A Derivation of the Etherington’s Distance-Duality Equation

Yuri Heymann

doi:doi:10.11648/j.ijass.20150304.13

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A Derivation of the Etherington’s Distance-Duality Equation

Yuri Heymann

Published in International Journal of Astrophysics and Space Science (Volume 3, Issue 4)

Received: 24 June 2015 Accepted: 4 July 2015 Published: 10 July 2015

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Abstract

The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular-diameter distance. This relationship has been validated from astronomical observations based on the X-ray surface brightness and the Sunyaev-Zel'dovich effect of galaxy clusters. In the present study, we propose a derivation of the Etherington's reciprocity relation in the dichotomous cosmology.

Published in	International Journal of Astrophysics and Space Science (Volume 3, Issue 4)
DOI	10.11648/j.ijass.20150304.13
Page(s)	65-69
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Etherington, Distance Duality, Dichotomous Cosmology

References

[1]	I.M.H. Etherington, “LX. On the Definition of Distance in General Relativity”, Philosophical Magazine, Vol. 15, S. 7 (1933), pp. 761-773.
[2]	G.F.R. Ellis, “Relativistic cosmology”, Proceedings of the 47th International School of Physics “Enrico Fermi”, edited by R.K. Sachs (Academic Press, New York and London), Vol. 15 (1971), pp. 104-182.
[3]	G.F.R. Ellis, “On the Definition of Distance in General Relativity: I.M.H. Etherington (Philosophical Magazine ser. 7, vol. 15, 761 (1933))”, General Relativity and Gravitation, Vol. 39 (2007), pp. 1047-1052.
[4]	Y. Heymann, “The Dichotomous Cosmology with a Static Material World and Expanding Luminous World”, Progress in Physics, Vol. 10, Issue 3 (2014), pp. 178-181.
[5]	Y. Heymann, “A Monte Carlo Simulation Framework for Testing Cosmological Models”, Progress in Physics, Vol. 10, Issue 4 (2014), pp. 217-221.
[6]	R.A. Sunyaev, and Ya.B. Zel’dovich, “The Observation of Relic Radiation as a Test of the Nature of X-Ray Radiation from the Clusters of Galaxies”, Comments on Astrophysics and Space Physics, Vol. 4 (1972), pp.173-178.
[7]	J. Silk, and S.D.M. White, “The Determination of qo Using X-Ray and Microwave Measurements of Galaxy Clusters”, The Astrophysical Journal Letters, Vol. 226 (1978), L103.
[8]	F. Bernardis, E. Giusarma, and A. Melchiorri, “Constraints on Dark Energy and Distance Duality from Sunyaev-Zel’dovich Effect and Chandra X-Ray Measurements”, International Journal of Modern physics D, Vol. 15, No. 5 (2006), pp. 759-766.
[9]	J.-P. Uzan, N. Aghanim, and Y. Mellier, “Distance Duality Relation from X-Ray and Sunyaev-Zel’dovich Observations of Clusters”, Physical Review D, Vol. 70, 083533 (2004).
[10]	R. Nair, S. Jhingan, and D. Jain, “Cosmic Distance Duality and Cosmic Transparency”, Preprint, arXiv: astro-ph/1210.2642 (2012).
[11]	R.S. Gonçalves, R.F.L. Holanda, and J.S. Alcaniz, “Testing the Cosmic Distance Duality with X-Ray Gas Mass Fraction and Supernovae Data”, Monthly Notice Letters of the Royal Astronomical Society, Vol. 420, Issue 1 (2012), L43-L47.
[12]	J.A.S. Lima, J.V. Cunha, and V.T. Zanchin, “Deformed Distance Duality Relations and Supernova Dimming”, The Astrophysical Journal Letters, Vol. 742, No. 2 (2011), L26.
[13]	B.A. Bassett, and M. Kunz, “Cosmic Distance-Duality as a Probe of Exotic Physics and Acceleration”, Physical Review D, Vol. 69, 101305 (2004).
[14]	M. Birkinshaw, J.P. Hughes, and K.A. Arnaud, “A Measurement of the Value of the Hubble Constant from the X-Ray Properties and the Sunyaev-Zel'dovich Effect of Abell 665”, The astrophysical Journal, Vol. 379 (1991), pp. 466-481.
[15]	Y. Inagaki, T. Suginohara, and Y. Suto, “Reliability of the Hubble-Constant Measurement Based on the Sunyaev-Zel'dovich Effect”, Publications of the Astronomical Society of Japan, Vol. 47 (1995), pp. 411-423.

