scholarly journals Gravitational Lagrangians, Mach’s Principle, and the Equivalence Principle in an Expanding Universe

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hanno Essén

Gravitational Lagrangians as derived by Fock for the Einstein-Infeld-Hoffmann approach, and by Kennedy assuming only a fourth rank tensor interaction, contain long range interactions. Here we investigate how these affect the local dynamics when integrated over an expanding universe out to the Hubble radius. Taking the cosmic expansion velocity into account in a heuristic manner it is found that these long range interactions imply Mach’s principle, provided the universe has the critical density, and that mass is renormalized. Suitable higher order additions to the Lagrangians make the formalism consistent with the equivalence principle.

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Kjell Prytz

AbstractIn a cosmological perspective, gravitational induction is explored as a source to mechanical inertia in line with Mach’s principle. Within the standard model of cosmos, considering the expansion of the universe and the necessity of retarded interactions, it is found that the assumed dynamics may account for a significant part of an object’s inertia.


1990 ◽  
Vol 05 (03) ◽  
pp. 157-168 ◽  
Author(s):  
JINWU YE ◽  
ROBERT H. BRANDENBERGER

The formation and evolution of vortices in an expanding 2+1 dimensional space-time is analyzed numerically. We test the Kibble mechanism and show that, starting with thermal initial conditions with random phases, vortices form with a mean separation smaller than the Hubble radius. Due to the long range forces, vortices and anti-vortices move together and annihilate. We show that the phase waves which are produced during the annihilation are emitted predominantly at 90° from the axis through the incident topological defects.


2016 ◽  
Vol 25 (12) ◽  
pp. 1644009 ◽  
Author(s):  
Douglas Singleton ◽  
Steve Wilburn

The equivalence principle is the conceptual basis for general relativity. In contrast, Mach’s principle, although said to have been influential on Einstein in his formulation of general relativity, has not been shown to be central to the structure of general relativity. In this paper, we suggest that the quantum effects of Hawking and Unruh radiation are a manifestation of a thermal Mach’s principle, where the local thermodynamic properties of the system are determined by the nonlocal structure of the quantum fields which determine the vacuum of a given spacetime. By comparing Hawking and Unruh temperatures for the same local acceleration we find a violation of the Einstein elevator version of the equivalence principle, which vanishes in the limit that the horizon is approached.


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