Relative continuum mechanics in general relativity

1978 ◽  
Vol 117 (1) ◽  
pp. 311-337 ◽  
Author(s):  
Enrico Massa
Keyword(s):  
General Relativity ◽  
Continuum Mechanics

scholarly journals On galaxy rotation curves from a continuum mechanics approach to modified gravity

2018 ◽  
Vol 27 (02) ◽  
pp. 1850007 ◽  
Author(s):  
Christian G. Böhmer ◽  
Nicola Tamanini ◽  
Matthew Wright
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Continuum Mechanics ◽  
Modified Gravity ◽  
Galactic Rotation ◽  
Dark Matter Halos ◽  
Additional Structure ◽  
Rotation Curves ◽  
Small Deviations ◽  
Galaxy Rotation Curves

We consider a modification of General Relativity motivated by the treatment of anisotropies in Continuum Mechanics. The Newtonian limit of the theory is formulated and applied to galactic rotation curves. By assuming that the additional structure of spacetime behaves like a Newtonian gravitational potential for small deviations from isotropy, we are able to recover the Navarro–Frenk–White profile of dark matter halos by a suitable identification of constants. We consider the Burkert profile in the context of our model and also discuss rotation curves more generally.

scholarly journals From continuum mechanics to general relativity

2014 ◽  
Vol 23 (12) ◽  
pp. 1442015 ◽  
Author(s):  
Christian G. Böhmer ◽  
Robert J. Downes
Keyword(s):  
General Relativity ◽  
Experimental Evidence ◽  
Continuum Mechanics ◽  
General Model ◽  
Spacetime Symmetries ◽  
Theory Of Gravity

Using ideas from continuum mechanics we construct a theory of gravity. We show that this theory is equivalent to Einstein's theory of general relativity; it is also a much faster way of reaching general relativity than the conventional route. Our approach is simple and natural: we form a very general model and then apply two physical assumptions supported by experimental evidence. This easily reduces our construction to a model equivalent to general relativity. Finally, we suggest a simple way of modifying our theory to investigate nonstandard spacetime symmetries.

scholarly journals Force, inertia, metric in Newtonian relativity and general relativity

2018 ◽  
Author(s):  
PierGianLuca Porta Mana
Keyword(s):  
General Relativity ◽  
Continuum Mechanics ◽  
Inertial Motion ◽  
General Relativistic

[Draft:] This note is an exploration of some notions around kinematics, dynamics, matter, inertia, and force in Newtonian- and general-relativistic continuum mechanics. The conceptual pivot of this exploration is this:"Neither in Newtonian relativity or in general relativity should there be any distinction between inertial and non-inertial motion, or between forced and unforced motion".

A First Course in Continuum Mechanics

2001 ◽  
Author(s):  
Oscar Gonzalez ◽  
Andrew M. Stuart
Keyword(s):  
Continuum Mechanics
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