A Phase Space Diagram for Gravity

Abstract

In modified theories of gravity including a critical acceleration scale a 0 , a critical length scale r M = (GM/a 0 ) 1/2 will naturally arise with the transition from the Newtonian to the dark matter mimicking regime occurring for systems larger than r M . This adds a second critical scale to gravity, in addition to the one introduced by the criterion v < c of the Schwarzschild radius, r S = 2GM/c 2 . 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.

An algorithm for coalescence of classical objects and formation of planetary systems

“…The phase space diagram for the gravitational system [29] differs from a traditional phase space diagram. A collection of objects will, without fusion collapse at low temperature (velocities of the objects) and relative high concentration in the collection [30], but at high temperatures and low concentrations the collection of objects expands continuously in the space.…”

Relativistic interpretation and cosmological signature of Milgrom's acceleration

“…In order to select an appropriate metric to evaluate (1) it is useful to examine the relation between Mass vs Radius for various self-gravitating systems displayed in figure 1 involving the two scales: R M and the Schwarzschild radius R S , first presented in [25].…”

Modified Newtonian dynamics and hadronic scales

“…The three points, namely (1) Planck: (r CS , m CS ), (2) Universe: (r M S , m M S ), and (3) Hadron: (r CM , m CM ) define the vertices of a triangle on the (log r, log m) phase space plot that was considered for purely astrophysical reasons in [15]. (In [15] the relevant plot involved only the vertex (r M S , m M S ) and the associated angle.)…”

“…The three points, namely (1) Planck: (r CS , m CS ), (2) Universe: (r M S , m M S ), and (3) Hadron: (r CM , m CM ) define the vertices of a triangle on the (log r, log m) phase space plot that was considered for purely astrophysical reasons in [15]. (In [15] the relevant plot involved only the vertex (r M S , m M S ) and the associated angle.) The interior of this 'Newtonian' triangle 5 , with its lower side (6) defining the quantum boundary, specifies the region where classical Newtonian physics is supposed to hold.…”

“…Their argument was based on the discussion of scaling laws connecting various self-gravitating astrophysical systems 6 and indicating the emergence of a M as a characteristic scale ruling such systems (see also Fig. 1 in [15]). The argument involved the discussion of the generalization of the Dirac mass quantization condition (12) to actions many times larger than h and the use of the observed scaling laws (see eg.…”