Relativistic stars in differential rotation: bounds on the dragging rate and on the rotational energy

TL;DR

This paper establishes bounds on the dragging rate and rotational energy in relativistic stars with differential rotation, showing positivity conditions and inequalities that constrain their rotational dynamics.

Contribution

It proves that for a broad class of rotation laws, the dragging rate and angular momentum density are positive, and derives an upper bound on the total rotational energy.

Findings

Dragging rate and angular momentum density are positive under certain rotation laws.

The mean dragging rate is less than the mean fluid angular velocity.

An upper bound on the total rotational energy is established.

Abstract

For general relativistic equilibrium stellar models (stationary axisymmetric asymptotically flat and convection-free) with differential rotation, it is shown that for a wide class of rotation laws the distribution of angular velocity of the fluid has a sign, say "positive", and then both the dragging rate and the angular momentum density are positive. In addition, the "mean value" (with respect to an intrinsic density) of the dragging rate is shown to be less than the mean value of the fluid angular velocity (in full general, without having to restrict the rotation law, nor the uniformity in sign of the fluid angular velocity); this inequality yields the positivity and an upper bound of the total rotational energy.