Dark matter in galaxies according to the tensor-four-scalars theory III

TL;DR

This paper extends the tensor-four-scalars theory of gravity to include normal matter, producing disk-like solutions that align with the Tully-Fisher relation but exhibit negative radial pressure.

Contribution

It introduces a method to incorporate matter into the tensor-four-scalars theory, resulting in physically relevant disk solutions with specific properties.

Findings

Matter density proportional to the fourth power of circular velocity

Disk solutions satisfy the Tully-Fisher relation

Radial pressure is negative at large radii

Abstract

We continue the study of the tensor-four-scalars theory which is a modification of general relativity. We include normal matter by applying the displace, cut, and reflect method to our previous vacuum solutions with dark halo. The resulting disklike solution has physical and unphysical features: the matter density for large radius is proportional to the forth power of the circular velocity in agreement with the Tully-Fisher relation; but the radial pressure is negative.