https://doi.org/10.1140/epjc/s10052-021-09080-1
Regular Article - Theoretical Physics
Regular black hole interior spacetime supported by three-form field
1
Department of Physics, University of the Basque Country UPV/EHU, 48080, Bilbao, Spain
2
IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain
3
Department of Physics and Center for Theoretical Sciences, National Taiwan University, 10617, Taipei, Taiwan
4
Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, 10617, Taipei, Taiwan
5
Institute of Physics, Academia Sinica, 11529, Taipei, Taiwan
6
Department of Physics Education, Pusan National University, 46241, Busan, Republic of Korea
7
Research Center for Dielectric and Advanced Matter Physics, Pusan National University, 46241, Busan, Republic of Korea
8
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 180 Siwangting Road, 225002, Yangzhou, Jiangsu, China
9
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, 200240, Shanghai, China
Received:
8
October
2020
Accepted:
22
March
2021
Published online:
2
April
2021
In this paper, we show that a minimally coupled 3-form endowed with a proper potential can support a regular black hole interior. By choosing an appropriate form for the metric function representing the radius of the 2-sphere, we solve for the 3-form field and its potential. Using the obtained solution, we construct an interior black hole spacetime which is everywhere regular. The singularity is replaced with a Nariai-type spacetime, whose topology is 
, in which the radius of the 2-sphere is constant. So long as the interior continues to expand indefinitely, the geometry becomes essentially compactified. The 2-dimensional de Sitter geometry appears despite the negative potential of the 3-form field. Such a dynamical compactification could shed some light on the origin of de Sitter geometry of our Universe, exacerbated by the Swampland conjecture. In addition, we show that the spacetime is geodesically complete. The geometry is singularity-free due to the violation of the null energy condition.
© The Author(s) 2021
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