# (Anti-)evaporation of Schwarzschild-de Sitter black holes revisited

## TL;DR

This paper challenges previous claims about black hole growth in de Sitter space, demonstrating that the Schwarzschild--de Sitter black hole does not exist within the effective action framework, requiring a reassessment of earlier results.

## Contribution

It clarifies that the Schwarzschild--de Sitter black hole does not exist in the effective action approach, revising prior assumptions about black hole evaporation and growth.

## Key findings

- Previous results rely on incorrect assumptions about Nariai spacetime.
- No Schwarzschild--de Sitter solution exists in the effective action framework.
- Revisiting earlier conclusions about black hole behaviour in de Sitter space is necessary.

## Abstract

It is widely believed that in the presence of a positive cosmological constant, heavy black holes can exhibit non-standard behaviour, namely there is a possibility that such objects would grow instead of evaporating. We point out that all those results (obtained in different frameworks) rely heavily upon the identification of the Nariai spacetime with the Schwarzschild--de Sitter (Kottler) black hole. In this note we argue that it is an incorrect assumption. As a result, previous treatments need revisiting. In particular, we show that within effective action approach, there is no solution corresponding to the Schwarzschild--de Sitter black hole.