An elastic constitutive model of spacetime and its applications
We introduce an elastic constitutive model of gravity that enables the interpretation of cosmological observations in terms of established ideas from Solid Mechanics and multiscale modeling. The behavior of physical space is identified with that of a material-like medium called "cosmic fabric,&...
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ndltd-MSSTATE-oai-library.msstate.edu-etd-10182018-1819522019-05-15T18:44:02Z An elastic constitutive model of spacetime and its applications Tenev, Tichomir G. Computational Engineering We introduce an elastic constitutive model of gravity that enables the interpretation of cosmological observations in terms of established ideas from Solid Mechanics and multiscale modeling. The behavior of physical space is identified with that of a material-like medium called "cosmic fabric," which exhibits constitutive behavior. This cosmic fabric is a solid hyperplate that is broad in the three ordinary spatial dimensions and thin in a fourth hyperspatial dimension. Matter in space is treated as fabric inclusions that prescribe in-plane (three-dimensional) strain causing the transverse bending of the fabric into the fourth hyperspatial dimension. The linearized Einstein-Hilbert action, which governs the dynamics of physical space, is derived from postulating Hookes Law for the fabric, and the Schwarzschild metric is recovered from investigating matter-fabric interactions. At the continuum length scale, the Principle of Relativity is shown to apply for both moving and stationary observers alike, so that the fabrics rest reference frame remains observationally indistinguishable at such a length scale. Within the Cosmic Fabric paradigm, the structural properties of space at different hierarchical length scales can be investigated using theoretical notions and computational tools from solid mechanics to address outstanding problems in cosmology and fundamental physics. For example, we propose and offer theoretical support for the "Inherent Structure Hypothesis", which states that the gravitational anomalies currently attributed to dark matter may in fact be manifestations of the inherent (undeformed) curvature of space. In addition, we develop a numerical framework wherein one can perform numerical "experiments" to investigate the implications of said hypothesis. Mark F. Horstemeyer Anzhong Wang Shantia Yarahmadian, Tomasz Haupt MSSTATE 2018-12-19 text application/pdf http://sun.library.msstate.edu/ETD-db/theses/available/etd-10182018-181952/ http://sun.library.msstate.edu/ETD-db/theses/available/etd-10182018-181952/ en unrestricted I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, Dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Mississippi State University Libraries or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, Dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, Dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, Dissertation, or project report. |
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Computational Engineering Tenev, Tichomir G. An elastic constitutive model of spacetime and its applications |
description |
We introduce an elastic constitutive model of gravity that enables the interpretation of cosmological observations in terms of established ideas from Solid Mechanics and multiscale modeling. The behavior of physical space is identified with that of a material-like medium called "cosmic fabric," which exhibits constitutive behavior. This cosmic fabric is a solid hyperplate that is broad in the three ordinary spatial dimensions and thin in a fourth hyperspatial dimension. Matter in space is treated as fabric inclusions that prescribe in-plane (three-dimensional) strain causing the transverse bending of the fabric into the fourth hyperspatial dimension. The linearized Einstein-Hilbert action, which governs the dynamics of physical space, is derived from postulating Hookes Law for the fabric, and the Schwarzschild metric is recovered from investigating matter-fabric interactions. At the continuum length scale, the Principle of Relativity is shown to apply for both moving and stationary observers alike, so that the fabrics rest reference frame remains observationally indistinguishable at such a length scale. Within the Cosmic Fabric paradigm, the structural properties of space at different hierarchical length scales can be investigated using theoretical notions and computational tools from solid mechanics to address outstanding problems in cosmology and fundamental physics. For example, we propose and offer theoretical support for the "Inherent Structure Hypothesis", which states that the gravitational anomalies currently attributed to dark matter may in fact be manifestations of the inherent (undeformed) curvature of space. In addition, we develop a numerical framework wherein one can perform numerical "experiments" to investigate the implications of said hypothesis. |
author2 |
Mark F. Horstemeyer |
author_facet |
Mark F. Horstemeyer Tenev, Tichomir G. |
author |
Tenev, Tichomir G. |
author_sort |
Tenev, Tichomir G. |
title |
An elastic constitutive model of spacetime and its applications |
title_short |
An elastic constitutive model of spacetime and its applications |
title_full |
An elastic constitutive model of spacetime and its applications |
title_fullStr |
An elastic constitutive model of spacetime and its applications |
title_full_unstemmed |
An elastic constitutive model of spacetime and its applications |
title_sort |
elastic constitutive model of spacetime and its applications |
publisher |
MSSTATE |
publishDate |
2018 |
url |
http://sun.library.msstate.edu/ETD-db/theses/available/etd-10182018-181952/ |
work_keys_str_mv |
AT tenevtichomirg anelasticconstitutivemodelofspacetimeanditsapplications AT tenevtichomirg elasticconstitutivemodelofspacetimeanditsapplications |
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1719086325129281536 |