Open research questions in Black Holes and Theoretical Physics

What the literature leaves open

• We have shown that closed superforms, contracted with commuting Killing spinors, produce equivariantly closed polyforms. We then illustrated our proposal in off-shell 4d N = 2 conformal supergravity. It is important to determine more precisely how broadly our arguments apply. A component-field anal- ysis using gauge-covariant supergravity transformations rather than super-Lie derivatives should also be possible. This may connect with the rheonomic approach to super- gravity [31], where gravitino one-forms may be replaced by Killing spinors; see the discussion around Eq. (14). A next natural step is to systematically adapt our anal- ysis to Euclidean supersymmetric backgrounds, where equivariant localization formulae are applied [4, 5, 13, 15– 30]. The construction should extend to broad classes of d-dimensional supergravities with Chern–Simons, Wess– Zumino, higher-form, and boundary couplings. In such cases, as already suggested by the BF example, gauge choices and boundary terms will play an important role [16–18, 21, 23, 24] and deserve a systematic superspace analysis. For example, our superspace results, together with the framework of [40], might be directly related to the relative equivariant cohomology results of [30]. Using off-shell superconformal techniques in various di- mensions, see, e.g., [64, 65, 80, 81], one can adapt the present analysis to higher-derivative supergravities, see, e.g., [9–11, 14, 25, 43, 55, 96–111], with direct applica- tions to holography. Superspace methods can also be employed for models with hypermultiplets [112–114]. An important implication is a gravitino-counting cri- terion. From (4) and (14), the lowest-degree component of a supergravity polyform is dictated by the highest- gravitino term in its superform expansion. Up to exact- term subtleties, gauging data from Fayet–Iliopoulos terms or hypermultiplet moment maps [81, 115–118] en- ter through (composite) linear-multiplet BF couplings, which contain at most two gravitini and hence start at degree two; see (24). Hence, such terms should only contribute to bolts, in agreement with the absence of cosmological-constant/gauging terms from the nut for- mula of [10, 14]. In higher dimensions, this criterion may help identify fixed-component contributions and lead to non-renormalization theorems extending, e.g., [111]. Looking further ahead, it would be worthwhile to re- visit the superform structures of 10d and 11d supergrav- ity; see, e.g., [31, 35, 37, 53, 59, 69, 70]. The aim would be to understand whether analogous equivariant construc- tions can be used to analyze BPS geometries, including compactified backgrounds. For example, combining the superspace results of [53] with our general prescription for constructing polyforms leads to structures recently obtained for 11d supergravity in [29, 30]. Further details will be reported elsewhere. 5 Our results indicate that the equivariant structures of supersymmetric gravitational observables are not acci-

  Superform Approach to Equivariant Localization in Supergravity · 2026

• 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 –

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

• Our results strongly indicate that black rings with dipole charge r > 1 do not contribute to the 5D index, but what prevents them to contribute remains unclear to us. While some steps in the derivation remain unclear, we ignore them since our aim is mainly to fix the normalization of the conifold gap condition. An open problem is to fix the prefactor P(d, g) in the approximate formula (3. Unfortunately, our results for the coefficient of the logarithmic correction are inconclusive and suggest, if anything, that this coefficient may vanish, rather than taking the value predicted by [32].

  Large Order Enumerative Geometry, Black Holes and Black Rings · 2026

• The literature has mainly focused on abelian domain-wall D-branes and their bound states, - The investigation is limited to non-abelian domain-wall D(d -2) branes, - The possibility of su(3) branes is not pursued further due to strict requirements on the NS field-strength

  A weakly non-abelian decay channel · 2026 · DOI

• Further investigation of non-abelian domain-wall D(d -2) branes and their role in vacuum decay, - Exploration of the possibility of su(3) branes in other contexts

  A weakly non-abelian decay channel · 2026 · DOI

• Ongoing research targets quantum gravity effects to refine entropy calculations, - Recent advances have elevated interest in Bekenstein-Hawking entropy generalizations, - Further study of non-extensive entropy models and their applications

  Non-extensive entropy signatures in compact star · 2026 · DOI

• The source of non-extensiveness in black hole entropy remains unresolved. There is a need to refine entropy calculations using quantum gravity effects.

  Non-extensive entropy signatures in compact star · 2026 · DOI

• One challenge is the difficulty in computing the embedding of a single localized D5-brane, which is a very challenging problem. Another challenge is the need to discard the holographic baryons due to their unrealistic pressures. The authors also face the challenge of selecting the appropriate parameters for the model, including the choice of κ.

  Properties of stable massive quark stars in holography · 2026 · DOI

• Further study of the D5-brane, including the computation of the embedding of a single localized D5-brane. Exploration of the phenomenology of quark matter at the core of heavy compact stars.

  Properties of stable massive quark stars in holography · 2026 · DOI

• It remains to be seen whether specific sub-sectors within this classification might accommodate such a construction while preserving the consistency of the Kerr-Schild framework.

  Rotating black holes with primary hair in five-dimensional generalized Proca theory · 2026

• One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals.

  Krylov Spread Complexity as Holographic Complexity beyond Jackiw-Teitelboim Gravity · 2025 · DOI

• In this Essay, I will discuss open problems in this area of research, considering recent developments and outlining future prospects towards a complete understanding of quantum gravity.

  Essay: Emergent Holographic Spacetime from Quantum Information · 2025 · DOI

• In contrast, the algorithm hints to the existence of a new minimal transition, whose geometry and physics need to be explored.

  Decay and Fission of Magnetic Quivers · 2024 · DOI

• Future research could focus on generalizing the results to other cases. Future research could explore the implications of the results for black hole quantum mechanics.

