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Dyonic RN-like and Taub-NUT-like black holes in Einstein-bumblebee gravity

Shoulong Li, Liang Liang, Liang Ma

TL;DR

This work constructs exact four-dimensional dyonic Reissner–Nordström–like black holes with topological horizons in Einstein-bumblebee gravity, a simple vector-tensor theory that implements spontaneous Lorentz symmetry breaking. By solving the coupled Einstein–bumblebee–Maxwell equations, the authors obtain an exact dyonic solution with metric functions h and f related by ℓ = b^2 γ, and electric/magnetic charges q and p, while imposing specific nonminimal couplings γ1, γ2 to ensure consistency (γ1 = γ/[4(2+3ℓ)], γ2 = -2γ(1+ℓ)/[(2+ℓ)(2+3ℓ)]). They then establish a consistent first law of black hole thermodynamics using the Wald formalism, calculating mass and entropy in a way that resolves previous ambiguities in these Lorentz-violating setups. The paper also extends to Taub–NUT–like dyonic solutions, and generalizes the RN-like construction to higher even dimensions, providing explicit expressions for thermodynamic quantities and Smarr relations. Together, these results illuminate the impact of spontaneous Lorentz symmetry breaking on black hole physics and offer a robust framework for exploring observational signatures in extended gravity models.

Abstract

Einstein-bumblebee gravity is one of the simplest vector-tensor theories that realizes spontaneous Lorentz symmetry breaking. In this work, we first construct an exact dyonic Reissner-Nordström-like black hole solution in four dimensions, carrying both electric and magnetic charges and admitting general topological horizons. We then study its thermodynamic properties, and employ the Wald formalism to compute the conserved mass and entropy, thereby establishing the first law of black hole thermodynamics. Furthermore, we generalize these results to Taub-Newman-Unti-Tamburino case and higher dimensions case.

Dyonic RN-like and Taub-NUT-like black holes in Einstein-bumblebee gravity

TL;DR

This work constructs exact four-dimensional dyonic Reissner–Nordström–like black holes with topological horizons in Einstein-bumblebee gravity, a simple vector-tensor theory that implements spontaneous Lorentz symmetry breaking. By solving the coupled Einstein–bumblebee–Maxwell equations, the authors obtain an exact dyonic solution with metric functions h and f related by ℓ = b^2 γ, and electric/magnetic charges q and p, while imposing specific nonminimal couplings γ1, γ2 to ensure consistency (γ1 = γ/[4(2+3ℓ)], γ2 = -2γ(1+ℓ)/[(2+ℓ)(2+3ℓ)]). They then establish a consistent first law of black hole thermodynamics using the Wald formalism, calculating mass and entropy in a way that resolves previous ambiguities in these Lorentz-violating setups. The paper also extends to Taub–NUT–like dyonic solutions, and generalizes the RN-like construction to higher even dimensions, providing explicit expressions for thermodynamic quantities and Smarr relations. Together, these results illuminate the impact of spontaneous Lorentz symmetry breaking on black hole physics and offer a robust framework for exploring observational signatures in extended gravity models.

Abstract

Einstein-bumblebee gravity is one of the simplest vector-tensor theories that realizes spontaneous Lorentz symmetry breaking. In this work, we first construct an exact dyonic Reissner-Nordström-like black hole solution in four dimensions, carrying both electric and magnetic charges and admitting general topological horizons. We then study its thermodynamic properties, and employ the Wald formalism to compute the conserved mass and entropy, thereby establishing the first law of black hole thermodynamics. Furthermore, we generalize these results to Taub-Newman-Unti-Tamburino case and higher dimensions case.

Paper Structure

This paper contains 16 sections, 106 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The theory and its EOMs
  3. Dyonic RN-like topological black holes in four dimensions
  4. Exact dyonic solution
  5. The difference from Liu:2024axg
  6. Thermodynamics
  7. Wald formalism
  8. Dyonic Taub-NUT-like black holes
  9. Exact solution
  10. Normal thermodynamic quantities
  11. Unnormal thermodynamic quantities
  12. Generalization to higher dimensions
  13. High dimensional dyonic RN-like solutions
  14. Thermodynamics
  15. Some explicit examples
  16. ...and 1 more sections

Figures (1)

  • Figure 1: Owing to the NUT charge, the Wald formalism has singularities at $u = \pm 1$. We select the integration path illustrated below to bypass these singularities.