Eur. Phys. J. C (2017) 77: 123
https://doi.org/10.1140/epjc/s10052-017-4670-7

Regular Article - Theoretical Physics

The golden ratio in Schwarzschild–Kottler black holes

¹ Departamento de Física, Facultad de Ciencia, Universidad de Santiago de Chile, Avenida Ecuador 3493, Estación Central, Casilla 307, Santiago 2, Chile
² Facultad de Ingeniería, Universidad Diego Portales, Avenida Ejército Libertador 441, Casilla 298-V, Santiago, Chile
³ Instituto de Física y Astronomía, Universidad de Valparaíso, Avenida Gran Bretaña 1111, Casilla 5030, Valparaíso, Chile

^* e-mail: jose.villanuevalob@uv.cl

Received: 16 January 2017
Accepted: 27 January 2017
Published online: 23 February 2017

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 . This is a general result which is independent of the value and sign of the cosmological constant .