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The binding energy of a Schwarzschild sphere in D space‐time dimensions
Author(s) -
Wolf C.
Publication year - 1991
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113120505
Subject(s) - schwarzschild radius , photon sphere , physics , schwarzschild metric , deriving the schwarzschild solution , radius , schwarzschild geodesics , newtonian fluid , spheres , binding energy , classical mechanics , space (punctuation) , total energy , mathematical physics , quantum mechanics , spacetime , kerr metric , charged black hole , general relativity , astronomy , psychology , linguistics , philosophy , computer security , computer science , displacement (psychology) , psychotherapist
We calculate the binding energy of a Schwarzschild gas sphere in D space time dimensions. To the post‐Newtonian approximation we demonstrate that the interior Schwarzschild solution does not exhibit an instability before the Schwarzschild radius is reached for D = 4. For D = 5, 6 we find binding energy is negativ to the post‐Newtonian approximation. Extending the approximation to the post‐post‐Newtonian approximation we find that the post‐post‐Newtonian contribution to the binding energy of a Schwarzschild gas sphere is positive for the cases D = 4, 5, 6. The effect of the post‐post‐Newtonian contribution to the binding energy on the stability of higher dimensional gas spheres is discussed.