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Register a new userDisformal transformation of physical quantities associated with relativistic stars
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Authors
Masato Minamitsuji
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We investigate how physical quantities associated with relativistic stars in the Jordan and Einstein frames are related by the generalized disformal transformations constructed by the scalar and vector fields within the slow-rotation approximation. We consider the most general scalar disformal transformation constructed by the scalar field, and by the vector field without and with the $U(1)$ gauge symmetry, respectively. At the zeroth order of the slow-rotation approximation, by imposing that both the metrics of the Jordan and Einstein frames are asymptotically flat, we show that the Arnowitt-Deser-Misner mass is frame invariant. At the first order of the slow-rotation approximation, we discuss the disformal transformations of the frame-dragging function, angular velocity, angular momentum, and moment of inertia of the star. We show that the angular velocity of the star is frame invariant in all the cases. While the angular momentum and moment of inertia are invariant under the scalar disformal transformation, they are not under the vector disformal transformation without and with the $U(1)$ gauge symmetry.
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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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