On some topological deformation of stationary spacetimes

TL;DR

This paper introduces a new topologically rotating Schwarzschild spacetime by redefining the polar angle, leading to a physically distinct solution with unique geodesic properties and closed timelike curves, applicable also to Reissner-Nordstrom cases.

Contribution

The paper proposes a novel topological deformation of Schwarzschild spacetime using a modified angular coordinate, resulting in a new class of solutions with potential implications for rotating black holes.

Findings

Introduction of a topologically rotating Schwarzschild spacetime.

Existence of closed timelike curves due to the coordinate transformation.

Application of the method to Reissner-Nordstrom solutions.

Abstract

We define a completely new space-time starting from the well known Schwarzschild Space time by defining a new polar angle $\phi '= \phi - \omega t$ and then redefining the periodicity: instead of demanding that the original angle be periodic, we demand that the new angle $\phi'$ be periodic, with period $2\pi$. This defines the "topologically rotating Schwarzchild space", which is physically different from the standard Schwarzschild space. For this space, we work out some properties of the geodesics and related properties.This method of generating solutions can be used also for the Reissner-Nordstrom case, both in the case of Reissner-Nordstrom Black hole as well as in the case where there are no horizons, the supercharged case. Horizon shall exist in this case, but with a real singularity, not removable one by a transformation in coordinate at the radius of the horizon of the original metric. This solution should be used as an external solution rather than the internal one. Another topic to notice is that the improper coordinate transformation that we consider introduces closed time like curves.The noticeable topic is that the improper coordinate transformation introduces closed time like curves which we can possibly find here too. This is a common effect in rotating spacetimes, noticeable the Godel universe and others.