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Generalized Parallel Transport and Coordinate Transformations in f(R) Gravity
Emre Dil 한국물리학회 2016 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.69 No.12
In this paper, we study the generalized parallel transport of vectors and generalized coordinate transformations between generalized reference frames described in f(R) gravity. After constructing the generalized parallel transport relations and the generalized transformation laws in f(R) gravity, we discuss the implications of these laws and present the differences between f(R) gravity and Einstein’s general relativity. For a constant Ricci scalar case with de Sitter-like behavior for a de Sitter space-time, we find that the parallel transport is invariant under the conformal transformation from general relativity to f(R) gravity. However, for a non-de Sitter space-time, parallel transport differs by an extra field term.
Gravitational Entropy of a Schwarzschild-Type Black Hole
Emre Dil 한국물리학회 2016 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.69 No.1
In this study, Clifton, Ellis and Tavakol’s gravitational entropy proposal is used to determine the entropy of free gravitational fields due to a spherical symmetric Schwarzschild-type black hole which is considered in the framework of f(R) gravity. In order to obtain the gravitational entropy, we calculate the Weyl tensor of the black hole to determine the Bel-Robinson tensor, giving the super energy density. By using the super energy density, we obtain the gravitational energy density and the gravitational temperature to calculate the gravitational entropy of the f(R) gravity black hole. This proposal can reproduce the Bekenstein-Hawking value in general relativity limit, but cannot reproduce it in the f(R) gravity case.