The quasinormal modes of the charged Kalb-Ramond black

The gap

Evidence profile

Sourced from the future work and stated research gap and future-work section of the source papers, classified as general, spanning 4 journals.

Supporting evidence — 4 representative gaps

• Dyonic Black Holes in Lorentz-Violating Gravity with a Background Kalb--Ramond Field (2026) · arXiv

  In this work, we introduced a nonminimal coupling between the Kalb–Ramond and electro- magnetic fields in the presence of both electric and magnetic charges, and obtained an exact four-dimensional static, spherically symmetric dyonic black hole solution. We have further investigated its geometric properties, orbital dynamics, and thermodynamic behavior in a systematic manner. From a geometrical perspective, we calculated several curvature invariants for the black- hole spacetime and analyzed their behavior in detail. Our results show that, although the Lorentz-violating parameter can significantly modulate the curvature strength and the di- vergence structure near the center, it cannot remove the intrinsic physical singularity at the spacetime origin. This indicates that spontaneous Lorentz-symmetry breaking alone is insuf- ficient to resolve the singularity problem. Further improvement of the central geometry will – 23 – ℓ=0ℓ=0.1ℓ=0.20.000.050.100.150.200.250.300.000.050.100.15TPQ=0.1,p=0.1p=0p=0.1p=0.20.00.10.20.30.40.000.050.100.150.200.250.30TPQ=0.1,ℓ=0.1Q=0Q=0.1Q=0.20.00.10.20.30.40.000.050.100.150.200.250.30TPp=0.1,ℓ=0.1likely require higher-curvature corrections, nonperturbative effects, or a more fundamental quantum-gravity mechanism. From the perspective of orbital dynamics, we investigated the photon sphere and black hole shadow for massless photons, as well as the ISCO for massive test particles. The results show that the electric charge, magnetic charge, and Lorentz-violating parameter all induce significant modifications to the effective potential, thereby leading to systematic changes in the photon-sphere radius, the shadow size, and the ISCO radius. In particular, the interplay between the electromagnetic charges and Lorentz-violating effects alters the stability bound- aries of particle orbits and may provide a possible astrophysical channel for constraining the Lorentz-violating parameter through observables such as black hole shadows, the inner-edge structure of accretion disks, and related strong-gravity measurements. On the thermodynamic side, by incorporating the modified energy and entropy derived from the Iyer–Wald formalism and interpreting the cosmological constant as thermodynamic pressure, we established the first law of black hole thermodynamics and the Smarr relation for the dyonic Kalb–Ramond black hole in the extended phase space. We then derived the basic thermodynamic quantities, including the Hawking temperature, entropy, thermodynamic vol- ume, electric potential, and magnetic potential. By analyzing the heat capacity at constant pressure, the Gibbs free energy, and the P –T coexistence curve, we found that the system exhibits characteristic van der Waals-type critical behavior, including a first-order phase tran- sition between small and large black holes, a second-order critical point, and phase coexistence. Our results also show that the electric charge, magnetic charge, and Lorentz-violating param- eter not only shift the critical point, but also significantly reshape the swallowtail structure of the free energy and the phase-transition trajectory. Overall, our analysis shows that Lorentz violation induced by the Kalb–Ramond field modifies not only the local and global structure of the black hole spacetime, but also leaves identifiable imprints on particle orbital dynamics and thermodynamic phase transitions. The present model therefore provides a black hole setup with a clear physical interpretation and substantial potential for further investigations of Lorentz-violating effects. Several directions remain worthy of further study. First, the present model can be ex- tended to slowly rotating, or even fully rotating, configurations in order to examine the in- fluence of angular momentum on the dyonic structure, horizon properties, orbital dynamics, and thermodynamic phase behavior. Second, one may consider more general self-interaction potentials for the Kalb–Ramond field, higher-order nonminimal coupling terms, or additional curvature corrections, so as to investigate the existence and stability of analytical solutions under different vacuum structures, together with possible new phase patterns. Finally, by combining quasinormal modes, gravitational lensing, black hole accretion-disk spectra, shadow observations, and astrophysical data from facilities such as the Event Horizon Telescope, one may hope to place more direct observational constraints on the Lorentz-violating parameter and the electromagnetic charges. Such studies should help clarify the physical implications of black holes in Kalb–Ramond gravity and provide further theoretical support for experimental and observational tests of Lorentz-violating scenarios. – 24 –

  generalfuture work
  Keywords: black lorentz hole violating thermodynamic phase kalb ramond magnetic further structure electric orbital dynamics behavior
• Spherically symmetric charged (anti-)de Sitter black hole in f(R,T) gravity coupled with nonlinear electrodynamics (2026) · Annals of Physics · doi

  The paper identifies a gap in the understanding of modified gravity theories, specifically f(R,T) gravity, and their applications to black hole physics. It notes that many f(R) models face stringent constraints from local gravitational tests and solar system observations. The paper aims to address this gap by deriving an analytical solution for a static spherically symmetric magnetically charged (anti)de Sitter black hole and systematically investigating its spacetime structure and photon orbit.

  generalstated research gapevidence 5/5
  Keywords: paper identifies gap understanding modified gravity theories specifically
• Stationary Multiple Euclidon Solutions to the Vacuum Einstein Equations (2026) · Gravitation and Cosmology · doi

  The paper suggests that future research could focus on applying the results to the study of black holes in a string-theoretic framework. The paper also suggests that future research could focus on using the solutions to describe N massive magnetic dipoles in which all gravitating centers coincide with each other.

  generalfuture-work sectionevidence 5/5
  Keywords: paper suggests future research focus applying results study
• Quasinormal modes of an electrically charged Kalb-Ramond black hole (2026) · Chinese Physics C · doi

  The quasinormal modes of the charged Kalb-Ramond black hole have not been studied before. The effect of Lorentz violation on the quasinormal modes is not well understood. The development of a new approach to distinguish between different modes in undecouplable systems is needed.

  generalstated research gapevidence 3/5
  Keywords: quasinormal modes charged kalb-ramond black hole have been

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