On a regular modified C-metric

Abstract

A particular form of the C-metric is investigated, giving it a non-standard interpretation and removing any singularity at $r=0$. In the weak field limit of the accelerating black hole, the proper acceleration $A$ of a static observer is constant and the geometry becomes conformally-flat (anti de Sitter). The stress tensor is of $\Lambda$-type ($\Lambda =-3a^2/8\pi G$) and its energy density is negative. We propose that $\Lambda$ is responsible of inertial forces that appear in uniformly accelerated systems (far from the accelerating source $m$ and for $r<<1/a$ the dominant term in the expression of $a^r$ is $-acos\theta$). The components of the stress tensor and all invariants of the conformally-flat Schwarzschild spacetime are regulated by means of the exponential factor $exp(-k/r),k>0$.

title changed, 7 pages, no figures

References in corpus (4)

• Interpreting the C-metric
• The algebraic structure of a cosmological term in spherically symmetric solutions
• Accelerating black holes in anti-de Sitter universe
• Uniformly accelerating black holes in a de Sitter universe

Cited by in corpus (1)

• Energy extraction from rotating regular black hole via Comisso-Asenjo mechanism