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a phase space diagram for gravity的相空间图重力
Entropy 2012, 14, 848-855; doi:10.3390/
OPEN ACCESS
entropy
ISSN 1099-4300
/journal/entropy
Article
A Phase Space Diagram for Gravity
Xavier Hernandez
´ ´ ´
Instituto de Astronomıa, Universidad Nacional Autonoma de Mexico, AP 70-264,
´
Distrito Federal 04510, Mexico; E-Mail: xavier@astro.unam.mx
Received: 20 March 2012; in revised form: 18 April 2012 / Accepted: 18 April 2012 /
Published: 4 May 2012
Abstract: In modified theories of gravity including a critical acceleration scale a , a critical
0
length scale r = (GM/a )1/2 will naturally arise with the transition from the Newtonian
M 0
to the dark matter mimicking regime occurring for systems larger than rM . This adds a
second critical scale to gravity, in addition to the one introduced by the criterion v c of
2
the Schwarzschild radius, rS = 2GM/c . The distinct dependencies of the two above length
scales give rise to non-trivial phenomenology in the (mass, length) plane for astrophysical
structures, which we explore here. Surprisingly, extrapolation to atomic scales suggests
gravity should be at the dark matter mimicking regime there.
Keywords: modified theories of gravity; dark energy; cosmology
1. Introduction
Over
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