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Register a new userThermodynamics of $f(R)$ Gravity with Disformal Transformation
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We study thermodynamics in $f(R)$ gravity with the disformal transformation. The transformation applied to the matter Lagrangian has the form of $g_{m } = A(phi,X)g_{m } + B(phi,X)pa_mfpa_ f$ with the assumption of the Minkowski matter metric $g_{m } = e_{m }$, where $phi$ is the disformal scalar and $X$ is the corresponding kinetic term of $phi$. We verify the generalized first and second laws of thermodynamics in this disformal type of $f(R)$ gravity in the Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) universe. In addition, we show that the Hubble parameter contains the disformally induced terms, which define the effectively varying equations of state for matter.
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The extended scalar-tensor and vector-tensor theories admit black hole solutions with the nontrivial profiles of the scalar and vector fields, respectively. The disformal transformation maps a solution in a class of the scalar-tensor or vector-tensor theories to that in another class, and hence it can be a useful tool to construct a new nontrivial solution from the known one. First, we investigate how the stationary and axisymmetric solutions in the vector-tensor theories without and with the $U(1)$ gauge symmetry are disformally transformed. We start from a stationary and axisymmetric solution satisfying the circularity conditions, and show that in both the cases the metric of the disformed solution in general does not satisfy the circularity conditions. Using the fact that a solution in a class of the vector-tensor theories with the vanishing field strength is mapped to that in a class of the shift-symmetric scalar-tensor theories, we derive the disformed stationary and axisymmetric solutions in a class of these theories, and show that the metric of the disformed solutions does not satisfy the circularity conditions if the scalar field depends on the time or azimuthal coordinate. We also confirm that in the scalar-tensor theories without the shift symmetry, the disformed stationary and axisymmetric solutions satisfy the circularity conditions. Second, we investigate the disformal transformations of the stationary and axisymmetric black hole solutions in the generalized Proca theory with the nonminimal coupling to the Einstein tensor, the shift-symmetric scalar-tensor theory with the nonminimal derivative coupling to the Einstein tensor, the Einstein-Maxwell theory, and the Einstein-conformally coupled scalar field theory. We show that the disformal transformations modify the causal properties of the spacetime.
We present a study of the generalized second law of thermodynamics in the scope of the f(R,T) theory of gravity, with R and T representing the Ricci scalar and trace of the energy-momentum tensor, respectively. From the energy-momentum tensor equation for the f(R,T) = R + f(T) case, we calculate the form of the geometric entropy in such a theory. Then, the generalized second law of thermodynamics is quantified and some relations for its obedience in f(R,T) gravity are presented. Those relations depend on some cosmological quantities, as the Hubble and deceleration parameters, and on the form of f(T).
Using dynamical system analysis, we explore the cosmology of theories of order up to eight order of the form $f(R, Box R)$. The phase space of these cosmology reveals that higher-order terms can have a dramatic influence on the evolution of the cosmology, avoiding the onset of finite time singularities. We also confirm and extend some of results which were obtained in the past for this class of theories.
A review of the new of the problem of dark energy using modified gravity approach is considered. An explanation of the difficulties facing modern cosmology is given and different approaches are presented. We show why some models of gravity may suffer of instabilities and how some are inconsistent with observations.
We investigate whether the new horizon first law proposed recently still work in $f(R)$ theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the new horizon first law holds true as a consequence of equations of motion in $f(R)$ theories. The formulas for the entropy and energy of black hole found here are in agreement with the results obtained in literatures. For applications, some nontrivial black hole solutions in $f(R)$ theories have been considered, the entropies and the energies of black holes in these models are firstly computed, which may be useful for future researches.
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