NDLI: Metric measure space as a framework for gravitation

Content Provider	Springer Nature Link
Author	Rahmanpour, Nafiseh Shojaie, Hossein
Copyright Year	2016
Abstract	In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar f, dubbed as density function, which here appears as a conformal degree of freedom. In this framework, we present conformally invariant field equations, the relevant identities and geodesic equations. In metric measure space, the volume element and accordingly the operators with integral based definitions are modified. For instance, the divergence operator in this space differs from the Riemannian one. As a result, a gravitational theory formulated in this space has a generalized second Bianchi identity and a generalized conservation of energy-momentum tensor. It is shown how, by using the generalized identity for conservation of energy-momentum tensor, one can obtain a conformally invariant geodesic equation. By comparison of the geodesic equations in metric measure space with the Bohmian trajectories, in both relativistic and non-relativistic regimes, a relation between density function f and the quantum potential is proposed. This suggests metric measure space to be considered as a suitable framework for geometric description of Bohm’s quantum mechanics. On the other hand, as it is known, Weyl geometry is one of the main approaches to construct conformally invariant gravitational models. Regarding the fact that the connection in the integrable Weyl space is modified and in metric measure space remains the same as it is in the Riemann space, the mathematical analogy between these two spaces is also discussed.
Starting Page	1
Ending Page	16
Page Count	16
File Format	PDF
ISSN	00017701
Journal	General Relativity and Gravitation
Volume Number	48
Issue Number	10
e-ISSN	15729532
Language	English
Publisher	Springer US
Publisher Date	2016-08-29
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Metric measure space Conformal transformation Bohmian trajectory Integrable Weyl space Theoretical, Mathematical and Computational Physics Classical and Quantum Gravitation, Relativity Theory Differential Geometry Astronomy, Astrophysics and Cosmology Quantum Physics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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