Essay Review:Topics in the Foundations of General Relativity and Newtonian Gravitation TheoryDavid Malament,Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. Chicago: University of Chicago Press (2012), xii+349 pp., $55.00 (cloth).

2012 ◽  
Vol 79 (4) ◽  
pp. 575-583 ◽  
Author(s):  
John Byron Manchak
Keyword(s):  
General Relativity ◽  
Gravitation Theory ◽  
University Of Chicago ◽  
Newtonian Gravitation ◽  
University Of Chicago Press

scholarly journals Turning Point Principle for Relativistic Stars

2021 ◽  
Vol 387 (2) ◽  
pp. 729-759
Author(s):  
Mahir Hadžić ◽  
Zhiwu Lin
Keyword(s):  
Equation Of State ◽  
Gravitational Collapse ◽  
Turning Point ◽  
Euler System ◽  
Gravitation Theory ◽  
Spherically Symmetric ◽  
University Of Chicago ◽  
Relativistic Stars ◽  
The University ◽  
University Of Chicago Press

AbstractUpon specifying an equation of state, spherically symmetric steady states of the Einstein-Euler system are embedded in 1-parameter families of solutions, characterized by the value of their central redshift. In the 1960’s Zel’dovich (Voprosy Kosmogonii 9:157–170, 1963) and Harrison et al. (Gravitation Theory and Gravitational Collapse. The University of Chicago press, Chicago, 1965) formulated a turning point principle which states that the spectral stability can be exchanged to instability and vice versa only at the extrema of mass along the mass-radius curve. Moreover the bending orientation at the extrema determines whether a growing mode is gained or lost. We prove the turning point principle and provide a detailed description of the linearized dynamics. One of the corollaries of our result is that the number of growing modes grows to infinity as the central redshift increases to infinity.

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