A modification to general relativity by use of the notion of local expansion of space-time

Hodgkinson, TF

Abstract

General Relativity (GR) is Einsteins' theory of gravity whereby the motions of
bodies are explained due to their following geodesic paths (the shortest distance
between two points) in a curved four dimensional space-time. The curvature being
attributed to the presence of mass
As such there is no explicit force present in this theory, contrary to Newtons' law
of gravity. However in the limit of GR (where the field is both weak and static and
bodies are travelling with velocities slow compared to that of light), then Newtons'
law is recovered in the approximation.
GR has explained all gravitational phenomena extremely well (eg solar system),
that is until one considers the measured motions of galaxies. The galaxies are
rotating too quickly to be consistent with GR/ Newton.
An explanation for this discrepancy has originally been suggested, concerning the
presence of extra mass, of as yet an unknown nature. However, to date not a hint
of this `Dark Matter' has been detected.
A second explanation is that of Modified Newtonian Dynamics (MOND), whereby
at a certain very small acceleration, the actual gravitational physics deviates from
that described by Newton. The MOND proposal seems to fit extremely well with
observations without the need to invoke the presence of DM.
The main problem with the MOND concept is that it does not fit in with the
standard GR.
ii
The following work details an exploration into the novel assumption that the
presence of mass is not only responsible for the curvature of space-time but also
for a local expansion of space-time.
By introducing an expansion factor at the very beginning of standard GR analysis,
one finds an extra term appears which is consistent throughout. With the inclusion
of this extra term, one can, in the weak, static and slow velocity limit, find a direct
link to the MOND phenomenology. It is found that the extra term is negligible for
small systems (eg Solar) yet it is the dominant term for large systems (eg galaxies).
The work is published in Physical Review D. `Gravitational Theoretical Development
Supporting MOND'.

Citation

Hodgkinson, T. A modification to general relativity by use of the notion of local expansion of space-time. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Sep 10, 2015
• Publicly Available Date: Sep 10, 2015
• Additional Information: Projects : 42-month PhD stipend
• Award Date: Sep 1, 2014