https://doi.org/10.1140/epjc/s10052-015-3481-y
Regular Article - Theoretical Physics
On static black holes solutions in Einstein and Einstein–Gauss–Bonnet gravity with topology 
1
Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi, 110025, India
2
Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Pune, 411 007, India
3
Departament d’Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos (ICCUB), Facultat de Fsica, Universitat de Barcelona, Diagonal 647, 08028, Barcelona, Catalonia, Spain
* e-mail: pons@ecm.ub.es
** e-mail: pons@ecm.ub.edu
Received:
15
January
2015
Accepted:
26
May
2015
Published online:
24
June
2015
We study static black hole solutions in Einstein and Einstein–Gauss–Bonnet gravity with the topology of the product of two spheres, , in higher dimensions. There is an unusual new feature of the Gauss–Bonnet black hole: the avoidance of a non-central naked singularity prescribes a mass range for the black hole in terms of 
. For an Einstein–Gauss–Bonnet black hole a limited window of negative values for 
is also permitted. This topology encompasses black strings, branes, and generalized Nariai metrics. We also give new solutions with the product of two spheres of constant curvature.
© The Author(s), 2015
