We investigate the interplay between the weak gravity conjecture (WGC) and weak cosmic censorship conjecture (WCCC) for Reissner-Nordström anti-de Sitter (RN-AdS) black holes surrounded by perfect fluid dark matter (PFDM) within restricted phase space thermodynamics (RPST) and conformal field theory (CFT) thermodynamics frameworks. The WGC ensures that gravity must be the weakest force in any consistent quantum gravity theory, while the WCCC asserts that singularities from gravitational collapse must be hidden behind event horizons. We derive complete thermodynamic descriptions including mass, temperature, entropy, and free energy in both formalisms, accounting for PFDM parameterized by γ . Our analysis reveals characteristic swallowtail patterns in free energy curves, indicating van der Waals-like first-order phase transitions under specific parameter conditions. We demonstrate that the PFDM parameter γ and AdS radius ℓ play crucial roles in satisfying both conjectures. Significantly, we find that the compatibility range for WGC in CFT thermodynamics ( 3 ℓ < γ < 10 ℓ ) is substantially wider than in RPST ( 2 / 3 ℓ < γ < 5 ℓ ). This result suggests that the holographic dictionary acts as a natural filter for Swampland constraints, rendering the boundary CFT description more fundamental for consistency checks than the bulk thermodynamic variables. At critical points of black hole parameters, we verify simultaneous satisfaction of WGC and WCCC, demonstrating robustness within the critical framework. Our results provide compelling evidence that the holographic boundary description naturally encodes quantum gravity consistency conditions more efficiently than bulk thermodynamic formalisms, with perfect fluid dark matter serving as a crucial mediator enabling the reconciliation of these fundamental principles.

A bstract Open effective field theories provide a systematic framework for describing systems coupled to an environment, where dissipation, noise, and modified conservation laws naturally arise. Working within the Schwinger-Keldysh formalism, we examine open extensions of three well-studied theories: the superfluid, Maxwell theory, and Einstein gravity. In gauge and gravitational theories, open terms that break advanced symmetries while preserving physical ones are not automatically consistent; they are allowed only if they lead to deformed identities among the equations of motion. We explicitly construct such a term in open gravity and show that it leads to a consistent deformation of the diffeomorphism identities.

Abstract Motivated by the study of entanglement island in the Karch-Randall braneworld, it has been conjectured and proven in general that entanglement island is not consistent with long-range (massless) gravity. In this paper, we provide a careful check of this conclusion in a model of massless gravity that is constructed using the Karch-Randall braneworld. We show that there is indeed no entanglement island and hence not a nontrivial Page curve due to the diffeomorphism invariance if we are studying the correct question. We will also clarify the subtlety that is important to put this question in a correct manner. Moreover, we show that this conclusion is not affected by deforming the set-up with the Dvali-Gabadadze-Porrati (DGP) terms. Furthermore, we show that the consistency of holography in this model will provide nontrivial constraints to the DGP parameters. This study provides an example that causality and holography in anti-de Sitter space can be used to constrain low energy effective theories. We also clarify several subtleties in the braneworld gravity which were overlooked in the literature. We show that a direct implication of these clarifications is a resolution of the causality paradox in the Karch-Randall braneworld. At the end, we discuss the robustness of the above results against possible coarse-graining protocols to define a subregion in a gravitational theory. Contents 1 Introduction 1 2 No Entanglement Island in Massless Gravity 4 2.1 The Set-up 4 2.2 The Question and the Result without DGP Terms 5 2.3 Adding DGP Terms Doesn't Change the Result 8 2.4 A Question in the Boundary Description 9 3 Consistency of Wedge Holography and the Swampland Bounds 10 4 The Intermediate Picture and Coarse-Graining 11 4.1 The Precise Description of the Intermediate Picture 12 4.2 An Implication-Resolution of the Causality Paradox 15 4.3 The Derivation of the Modified Island Formula 19 4.4 A Potential Puzzle and Its Resolution 21 4.5 Robustness of the Result Under Coarse Graining 22 5 Conclusion 23

Absence of gravitationally induced entanglement in certain semi-classical theories of gravity

