# Generating functions of wormholes

## TL;DR

This paper explores the derivation of generating functions for wormhole geometries within Einstein's theory, using different approaches to solve field equations and analyze the properties of these functions.

## Contribution

It introduces methods to obtain wormhole generating functions by assuming different combinations of metric functions and solving the Einstein field equations.

## Key findings

- Derived explicit forms of generating functions for wormholes.
- Analyzed the impact of assumptions on wormhole geometry.
- Provided new insights into the nature of exotic matter distributions.

## Abstract

It is known that wormhole geometry could be found solving the Einstein field equations by tolerating the violation of null energy condition (NEC). Violation of NEC is not possible for the physical matter distributions, however, can be achieved by considering distributions of "exotic matter". The main purpose of this work is to find generating functions comprising the wormhole like geometry and discuss the nature of these generating functions. We have used the Herrera et al. \cite{1} approaches of obtaining generating functions in the background of wormhole spacetime. Here we have adopt two approaches of solving the field equations to find wormhole geometry. In the first method, we have assumed the redshift function $f(r)$ and the shape function $b(r)$ and solve for the generating functions. In an another attempt we assume generating functions and redshift functions and then try to find shape functions of the wormholes.