Mathematical problems in the Theory of ECO

TL;DR

This paper critically examines the mathematical foundations of the ECO paradigm, arguing that claims of black hole formation and ECO existence are unfounded and based on ad-hoc analysis, ultimately questioning the reality of black holes.

Contribution

The paper provides a detailed critique of ECO concepts, analyzing trapped surfaces, coordinate singularities, and black hole mass claims to challenge their validity and establish their baselessness.

Findings

ECOs are mathematically unfounded.

Black hole formation involving trapped surfaces is not conclusively proven.

Claims of zero mass black holes are critically examined and challenged.

Abstract

A critical overview of the concepts that govern the principles of the Eternally Collapsing Object (ECO) is entailed in this article. The mathematical analysis will be dealt to conclude the proof required for the ECO paradigm is ad-hoc in nature at best. The first section details in rejecting black holes always considers the possibility of formation of trapped surfaces, so we will begin our work by looking into "non occurrence of trapped surfaces" then we analyze Dr. Mitra's indirect claim regarding how $ R = 0$ (inside black hole) could also be treated as another coordinate singularity. After this a detailed analysis on the claim that the mass of the Schwarzschild black hole being zero is in actuality a valid claim or not. The main aim of this article is address the core issue of whether black holes indeed do exist or is it a consequence of biases that circumvent common sense over the years. This article aims to bridge the gap between ECOs and black holes and if at all black holes do exist, which was vehemently denied by the person whose paper I am reviewing. The analysis presented here will show us, why ECOs are baseless and can not really be the solution to black hole problem.