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

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 $$b(r)/r\sim r^{-1-\beta }$$ b ( r ) / r ∼ r - 1 - β . 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.

Accretion disc luminosity for black holes surrounded by dark matter

“…Frequently, "exotic" matter contributions seem to be needed to describe hypothetical objects that are massive and compact, in order to fulfill stability criteria. Similar examples can often be found for wormholes and cosmological backgrounds [12][13][14], and likely exotic matter could indicate a possible signature of general relativity's breakdown [15,16].…”

Traversable Wormholes in the Extended Teleparallel Theory of Gravity with Matter Coupling

“…can be found in the literature. [ 18–26 ] In a recent work physically viable wormhole solutions in the theory of gravity with exponential model have been discussed by Mustafa et al. [ 30 ] Recently, Falco et al.…”

“…[17] Classical works comprising the modified theory of f (R) gravity by Capozziello et al can be found in the literature. [18][19][20][21][22][23][24][25][26] In a recent work physically viable wormhole solutions in the f (R) theory of gravity with exponential model have been discussed by Mustafa et al [30] Recently, Falco et al have discussed the wormhole solutions through the Poynting-Robertson effect. [27,28] Non-extremal spherically symmetric instanton wormhole solution in string theory have been discussed by Bergshoeff et al [31] Maldacena et al have presented a study of some traversable wormhole geometries in the background of AdS 2 gravity.…”

Viable Wormhole Solutions in Energy-Momentum Squared Gravity

“…Recently, Capozziello et al [39] derived the exact traversable WH solutions as well as stable conditions in the absence of exotic matter in f (R) theory and found that small deviation from GR give stable solutions. De Falco et al [40] formulated the static spherically symmetric WH solutions in the same framework.…”