# Energy conditions for a $T^2$ wormhole at the center

## TL;DR

This paper investigates the energy conditions necessary for the existence of a toroidal $T^2$ wormhole in general relativity, deriving inequalities for energy density, pressures, and metric components.

## Contribution

It introduces specific energy condition inequalities for a $T^2$ wormhole, focusing on the second derivatives of metric components related to the wormhole's throat.

## Key findings

- Derived inequalities for energy density and pressures
- Identified conditions for the increase in cross-sectional size
- Provided criteria for the metric components

## Abstract

Within general relativity, we determine the energy conditions needed for the existence of a toroidal $T^2$ wormhole. For this purpose, we employ the conditions of the positiveness of the second derivatives of the relevant components of the metric, which describe an increase in the linear sizes (or the area) of the cross section of the throat. The corresponding inequalities for the central energy density and pressures of the matter and for the metric are obtained.