Two Branches of Black Holes Discovered in Einstein-Weyl and Reissner-Nordström Theories

In Einstein-Weyl theory, two black hole branches exist: Schwarzschild and a numerically constructed solution. Similarly, Einstein-Weyl-Maxwell theory yields two charged black holes branching from neutral solutions when introducing charge. One charged black hole differs from Reissner-Nordström (RN), while the other resembles it, approaching RN as charge increases. The RN-like black hole’s near-extremal charge-to-mass ratio is lower than extremal RN, establishing a lower bound for the Weak Conjecture by treating the Weyl term as classical.

The Einstein-Weyl-Maxwell theory, which incorporates higher-derivative terms such as the Weyl square term, offers a unique framework for exploring black hole solutions. In their study, Ze Li and Hai-Shan Liu from Tianjin University’s Center for Joint Quantum Studies investigated charged black holes within this theory. Their research revealed two distinct branches: one resembling the Reissner-Nordström (RN) solution and another that is entirely different. Notably, the RN-like solution approaches the standard RN black hole as charge increases. Still, it exhibits a lower charge-to-mass ratio in the near-extremal limit, establishing a lower bound relevant to the Weak Conjecture. This work contributes valuable insights into the behavior of charged black holes under modified gravitational theories.

Charged black holes under Einstein-Maxwell-Weyl gravity display distinctive thermodynamic characteristics.

The article delves into charged black hole solutions within the framework of Einstein-Maxwell-Weyl gravity, a theory that merges general relativity, electromagnetism, and conformal symmetry through Weyl terms. This approach introduces higher-derivative gravity elements, such as Ricci tensor squared, into the Einstein-Maxwell model, leading to distinct black hole solutions compared to the standard Reissner-Nordström case.

These new solutions exhibit a dependency between mass and charge due to the influence of higher-order terms in their equations of motion. This interdependence affects whether these black holes can attain extremal states, where their temperature theoretically reaches zero. The thermodynamic analysis within the paper reveals that entropy and temperature calculations incorporate corrections from these higher-derivative terms, suggesting that entropy may depend on factors beyond just the event horizon’s area.

The stability of these solutions depends on specific conditions, as the higher-order terms influence perturbation behavior around the black holes. Additionally, the study explores potential thermodynamic phase transitions, which could indicate shifts in black hole stability or evaporation rates via Hawking radiation.

The implications of this research extend into astrophysics, suggesting that phenomena such as black hole radiation emission and merger dynamics might differ from those predicted by standard models. By referencing foundational works by Stelle, Wald, and Smilga, the paper situates its findings within the broader context of higher-derivative gravity theories, contributing to a deeper understanding of black hole physics and their role in astrophysical processes.

Derived exact solutions for electrically charged black holes under Einstein-Maxwell-Weyl gravity.

The study investigates charged black holes within the Einstein-Maxwell-Weyl gravity framework, combining electromagnetism with a gravitational theory incorporating conformal symmetry. By assuming spherical symmetry and specific ansatz for the metric and electromagnetic fields, the researchers derive exact solutions for electrically charged black holes. This approach simplifies the complex Einstein-Maxwell-Weyl equations while maintaining essential physical characteristics.

Thermodynamic analysis determines key quantities such as mass, charge, temperature, entropy, and electric potential. The first law of black hole thermodynamics, expressed as ( dM = T dS + Phi dQ ), is employed to ensure consistency among these derived quantities. This foundational relationship underscores the energy exchange dynamics in black hole systems.

The research extends into phase transitions by considering pressure as a variable in an extended phase space. This analysis explores how Weyl gravity’s higher derivative terms influence black hole behavior, potentially revealing distinct thermodynamic phases compared to standard Einstein-Maxwell theory. The Smarr formula is derived to relate mass, entropy, and charge, providing additional insights into the thermodynamic structure of these solutions.

Stability is assessed through specific heat analysis, where sign changes indicate phase transitions. Positive specific heat suggests stability, while negative values imply instability. Comparisons with other modified gravity theories highlight how Weyl gravity uniquely impacts black hole thermodynamics, offering novel perspectives on gravitational physics within this framework.

Charged black holes exhibit mass-dependent charge in Einstein-Maxwell-Weyl gravity.

The paper investigates charged black hole solutions within Einstein-Maxwell-Weyl gravity, integrating general relativity, electromagnetism, and conformal symmetry via Weyl tensor terms. This framework introduces higher-derivative gravity elements, such as squared Ricci or Riemann curvature terms, which alter the standard Einstein-Maxwell equations. These modifications yield novel black hole solutions characterised by a mass-dependent charge, diverging from the independence observed in conventional theory.

The thermodynamic analysis reveals corrections to entropy and Hawking temperature due to higher-derivative terms, potentially modifying the area law for entropy. Additionally, phase transitions like the Hawking-Page transition may exhibit new behaviours under these modified conditions. The solutions are within critical gravity models, which mitigate instabilities through specific parameter relations, ensuring physical validity.

These findings enhance our understanding of black hole formation and evolution in modified theories. They have implications for astrophysical phenomena and broader theoretical frameworks such as string theory, where higher-derivative terms often serve as effective descriptions. The research underscores the role of modified gravity in expanding black hole physics and thermodynamics.

The first law of black hole thermodynamics persists under gravitational modifications.

The analysis demonstrates that the first law of black hole thermodynamics ( dM = T ds + Phi dq) remains valid in the presence of higher derivative terms introduced by a Weyl term. The derivation shows that while the expressions for temperature ( T ) and electric potential ( Phi ) acquire corrections due to these terms, the thermodynamic consistency of the first law is preserved. This result underscores the robustness of black hole thermodynamics under modifications to the gravitational action.

Future work could explore the implications of this result in more general spacetime configurations, such as rotating or charged black holes with higher derivative terms. Additionally, investigating the thermodynamic properties of black holes in theories with multiple higher derivative terms or alternative gravity frameworks could provide further insights into the interplay between black hole physics and modified gravitational dynamics.