Reply to the "Comment on The Tully-Fisher law and dark matter effects derived via modified symmetries by I. Arraut"

TL;DR

This paper defends the validity of a modified symmetry approach to the Tully-Fisher law and dark matter effects, clarifying misconceptions and correcting misinterpretations in a critical comment.

Contribution

It provides a detailed rebuttal demonstrating that the original results are correct and addresses misunderstandings about the metric solution and energy conditions.

Findings

Original results are valid and consistent with energy conditions

Misinterpretations in the comment are clarified and corrected

The modified symmetry approach remains a viable explanation for dark matter effects

Abstract

It has been claimed in \cite{1}, that the idea proposed in \cite{2} has certain mistakes based on arguments of energy conditions and others. Additionally, some of the key arguments of the paper are criticized. Here we demonstrate that the results obtained in \cite{2} are correct and that there is no violation of any energy condition. The statements claimed in \cite{1} are based on three things: 1). Misinterpretation of the metric solution. 2). Language issues related to the physical quantities obtained in \cite{1}, where the authors make wrong interpretations about certain results over the geometry proposed in \cite{2}. 3). Non-rigorous evaluations of the vacuum condition defined via the result over the Ricci tensor $R_{\mu\nu}=0$