Abstract
The existence of traversable wormhole (TW) in the Einstein’s general theory of relativity is explored with density profile obtained from modified Newtonian dynamics (MOND) with or without a scalar field. The shape functions for wormholes and the null energy conditions (NEC) of matter in the wormhole are determined with a constant redshift function. Wormholes are found to exist with MOND density profile in the presence of exotic matter and determine the mass of a asymptotic flat wormhole geometry. The addition of an extra massless scalar field with MOND density profile permits wormholes even when NEC is obeyed at the throat depending on the initial value of the scalar field. Considering a non-linear equation of state (EoS) , (where A, B and ρ c are constants) in Einstein gravity we obtain TW. In this case new classes of TW solutions are determined which depends on the EoS parameters A and B. TW exists with normal matter when ρ(r 0) ⩾ ρ c and with exotic matter when ρ(r 0) < ρ c at the throat where .
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