# Unified approach to redshift in cosmological /black hole spacetimes and synchronous frame

## TL;DR

This paper presents a unified framework for understanding redshift in both static and cosmological spacetimes by transitioning between frames, aiding in the conceptual clarity of gravitational effects in general relativity.

## Contribution

It introduces a method to unify redshift interpretation in static and cosmological spacetimes through frame transformations, generalizing known frames like Lemaitre and Painlevé–Gullstand.

## Key findings

- Unified interpretation of redshift in different spacetimes
- Construction of generalized spherically symmetric frames
- Clarification of gravitation's role in general relativity

## Abstract

Usually, interpretation of redshift in static spacetimes (for example, near black holes) is opposed to that in cosmology. In this methodological note we show that both explanations are unified in a natural picture. This is achieved if considering the static spacetime one (i) makes a transition to a synchronous frame, (ii) returns to the original frame by means of local Lorentz boost. To reach our goal, we consider a rather general class of spherically symmetric spacetimes. In doing so, we construct frames that generalize the well-known Lemaitre and Painlev\'{e}--Gullstand ones and elucidate the relation between them. This helps to understanding in an unifying approach, how gravitation reveals itself in different branches of general relativity. This can be useful for general relativity university courses.