We develop a constraint-free formulation that generalizes Padmanabhan’s method for deriving the first law of black hole thermodynamics directly from the Einstein field equations. In previous studies, even for multi-horizon black holes, variations were restricted to the outer horizon by imposing an additional constraint, and the PdV term was introduced by multiplying the field equations evaluated at the outer horizon by the corresponding volume variation dV. However, since general variations of the black hole parameters shift both horizons, variations at both horizons must be taken into account. To this end, we propose multiplying the horizon field equations by the entropy variation dS under such unconstrained variations. We show that this method remains valid even in higher-derivative theories of gravity. In addition, we find that r±-based variation schemes generically break down for black holes characterized by three independent parameters (M,J,Q). By working directly in the thermodynamic state space (M,J,Q), we show that the Einstein field equations evaluated at the outer horizon can be also interpreted as the first law of black hole thermodynamics for general variations without imposing any additional constraints.

The investigation of gravity in higher-dimensional spacetime has transitioned from a mathematical curiosity to a fundamental framework in theoretical physics, catalyzed by the dimensional requirements of String theory and M-theory. In this paper, we explicitly construct a spherically symmetric charged black hole solution in D ≥ 5 dimensions within a gravity theory featuring an infinite tower of higher-curvature corrections. For a given mass and electric charge, the model admits a unique static spherically symmetric solution. We demonstrate that, with an appropriate choice of coupling coefficients αn , the central singularity is progressively mitigated as the correction order increases, ultimately resolving into a globally regular spacetime in the limit of infinite-order corrections. Furthermore, the criteria for the existence of extremal black holes are determined.

Feasible stellar interiors beyond Einstein gravity: Insights from non-metricity-matter coupled gravitational theory

Abstract We argue that the polynomial degeneracies of curvature invariants can act as geometric selection rules for spacetime singularities in modified theories of gravity. The degeneracies arise purely from the algebraic structure of Riemannian geometry and impose non-trivial constraints on the effective energy–momentum tensor. We derive these constraints for metric f ( R ) gravity and a wide class of scalar–tensor theories to show that a singularity formation is generally occluded by curvature and/or scalar-induced anisotropies. Therefore, formation of a singularity in modified theories of gravity is not always a generic outcome but can occur only along algebraically admissible branches selected by Riemannian curvature invariants.

Correction: Effective Potentials in General Scalar-Tensor Theories of Gravity

This paper examines dark-energy compact stars under the paradigm of modified Rastall teleparallel gravity. This is the primary analysis of dark energy celestial phenomena under this modified gravitational theory. Utilizing the torsion-based functions, [Formula: see text] and [Formula: see text], we examined their impacts within a spherically symmetric space-time designated as the inner geometry, while employing the Schwarzschild geometry as the outside space-time. This study examines several features of dark energy in stars, encompassing dark energy pressure components, energy conditions, and equation of state components. Our findings indicate that the detected adverse behavior of certain stellar parameters provided substantial evidence, ensuring the presence of dark energy in celestial configurations. Thorough examinations of energy conditions, pressure profiles, sound speeds, adiabatic index, gradients, mass function, compactness, and redshift function provide a full evaluation, confirming the viability and authenticity of the analyzed stellar configuration.

In this study, we explore traversable wormhole solutions within the framework of [Formula: see text] gravity, utilizing the modified Gauss-Bonnet term [Formula: see text] and a scalar field [Formula: see text] to investigate their impact on wormhole geometry. By constructing an appropriate shape function, we ensure a smooth connection between two asymptotically flat spacetime regions while satisfying the fundamental traversability conditions. Our analysis examines the geometric structure of these wormholes and assesses the energy conditions at the throat to determine the role of exotic matter. Notably, the violation of the energy condition in our models suggests the necessity of non-standard matter sources to sustain the wormhole configuration. The results affirm that within [Formula: see text] gravity, all essential criteria for the existence of traversable wormholes are satisfied, offering new insights into modified gravity theories and their implications for astrophysical phenomena.

