# The golden ratio in Schwarzschild-Kottler black holes

## TL;DR

This paper demonstrates that the golden ratio appears in the properties of null geodesics in Schwarzschild-Kottler black holes, with orbit turning points related by the golden ratio regardless of the cosmological constant.

## Contribution

It reveals a universal presence of the golden ratio in Schwarzschild-Kottler black hole geodesics, independent of the cosmological constant's value or sign.

## Key findings

- Turning points of null geodesics are in the golden ratio
- The result is independent of the cosmological constant
- Golden ratio appears in Schwarzschild-Kottler metrics

## Abstract

In this paper we show that the golden ratio is present in the Schwarzschild-Kottler metric. For null geodesics with maximal radial acceleration, the turning points of the orbits are in the golden ratio $\Phi = (\sqrt{5}-1)/2$. This is a general result which is independent of the value and sign of the cosmological constant $\Lambda$.