Thus, it appears that many puzzling observations, that are difficult to understand in the
CDM context (and/or require an extreme fine-tuning of the DM distribution), are well
summarized by a single heuristic law. Therefore, it would appear natural that this law
derives from a universal force law, and would reflect a modification of dynamics rather than
the addition of massive particles interacting (almost) only gravitationally with baryonic
matter20.
However, applying blindly Eq. 7
to a set of massive bodies directly leads to serious problems [150, 293
]
such as the non-conservation of momentum. In a two-body configuration, as the implied force is not
symmetric in the two masses, Newton’s third law (action and reaction principle) does not hold, so the
momentum is not conserved. Consider a translationally invariant isolated system of two such masses
and
small enough to be in the very weak acceleration limit, and placed at rest on the
-axis. The
amplitude of the Newtonian force is then
, and applying blindly Eq. 7
,
would lead to individual accelerations
. This then immediately leads to
http://www.livingreviews.org/lrr-2012-10 |
Living Rev. Relativity 15, (2012), 10
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