Taub-NUT-like Black Holes in Einstein-Bumblebee Gravity

TL;DR

This paper constructs new Taub-NUT-like black hole solutions in Einstein-Bumblebee gravity, analyzes their thermodynamics, and extends the solutions to include a cosmological constant, confirming the validity of thermodynamic laws.

Contribution

The paper introduces novel Taub-NUT-like black hole solutions in Einstein-Bumblebee gravity and explores their thermodynamics, including the AdS extension with a cosmological constant.

Findings

Constructed non-Ricci-flat Taub-NUT-like black hole solutions.

Confirmed the first law and Smarr relation for these solutions.

Extended solutions to include a cosmological constant with consistent thermodynamics.

Abstract

We consider Einstein-Bumblebee gravity and construct a novel Taub-NUT-like black hole solution within this theory. Different from the Taub-NUT black hole in Einstein gravity (which is Ricci-flat), our newly constructed Taub-NUT-like black hole is not Ricci-flat. Armed with the Wald formalism, we extensively study the thermodynamics of this black hole solution and confirm that both the first law of thermodynamics and the Smarr relation hold. We then take a further step by adding a cosmological constant to the Einstein-Bumblebee theory, and successfully construct a Taub-NUT-AdS-like black hole. We derive all the thermodynamic quantities, including treating the cosmological constant as a pressure, and confirm that the first law and Smarr relation hold as well.