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

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.