Modified Newtonian Dynamics as an Entropic Force

Diego A. Carranza^*, Sergio Mendoza

Instituto de Astronoma, Universidad Nacional Autónoma de México, México D.F., México.

DOI: 10.4236/jmp.2015.66084                

Abstract

Under natural assumptions on the thermodynamic properties of space and time with the holo-graphic principle, we reproduce a MOND-like behaviour of gravity on particular scales of mass and length, where Newtonian gravity requires a modification or extension if no dark matter component is introduced in the description of gravitational phenomena. The result is directly obtained with the assumption that a fundamental constant of nature with dimensions of acceleration needs to be introduced into gravitational interactions. This in turn allows for modifications or extensions of the equipartion law and/or the holographic principle. In other words, MOND-like phenomenology can be reproduced when appropriate generalised concepts at the thermodynamical level of space and/or at the holographic principle are introduced. Thermodynamical modifications are reflected in extensions to the equipartition law which occur when the temperature of the system drops below a critical value, equals to Unruh’s temperature evaluated at the acceleration constant scale introduced for the description of the gravitational phenomena. Our calculations extend the ones by [1] in which Newtonian gravity is shown to be an emergent phenomenon, and together with it reinforces the idea that gravity at all scales is emergent.

Keywords

Alternative Theories of Gravity, Modified Newtonian Dynamics, Classical Black Holes, Entropy, Thermodynamics of Black Holes

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Verlinde, E. (2011) Journal of High Energy Physics, 4, 29. http://dx.doi.org/10.1007/JHEP04(2011)029
[2]	Bekenstein, J.D. (1973) Physical Review D, 7, 2333-2346. http://dx.doi.org/10.1103/PhysRevD.7.2333
[3]	Bekenstein, J.D. (1974) Physical Review D, 9, 3292-3300. http://dx.doi.org/10.1103/PhysRevD.9.3292
[4]	Bardeen, J.M., Carter, B. and Hawking, S.W. (1973) Communications in Mathematical Physics, 31, 161-170. http://dx.doi.org/10.1007/BF01645742
[5]	Hawking, S.W. (1974) Nature (London), 248, 30-31. http://dx.doi.org/10.1038/248030a0
[6]	Townsend, P.K. (1997) Black Holes. ArXiv General Relativity and Quantum Cosmology e-Prints.
[7]	Padmanabhan, T. (2010) Reports on Progress in Physics, 73, Article ID: 046901. http://dx.doi.org/10.1088/0034-4885/73/4/046901
[8]	Jacobson, T. (1995) Physical Review Letters, 75, 1260-1263. http://dx.doi.org/10.1103/PhysRevLett.75.1260
[9]	Hernandez, X. and Jimenez, M.A. (2012) Astrophysical Journal, 750, 9. http://dx.doi.org/10.1088/0004-637X/750/1/9
[10]	Hernandez, X., Jimenez, M.A. and Allen, C. (2012) European Physical Journal C, 72, 1884. http://dx.doi.org/10.1140/epjc/s10052-012-1884-6
[11]	Mastropietro, C. and Burkert, A. (2008) Monthly Notices of the Royal Astronomical Society, 389, 967-988. http://dx.doi.org/10.1111/j.1365-2966.2008.13626.x
[12]	Lee, J. and Komatsu, E. (2010) The Astrophysical Journal, 718, 60-65. http://dx.doi.org/10.1088/0004-637X/718/1/60
[13]	Thompson, R. and Nagamine, K. (2012) Monthly Notices of the Royal Astronomical Society, 419, 3560-3570. http://dx.doi.org/10.1111/j.1365-2966.2011.20000.x
[14]	Moffat, J.W. and Toth, V.T. (2010) Can Modified Gravity (MOG) Explain the Speeding Bullet (Cluster)? http://arxiv.org/abs/1005.2685
[15]	Mendoza, S., Hernandez, X., Hidalgo, J.C. and Bernal, T. (2011) Monthly Notices of the Royal Astronomical Society, 411, 226-234. http://dx.doi.org/10.1111/j.1365-2966.2010.17685.x
[16]	Milgrom, M. (1982) The Astrophysical Journal, 270, 371-389. http://dx.doi.org/10.1086/161131
[17]	Bernal, T., Capozziello, S., Hidalgo, J.C. and Mendoza, S. (2011) European Physical Journal C, 71, 1794. http://dx.doi.org/10.1140/epjc/s10052-011-1794-z
[18]	Carranza, D.A., Mendoza, S. and Torres, L.A. (2013) European Physical Journal C, 73, 2282. http://dx.doi.org/10.1140/epjc/s10052-013-2282-4
[19]	Mendoza, S., Bernal, T., Hernandez, X., Hidalgo, J.C. and Torres, L.A. (2013) Monthly Notices of the Royal Astronomical Society, 433, 1802-1812. http://dx.doi.org/10.1093/mnras/stt752
[20]	Sheykhi, A. and Sarab, K.R. (2012) Journal of Cosmology and Astroparticle Physics, 2012, 12. http://dx.doi.org/10.1088/1475-7516/2012/10/012
[21]	Sedov, L.I. (1959) Similarity and Dimensional Methods in Mechanics. Academic Press, Waltham.
[22]	Famaey, B. and McGaugh, S.S. (2012) Living Reviews in Relativity, 15, 10. http://dx.doi.org/10.12942/lrr-2012-10
[23]	Mendoza, S. (2011) Extending Cosmology: The Metric Approach. http://arxiv.org/abs/1208.3408
[24]	Mendoza, S. and Olmo, G. (2012) Living Reviews in Relativity, 15, 10.
[25]	Will, C.M. (1992) Theory and Experiment in Gravitational Physics. Cambridge University Press, Cambridge.
[26]	Pazy, E. and Argaman, N. (2012) Physical Review D, 85, Article ID: 104021. http://dx.doi.org/10.1103/PhysRevD.85.104021