Abstract We perform a topological classification of the phase structure of a four-dimensional AdS black hole with non-minimal Maxwell coupling. Critical points are treated as topological defects, allowing us to assign a winding number to each black hole branch and compute the global topological invariant \(W\).&amp;#xD;The system exhibits a duality governed by its Maxwell charge \(Q\): for large \(Q\) it falls into the class \(W = +1\), displaying van der Waals–type behavior with a first-order small/large black hole transition. For small \(Q\), it shifts to \(W = 0\), characteristic of a Hawking–Page transition. This topological classification provides a model-independent validation of the conventional thermodynamic analysis. Crucially, we find that the non-minimal coupling \(\lambda\) stabilizes the Hawking–Page universality class (\(W=0\)) for black holes with non-zero charge, a phenomenon absent in the standard Reissner–Nordström–AdS case. This establishes a direct link between the microscopic coupling and the macroscopic topological class, demonstrating the power of topological methods in decoding thermodynamic universality across modified gravity theories.

Abstract The relativistic precession of the perihelion provides key evidence for general relativity and remains a powerful example for introducing students to gravitational physics. Existing approaches, however, are often too mathematically involved for many undergraduates. In this article, we present a simpler pedagogical framework that requires minimal coding and treats General Relativity and alternative theories as perturbations to the Newtonian central-force problem. The apsidal angle formalism yields compact analytical expressions for perihelion advance in four contexts: the weak-field limit of General Relativity, Yukawa modifications, $f(R)$ power-law corrections, and Brans--Dicke scalar--tensor theory. We solve the orbital equation numerically with and without these corrections, demonstrating that precession emerges universally from any deviation from the inverse-square law, including the retrograde shift characteristic of certain $f(R)$ models. Quantitative precession rates are then extracted and compared across theories through strategic parameter scaling. This approach establishes classical orbital mechanics as a versatile testing ground for gravitational theories, enabling a direct comparison of their predictions through observable dynamical consequences.

In this work we obtained solutions of field equations for perfect fluid spherically symmetric static spacetimes and found their concircular vector fields (CCVFs) in $f(R,T)$ gravity theory. It came out that special classes of these spacetimes possess either $4$-dimensional or $15$-dimensional CCVFs. In [28] the author obtained CCVFs for the same spacetimes in general relativity and it is argued that such spacetimes possess CCVFs of $4-$, $5-$, $6-$ and $15$ dimensions. Our results revealed that the $f(R,T)$ theory restricted the number of CCVFs for the same spacetime. $f(R,T)$ theory allows such spacetimes to admit either the $4$ basic Killing vector fields as CCVFs or compel the spacetime to be conformally flat and admit $15$ CCVFs. We also calculated the energy density, fluid pressure, trace of the energy-momentum tensor $T$, Ricci scalar $R$ and the function $f(R,T)$. It is observed that energy density and fluid pressure of some solutions are related as $p=-\rho$ which means that such particular metrics behave like dark energy models.

Our paper studies a novel gravastar model, building on Mazur and Mottola (M-M)’s work, within Lorentz-violating gravity configurations, focusing on the Hořava gravity and Einstein-aether theory. The M-M mechanism forms the basis for gravastars, a potential black hole (BH) substitute. This approach facilitates a three-stage model for the gravastars. Our modeled structure includes three regions: an inner region, a thin shell with ultra-relativistic fluid and the outer vacuum region and our obtained solutions for all the regions have supported the viability of our model. Different physical features for the shell region have been gone through in our study which have characterized our gravastar structure. We have shown our thin shell model’s stability through the energy condition analysis which has enhanced its physical acceptability. Thus, our research has yielded singularity-free gravastar solutions avoiding the event horizon in Hořava gravity and Einstein-aether theory, producing an alternative to the classical BH theory.

