Abstract

This article aims at presenting a relativistic origin of the cutoff parameter \(\epsilon\) in exotic compact objects (ECOs). The cutoff parameter \(\epsilon\) is defined as the distance between the ECO surface of radius \(r\) and the Schwarzschild radius \(r_{s}\); \(\epsilon\) is a measure of the compactness of the exotic compact objects. The parameter is estimated by observing a spherical thin shell of dust as it collapses from infinity to the Schwarzschild radius \(r_{s}\) in the frame of a fiducial observer (FIDO). This is key because it distinguishes a black hole (BH) from other types of ECOs in the frame of a FIDO. If the cutoff parameter \(\epsilon\to 0\), this implies that the geometry outside the ECO is consistent with that of a BH. This model can estimate \(\epsilon\) without knowledge of quantum gravity details.

中文翻译：

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奇异致密天体中截止参数的相对论起源

摘要

本文旨在展示奇异紧凑物体 (ECO) 中截止参数\(\epsilon\)的相对论起源。截断参数\(\epsilon\)定义为半径为\(r\)的 ECO 表面与史瓦西半径\(r_{s}\)之间的距离；\(\epsilon\)是对奇异致密物体的致密性的度量。该参数是通过在基准观察者 (FIDO) 的框架中观察从无穷远到 Schwarzschild 半径\(r_{s}\)坍缩的球形薄尘埃壳来估计的。这是关键，因为它将黑洞 (BH) 与 FIDO 框架中的其他类型的 ECO 区分开来。如果截止参数\(\epsilon\to 0\)，这意味着 ECO 外部的几何形状与 BH 的几何形状一致。该模型可以在不了解量子引力细节的情况下估计\(\epsilon\)。