Existence of Thin Shell Wormholes using non-linear distributional geometry

Abstract

We study for which polynomials $F$ a thin shell wormhole with a continuous metric (connecting two Schwarzschild spacetimes of the same mass) satisfy the null energy condition (NEC) in $F(R)$-gravity. We avoid junction conditions by using the mathematical framework of the Colombeau algebra which describes a generalized framework of the distributional geometry such that one can define multiplications between distributions generalizing the tensor product of smooth tensors. The aim for physics is to motivate a conjecture about the satisfaction of the NEC for suitable quadratic $F$ while the aim for mathematics is to derive a rigorous framework describing this situation. Here the $F(R)$-gravity should be seen as a toy model, important is that the NEC may be satisfied by some form of "microstructure" which does not arise in the classical setting and may have interesting physical meanings.

This paper summarizes the results of my master thesis (handed in on 4. of August 2017, defended on 24. of August 2017)

References in corpus (3)

• The use of Generalised Functions and Distributions in General Relativity
• Junction conditions for F(R)-gravity and their consequences
• Cylindrical wormholes in DGP gravity