Volume 7, Issue 6, December 2019, Page: 84-87
The Schwarzschild Mass in General Relativity
Praveen Singh Negi, Department of Physics, Faculty of Science, Kumaun Universsity, Nainital, India
Received: Nov. 23, 2019;       Accepted: Dec. 18, 2019;       Published: Dec. 30, 2019
DOI: 10.11648/j.ijass.20190706.13      View  474      Downloads  91
The central (surface) energy-density, E0 (ER), which appears in the expression of total static and spherical mass, M (corresponding to the total radius R) is defined as the density measured only by one observer located at the centre (surface) in the Momentarily Co-moving Reference Frame (MCRF). Since the mass, M, depends only on the central (surface) density for most of the equations of state (EOSs) and/or exact analytic solutions of Einstein’s field equations available in the literature, the central (surface) density measured in the preferred frame (that is, in the MCRF) appears to be not in agreement with the coordinate invariant form of the field equations that result for the source mass, M. In order to overcome the use of any preferred coordinate system (the MCRF) defined for the central (surface) density in the literature, we argue for the first time that the said density may be defined in the coordinate invariant form, that is, in the form of the average density, (3M/4πR3), of the configuration which turns out to be independent of the radial coordinate r and depends only on the central (surface) density of the configuration. In this connection, we further argue that the central (surface) density of the structure should be independent of the density measured on the other boundary (surface/central) because there exists no a priori relation between the radial coordinate r and the proper distance from the centre of the sphere to its surface [1]. In the light of this reasoning, the various EOSs and analytic solutions of Einstein’s field equations in which the central and the surface density are interdependent can not fulfill the definition of central (surface) density measured only by one observer located in the MCRF at the centre (surface) of the configuration.
Static Spherical Structures, Analytic Solutions, Neutron Stars, Dense Matter, Equation of State
To cite this article
Praveen Singh Negi, The Schwarzschild Mass in General Relativity, International Journal of Astrophysics and Space Science. Vol. 7, No. 6, 2019, pp. 84-87. doi: 10.11648/j.ijass.20190706.13
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