"Information Paradox" and Schwarzschildian geodesics

TL;DR

This paper argues that the black hole information paradox arises from misinterpretations of Schwarzschild geodesics, emphasizing that previous analyses overlooked key aspects of the metric and orbit conditions.

Contribution

It clarifies the limitations of the differential equation for Schwarzschild geodesics, highlighting overlooked regions and conditions relevant to the information paradox.

Findings

The geodesic equation does not fully capture all consequences of the metric.

Circular orbit conditions are not derived from the standard geodesic equation.

The analysis neglects regions where the radial coordinate is less than or equal to twice the mass.

Abstract

We show that the "Information Paradox" follows from inappropriate considerations on the geodesics of a Schwarzschildian manifold created by a gravitating point-mass. In particular, we demonstrate that the geometric differential equation which gives the radial coordinate as a function of the angular coordinate of the geodesics does not represent fully all the consequences following from the metric tensor. We remark that: i) it does not yield the conditions characterizing the circular orbits; (this fact has been ignored in the previous literature); ii) it "neglects" the space region in which the radial coordinate is minor or equal to twice the mass of the gravitating point (in suitable units of measure).