# Coordinate effect: Vaidya solutions without integrating the field equations

## TL;DR

This paper extends Vaidya's algorithm to arbitrary radial radiation and shows how to algebraically derive Vaidya solutions without solving field equations, highlighting the role of curvature coordinates.

## Contribution

It introduces an algebraic method for deriving Vaidya solutions and explores the implications for variable mass functions in spacetime.

## Key findings

- Algebraic derivation of Vaidya solutions without integrating field equations
- Extension of Vaidya's algorithm to arbitrary radial radiation
- Discussion on the problem of variable mass in spacetime

## Abstract

We extend Vaidya's algorithm for the description of a central mass losing or gaining energy due to electromagnetic-type radiation (`null dust') to the case of arbitrary radial corpuscular radiation. We also demonstrate the remarkable possibility of purely algebraic deduction of the Vaidya solution without integrating the field equations, and interpret this possibility as an artifact of curvature coordinates. Since Vaidya's approach by itself cannot lead to certain dependence of mass on spacetime coordinates, the search for a corresponding mass-function represents an independent issue. In this regard, as a perspective, we discuss an outlook on the problem of variable masses as a whole.