Constraining modified theories of gravity through the detection of one extremely large mass-ratio inspiral

While the quantum emergence of spacetime is becoming a major research topic in physics, the quantum emergence of intelligence has not been widely researched in quantum information science (QIS). Following causal-logical quantum gravity theory, bipolar entropy vs. entropy and negative entropy (or negentropy) are reviewed and distinguished for quantum emergence/submergence of quantum agent (QA) and quantum intelligence (QI) in algebraic terms. This work refers to QA as an entangled bipolar string/superstring in bipolar dynamic equilibrium (BDE) and QI being centered on logically definable causality in regularity, mind-light-matter unity, and brain-universe similarity. ER = EPR is extended to ER ≥≥ EPR for the mathematical scalability of bipolar strings and their collective entanglement. The extension leads to a number of conjectures, testable predictions, and theorems. The term “equilibraton” is proposed as a type of EPR or bipolar generic string to serve as an entropic stitch to collectively hold the universe together as a quantum entanglement in BDE with ubiquitous, regulated local emergence and submergence of QA&amp;QI. Equilibraton leads to the concept of bipolar entropy square—a complete entropic solution to the background issue in quantum gravity. With complete background independence, energy/information conservational bipolar entropy, energy/information invariance, bipolar entropy non-additivity, and equilibrium-based plateau concavity are introduced. The nature of the one-dimensional arrow of time is conjectured. As a unification of order and disorder for equilibrium-based regulation, bipolar entropy bridges QA&amp;QI to agentic AI, where quantum-bio-economics can be viewed as a topological intervention of a natural dynamic equilibrium in a social or natural world. Use cases are reviewed to illustrate the practical and theoretical aspects of bipolar entropy in business management, quantum-bio-economics, quantum cryptography, physics, and biology. Eddington–Einstein’s comments on entropy are revisited. It is expected that bipolar entropy will bring quantum emergence/submergence to agentic AI&amp;QI for entangled machine thinking and imagination as a naturally scalable and testable foundation of real-world quantum gravity, quantum information science (QIS), quantum cognition, and quantum biology (QCQB) to enhance Large Language AI Models (LLMs) and machine intelligence.

In this paper, we present the spinor structure associated with the Hyperbolic Clifford algebra of a real n-dimensional vector space V, which is denoted by ClHV. Unlike the standard Clifford algebra, the Hyperbolic Clifford algebra Cl(HV) simultaneously accommodates both multiforms and multivectors in a single algebraic structure, making it the natural framework—known as the “mother algebra”—for the study of superfields in theoretical physics and for generalizing the Clifford bundle formalism to hyperbolic structures arising in gravitational theories. The orthogonal groups and orthogonal transformations associated to the hyperbolic space HV are presented. The Clifford–Lipschitz group and the Pin and Spin groups associated with ClHV are defined. Then, the frame bundle and spinor structure associated to Hyperbolic Clifford algebra is derived.

Weyl conformal gravity was originally proposed in the early twentieth century as an attempt to unify gravitation and electromagnetism. Since 1989, renewed interest in this fourth-order theory of gravity has emerged following the discovery of several exact black hole solutions. In this work, we investigate the timelike circular geodesics of a spherically symmetric Weyl black hole. The effective potential, the circular geodesics and their Jacobi and Lyapunov stability are discussed. Our analysis provides new insights into the stability properties of Weyl black holes and the role of the free parameters appearing in their solutions.

Abstract We investigate the influence of boundary terms in gravitational field theories, by considering that in the Einstein–Hilbert action the boundary can be described by a non-metric Weyl-type geometry. The gravitational action and the the field equations, are thus generalized to include new geometrical terms, coming from the non-metric nature of the boundary, and depending on the Weyl vector, and its covariant derivatives. The field equations obtained within this framework generalize the standard Einstein equations by including in their mathematical structure the Weyl vector, and its covariant derivatives. As an applications of the general formalism we investigate the cosmological evolution in a flat FLRW geometry. We obtain the generalized Friedmann equations, which contain extra terms depending on the Weyl vector and its derivatives, arising due to the presence of the Weylian boundary, and which describe an effective, time dependent dark energy. By imposing to the dark energy an equation of state parameter of the Barboza–Alcaniz type, the Friedmann equations can be solved numerically. We compare the predictions of the Weylian boundary gravitational theory with late-time observational data and the predictions of the $$\Lambda $$ Λ CDM paradigm. Our results show that the Weylian boundary cosmological models give a good description of the observational data, and they can reproduce almost exactly the predictions of the $$\Lambda $$ Λ CDM paradigm. Hence, the extension of gravitational theories through the addition of Weylian boundary terms, in which dark energy has a purely geometric origin, emerges as a viable alternative to standard general relativity.