  Black hole quantum mechanics and generalized error functions · 2026 · DOI

• The gap is the need for a general non-holomorphic completion for an arbitrary number of centers. The gap is the need for a general derivation of the Witten index of supersymmetric quantum mechanics.

  Black hole quantum mechanics and generalized error functions · 2026 · DOI

• While hierarchical mergers of black holes are suggested by some observed events (GW241011, GW241110), it cannot be said with certainty that these black holes are indeed of second-generation or that hierarchical mergers definitively occur in the universe.

  Using thermodynamics to learn gravitational wave physics · 2026 · DOI

• The paper identifies a gap in the understanding of the influence of higher curvature terms on holographic transport properties. The study aims to address the lack of knowledge about the robustness of foundational principles in gravity and their implications for holographic dualities and strongly coupled field theories.

  Viscosity of $$R^2$$ modified AdS black brane · 2026 · DOI

• The effects of pure R2 term on holographic transport had remained obscured in studies of more complex combinations of curvature invariants prior to this work.

  Viscosity of $$R^2$$ modified AdS black brane · 2026 · DOI

• The paper does not provide a general solution to the equations of motion. The analysis is limited to second order in α. The paper does not discuss the physical implications of the results.

  Stringy Corrections to Heterotic SU(3)-Geometry · 2026 · DOI

• There is a gap in the literature regarding the geometry of heterotic compactifications on SU(3) manifolds. The paper identifies a need to extend Strominger's analysis from linear order in α to second order α 2.

  Stringy Corrections to Heterotic SU(3)-Geometry · 2026 · DOI

• The paper suggests that future research should focus on developing a deeper understanding of the Bosonic Vacuum idea and its application to various phenomena in theoretical physics. The paper notes that further study is needed to fully understand the implications of the formulation and controlled laboratories.

  Bosonic Vacuum and the Dilaton: From Condensate Logic to Controlled Holonomy/Radion EFT and Quantum-Curve Geometry · 2026 · DOI

• The paper identifies a gap in the understanding of the Bosonic Vacuum idea and its application to vacuum response, defect physics, and topological inflow. The paper notes that prior work has not developed a conservative, EFT-first formulation of the Bosonic Vacuum idea.

  Bosonic Vacuum and the Dilaton: From Condensate Logic to Controlled Holonomy/Radion EFT and Quantum-Curve Geometry · 2026 · DOI

• The topology of the compactified space, the role of the natural double cover, and the precise geometry of conformal infinity are not well understood. The standard realization of the compactified space is often described in a manner that obscures its true structure.

  Conformally Compactified Minkowski Space: A Re-Examination with Emphasis on the Double Cover and Conformal Infinity · 2026 · DOI

• Further study of the properties of the spectrum-generating algebra in the linear dilaton background. Investigation of the implications of the results for the study of black holes and string theory.

  The spectrum-generating algebra for bosonic strings in a linear dilaton background · 2026 · DOI

• The formulation of higher-spin vertex operators in curved backgrounds remains an active frontier of research. The study of higher-spin string states beyond flat spacetime is an open problem.

  The spectrum-generating algebra for bosonic strings in a linear dilaton background · 2026 · DOI

Most-cited papers in Black Holes and Theoretical Physics

• Replica wormholes and the black hole interior · Journal of High Energy Physics · 2022 · 505 citations
• Topological defect lines and renormalization group flows in two dimensions · Journal of High Energy Physics · 2019 · 377 citations
• Notes on Anomaly Induced Transport · Acta Physica Polonica B · 2016 · 233 citations
• Gravitational Condensate Stars: An Alternative to Black Holes · Universe · 2023 · 198 citations
• Quantum Oppenheimer-Snyder and Swiss Cheese Models · Physical Review Letters · 2023 · 179 citations
• Non-invertible Condensation, Duality, and Triality Defects in 3+1 Dimensions · Communications in Mathematical Physics · 2023 · 170 citations
• Large N algebras and generalized entropy · Journal of High Energy Physics · 2023 · 134 citations
• Primordial non-Gaussianity up to all orders: Theoretical aspects and implications for primordial black hole models · Physical review. D/Physical review. D. · 2023 · 125 citations
• Topological classes of thermodynamics of rotating AdS black holes · Physical review. D/Physical review. D. · 2023 · 124 citations
• Noninvertible Symmetries from Holography and Branes · Physical Review Letters · 2023 · 115 citations

Most recent work

• The Carrollian kaleidoscope · The European Physical Journal C · 2026
• Gravitational quasinormal modes of the Hayward spacetime · The European Physical Journal C · 2026
• Long-lived quasinormal modes, shadows and particle motion in four-dimensional quasi-topological gravity · The European Physical Journal C · 2026
• Thermodynamics and topological classifications of static non-extremal four-charge AdS black hole in the five-dimensional $$\mathcal {N}= 2$$, $$STU-W^2U$$ gauged supergravity · The European Physical Journal C · 2026
• Topological and optical signatures of modified black-hole entropies · The European Physical Journal C · 2026
• Exact BPS double-kinks in generalized $$\phi ^4$$, $$\phi ^6$$ and sine-Gordon models · The European Physical Journal C · 2026
• A Carroll limit of AdS/CFT: A triality with flat space holography? · Physics Letters B · 2026
• Thermodynamic topology of Einstein–Maxwell-dilaton theories · The European Physical Journal C · 2026
• Simpson-visser-ads black holes: thermodynamics and binary merger · The European Physical Journal C · 2026
• Lyapunov Exponent Approach to Phase Structure of Schwarzschild AdS Black Holes Surrounded by a Cloud of Strings · Chinese Journal of Physics · 2026

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