Disformal transformation of physical quantities associated with relativistic stars

TL;DR

This paper studies how physical quantities of relativistic stars transform under disformal transformations involving scalar and vector fields, revealing invariances and differences in key star properties across frames.

Contribution

It provides a comprehensive analysis of disformal transformations' effects on relativistic star quantities in the slow-rotation approximation, including invariance properties and new insights.

Findings

Mass is frame invariant at zeroth order.

Star's angular velocity is frame invariant.

Angular momentum and moment of inertia are invariant under scalar disformal transformation but not under vector disformal transformations.

Abstract

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.