stars. Rev Mod Phys 18(1):148–149CrossRefGoogle Scholar
- Fahr HJ, Siewert M (2006a) Does pioneer measure local spacetime expansion? www.arxiv.org/abs/gr-qc/0610034
- Fahr HJ, Siewert M (2006b) Kinetic study of the ion passage over the solar wind termination shock. A&A 458:13–20. doi: 10.1051/0004-6361:20065540 CrossRefGoogle Scholar
- Fahr HJ, Siewert M (2007) Local spacetime dynamics, the einstein–straus vacuole and the pioneer anomaly: a new access to these problems. Z Naturforsch 62a:1–10Google Scholar
- Goenner H (1997) Einführung in die Kosmologie. Spektrum Akademischer Verlag, HeidelbergGoogle Scholar
- Harrison ER (1988) Cosmology: the science of the universe. Cambrigde University Press, CambridgeGoogle Scholar
- Masreliez CJ (2004) Scale expanding cosmos theory i—an introduction. Apeiron 11:99–133 (http://redshift.vif.com)Google Scholar
- Pearce FR, Jenkins A, Frenk CS, White SDM, Thomas PA, Couchman HPM, Peacock JA, Efstathiou G (2001) Simulations of galaxy formation in a cosmological volume. MNRAS 326:649–666CrossRefGoogle Scholar
- Petry W (2005) Further results of flat space-time theory of gravitation. Z Naturforsch 60a:255–264Google Scholar
- Petry W (2006) An explaination of the anomaleous doppler frequency shift of the pioneers. In: Physical Interpretations of relativity theory X, vol 13. Imperial College, London, pp 1057–1071Google Scholar
- Rosales JL (2002) The pioneer’s acceleration anomaly and hubble’s constant. www.arxiv.org/abs/gr-qc/0212019
- Rosales JL, Sanchez-Gomez JL (1999) The “pioneer effect” as a manifestation of the cosmic expansion in the solar system. www.arxiv.org/abs/gr-qc/9810085
- Scholz E (2007) Another look at the pioneer anomaly. www.arxiv.org/abs/astro-ph/0701032
- Schücking E (1954) Das schwarzschildsche linienelement und die expansion des weltalls. Z Phys 134:595–603Google Scholar
- Silk J, Bouwens R (2001) The formation of galaxies. New Astron Rev 45:337–350CrossRefGoogle Scholar
- Tomilchik LM (2007) The pioneer anomaly: the data, its meaning and a future test. www.arxiv.org/abs/0704.2745