Mathematical Analyses of an accelerating (Griffiths-Podolsky) Black Hole

TL;DR

This paper provides a detailed mathematical analysis of an exact solution describing accelerating and rotating black holes, focusing on Riemann components and optical properties using advanced formalisms.

Contribution

It offers a comprehensive mathematical examination of the Griffiths-Podolsky black hole solution, including Riemann tensor components and optical characteristics.

Findings

Explicit form of the spinning C-metric derived

Riemann components analyzed in detail

Optical properties studied via Newman-Penrose formalism

Abstract

An exact solution of Einsteins equations which represents a pair of accelerating and rotating black holes was presented by J. B. Griffiths and J. Podolsky [2]. In the paper [2] they have shown the explicit form of a spinning C-metric starting from the Plebanski-Demianski metric, and transformed it using NUT and angular velocity parameters in addition to the usual parameters and thus gave a generalized form of such solutions. In the forthcoming discussion, an attempt has been made to realize the Riemann components of the proposed metric. Furthermore, certain optical characteristics of the metric have been analyzed using the Newman-Penrose formalism.