Traversable wormholes with vanishing sound speed in f(R) gravity

Salvatore Capozziello; Orlando Luongo; Lorenza Mauro

doi:10.1140/epjp/s13360-021-01104-9

2023 Impact factor 2.8

EPJ PLUS - Condensed Matter and Complex Systems

Focus Point on Modified Gravity Theories and Cosmology

Open Access

Eur. Phys. J. Plus (2021) 136: 167
https://doi.org/10.1140/epjp/s13360-021-01104-9

Regular Article

Traversable wormholes with vanishing sound speed in f(R) gravity

Salvatore Capozziello¹^,2^,3^,4^a, Orlando Luongo⁵^,6^,7 and Lorenza Mauro⁸^,9

¹ Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Via Cinthia, 80126, Napoli, Italy
² Scuola Superiore Meridionale, Largo S. Marcellino 10, 80138, Napoli, Italy
³ Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Napoli, Via Cinthia, Napoli, Italy
⁴ Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), Tomsk, Russia
⁵ Physics Division, University of Camerino, Via Madonna delle Carceri, Camerino, Italy
⁶ Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo, Pisa, Italy
⁷ National Nanotechnology Laboratory of Open Type (NNLOT), Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040, Almaty, Kazakhstan
⁸ Dipartimento di Matematica e Fisica, Università degli Studi “Roma Tre”, Via della Vasca Navale, Rome, Italy
⁹ Istituto Nazionale di Fisica Nucleare, Sezione di Frascati, Via Enrico Fermi, Rome, Italy

^a capozziello@na.infn.it

Received: 27 December 2020
Accepted: 11 January 2021
Published online: 3 February 2021

Abstract

We derive exact traversable wormhole solutions in the framework of f(R) gravity with no exotic matter and with stable conditions over the geometric fluid entering the throat. For this purpose, we propose power-law f(R) models and two possible approaches for the shape function b(r)/r. The first approach makes use of an inverse power-law function, namely $b (r) / r \sim r^{- 1 - β}$ $b(r)/r\sim r^{-1-\beta }$ . The second one adopts Padé approximants, used to characterize the shape function in a model-independent way. We single out the P(0, 1) approximant where the fluid perturbations are negligible within the throat, if the sound speed vanishes at $r = r_{0}$ $$r=r_0$$ . The former guarantees an overall stability of the geometrical fluid into the wormhole. Finally, we get suitable bounds over the parameters of the model for the above discussed cases. In conclusion, we find that small deviations from general relativity give stable solutions.

© The Author(s) 2021

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