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Yuri Heymann. (2015). A Derivation of the Etherington’s Distance-Duality Equation. International Journal of Astrophysics and Space Science, 3(4), 65-69. https://doi.org/10.11648/j.ijass.20150304.13

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Yuri Heymann. A Derivation of the Etherington’s Distance-Duality Equation. Int. J. Astrophys. Space Sci. 2015, 3(4), 65-69. doi: 10.11648/j.ijass.20150304.13

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Yuri Heymann. A Derivation of the Etherington’s Distance-Duality Equation. Int J Astrophys Space Sci. 2015;3(4):65-69. doi: 10.11648/j.ijass.20150304.13

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@article{10.11648/j.ijass.20150304.13,
  author = {Yuri Heymann},
  title = {A Derivation of the Etherington’s Distance-Duality Equation},
  journal = {International Journal of Astrophysics and Space Science},
  volume = {3},
  number = {4},
  pages = {65-69},
  doi = {10.11648/j.ijass.20150304.13},
  url = {https://doi.org/10.11648/j.ijass.20150304.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20150304.13},
  abstract = {The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular-diameter distance. This relationship has been validated from astronomical observations based on the X-ray surface brightness and the Sunyaev-Zel'dovich effect of galaxy clusters. In the present study, we propose a derivation of the Etherington's reciprocity relation in the dichotomous cosmology.},
 year = {2015}
}

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TY  - JOUR
T1  - A Derivation of the Etherington’s Distance-Duality Equation
AU  - Yuri Heymann
Y1  - 2015/07/10
PY  - 2015
N1  - https://doi.org/10.11648/j.ijass.20150304.13
DO  - 10.11648/j.ijass.20150304.13
T2  - International Journal of Astrophysics and Space Science
JF  - International Journal of Astrophysics and Space Science
JO  - International Journal of Astrophysics and Space Science
SP  - 65
EP  - 69
PB  - Science Publishing Group
SN  - 2376-7022
UR  - https://doi.org/10.11648/j.ijass.20150304.13
AB  - The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular-diameter distance. This relationship has been validated from astronomical observations based on the X-ray surface brightness and the Sunyaev-Zel'dovich effect of galaxy clusters. In the present study, we propose a derivation of the Etherington's reciprocity relation in the dichotomous cosmology.
VL  - 3
IS  - 4
ER  -

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Author Information

Yuri Heymann

Athens Institute for Education and Research, Physics, Geneva, Sw

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APA Style

Yuri Heymann. (2015). A Derivation of the Etherington’s Distance-Duality Equation. International Journal of Astrophysics and Space Science, 3(4), 65-69. https://doi.org/10.11648/j.ijass.20150304.13

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ACS Style

Yuri Heymann. A Derivation of the Etherington’s Distance-Duality Equation. Int. J. Astrophys. Space Sci. 2015, 3(4), 65-69. doi: 10.11648/j.ijass.20150304.13

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AMA Style

Yuri Heymann. A Derivation of the Etherington’s Distance-Duality Equation. Int J Astrophys Space Sci. 2015;3(4):65-69. doi: 10.11648/j.ijass.20150304.13

Copy | Download

@article{10.11648/j.ijass.20150304.13,
  author = {Yuri Heymann},
  title = {A Derivation of the Etherington’s Distance-Duality Equation},
  journal = {International Journal of Astrophysics and Space Science},
  volume = {3},
  number = {4},
  pages = {65-69},
  doi = {10.11648/j.ijass.20150304.13},
  url = {https://doi.org/10.11648/j.ijass.20150304.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20150304.13},
  abstract = {The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular-diameter distance. This relationship has been validated from astronomical observations based on the X-ray surface brightness and the Sunyaev-Zel'dovich effect of galaxy clusters. In the present study, we propose a derivation of the Etherington's reciprocity relation in the dichotomous cosmology.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - A Derivation of the Etherington’s Distance-Duality Equation
AU  - Yuri Heymann
Y1  - 2015/07/10
PY  - 2015
N1  - https://doi.org/10.11648/j.ijass.20150304.13
DO  - 10.11648/j.ijass.20150304.13
T2  - International Journal of Astrophysics and Space Science
JF  - International Journal of Astrophysics and Space Science
JO  - International Journal of Astrophysics and Space Science
SP  - 65
EP  - 69
PB  - Science Publishing Group
SN  - 2376-7022
UR  - https://doi.org/10.11648/j.ijass.20150304.13
AB  - The Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular-diameter distance. This relationship has been validated from astronomical observations based on the X-ray surface brightness and the Sunyaev-Zel'dovich effect of galaxy clusters. In the present study, we propose a derivation of the Etherington's reciprocity relation in the dichotomous cosmology.
VL  - 3
IS  - 4
ER  -

Copy | Download