arXiv subjects

Bayram Tekin

Publications and source records attributed to Bayram Tekin.

At least 19 recordsLinked to original sources

arXiv2026

Conserved Gravitational Charges as Curvature Fluxes

Conserved gravitational charges are commonly expressed as surface integrals of the metric perturbation and its first derivatives. We show that, in the usual asymptotically AdS and asymptotically flat settings, the standard charges admit equivalent representatives as fluxes of linearized curvature. The construction uses a divergence-free rank-four tensor whose trace is proportional to the cosmological Einstein tensor. On a maximally symmetric AdS background, it reproduces the known curvature representation of the Abbott-Deser charges. The asymptotically flat construction is not obtained by taking a naive $\Lambda \rightarrow 0$ limit, since the Killing two-form vanishes for translations. We instead introduce an antisymmetric Poincar\'e Killing potential. A representative Killing potential adapted to the algebraic Bianchi identity converts the linearized Einstein current into a total divergence and yields a single curvature-flux formula. Its translation sector reproduces the ADM energy--momentum, while in four dimensions its Lorentz sector reproduces the angular momentum and boost/center-of-mass charges under the standard Regge-Teitelboim falloff and parity conditions. The normalization is checked explicitly for Schwarzschild, boosted Schwarzschild, and Kerr data. On non-maximally symmetric Einstein backgrounds, background Weyl curvature generates additional terms, so the maximally symmetric construction does not directly extend to a pure codimension-two curvature-flux formula.

gr-qc↗

arXiv2026

Landau Levels on the Surface of a Cube

We study the quantum mechanics of a charged particle confined to the surface of a cube enclosing a magnetic monopole. The magnetic field is chosen to have a constant magnitude on each face and to point along the outward normal, preserving the rotational symmetry of the cube. We formulate the continuum problem using two gauge patches on the cube surface and show that consistency of the wavefunction gives the Dirac quantization condition. Since an explicit vector potential does not remain invariant under ordinary rotations, we construct gauge-modified rotation operators and use them to classify the eigenstates. Even monopole charges are described by the irreducible representations of the cubic rotation group O, while odd monopole charges require the spinorial representations of the binary octahedral group 2O. We compute the spectrum with a gauge-covariant finite-difference discretization and find Landau-level-like manifolds whose degeneracies are split by the discrete cubic symmetry. We also study the corresponding tight-binding Hofstadter problem on the discretized cube. The resulting spectrum contains the usual magnetic subband structure together with additional gap states localized near the cube corners.

quant-ph↗

arXiv2026

Dynamical Completion of Coupling-Charge Thermodynamics

The scalar-gauge pair formulation promotes gravitational coupling constants to conserved charges, clarifying their role in extended black hole thermodynamics. However, its original incarnation restricts these auxiliary scalar fields to rigid, non-dynamical configurations. In this paper, we introduce a local, dynamical completion of this framework. By constructing the kinetic sector from a defect, which is the difference between the top-form field strength and the associated gravitational Lagrangian density, we allow the scalar to propagate as a genuine massive degree of freedom. Crucially, this local sector acts as a charge-preserving massive scalar backreaction, ensuring the thermodynamic coupling remains a conserved integration constant rather than a locally varying field. When evaluated on constant-coupling configurations, the auxiliary stress-energy contributions vanish entirely, perfectly preserving the original black hole solutions, the first law, and the Smarr relation. We illustrate this construction using the cosmological constant and the Gauss-Bonnet coupling.

gr-qc↗

arXiv2026

The auxiliary-metric formulation of Born-Infeld New Massive Gravity

Born-Infeld New Massive Gravity (BINMG) completes New Massive Gravity to all orders in curvature through the determinant of the metric shifted by the Einstein tensor. We recast it with an independent auxiliary metric $q_{\mu\nu}$, whose algebraic equation of motion $q_{\mu\nu}=g_{\mu\nu}+\frac{\sigma}{m^2}G_{\mu\nu}(g)$ recovers the determinant action exactly on the regular branch and resums the infinite curvature series into a single relation. In the densitized variable $P^{\mu\nu}=\sqrt{-q}\,q^{\mu\nu}$ the three-dimensional action is polynomial, with all derivative dependence carried by the coupling $P^{\mu\nu}G_{\mu\nu}(g)$. The formulation makes known properties follow with substantially less algebra: the unique vacuum follows in one line, and the quadratic action yields a single Pauli-Fierz massive spin-2 field with the Fierz-Pauli tuning generated rather than imposed. On locally AdS backgrounds the conserved charges, BTZ mass and angular momentum, central charge, and entropy reduce to the Einstein results times a common factor. The formulation also isolates the nonlinear degree-of-freedom problem in the right variables, leaving the full Dirac count to separate work.

gr-qc↗

arXiv2026

The Flat Critical Branch Between Nariai and Bertotti-Robinson Geometries as a Solution of Cosmological Einstein-Maxwell Theory

We analyze a class of product geometries of the form $\mathbb{R}^{1,1}\times Σ_2$ supported by electric, magnetic, or dyonic flux in the Einstein-Maxwell-$Λ$ theory. These spacetimes belong to a unified family of direct products $(dS_2,\mathbb{R}^{1,1},AdS_2)\times Σ_2$ distinguished solely by the sign of the Lorentzian curvature of the two-dimensional factor. We focus on the critical configuration for which the Lorentzian curvature vanishes. At this balance point between the cosmological curvature and the Maxwell stress, the longitudinal geometry becomes exactly flat while the transverse sphere radius is fixed algebraically by the conserved flux. We refer to this geometry as the critical Maxwell flux string: a homogeneous flux-supported geometry curved only in the transverse directions and invariant along a two-dimensional null worldvolume. It represents the algebraic midpoint interpolating between the Nariai $(dS_2\times S^2)$ and Bertotti-Robinson $(AdS_2\times S^2)$ spacetimes. A qualitative structural change occurs precisely at this midpoint. The spacetime is Petrov type-D with constant scalar curvature invariants, placing it in the degenerate Kundt/CSI class. Because the curvature structure reduces any polynomial rank-two tensor to a linear combination of the metric and the Maxwell stress tensor, the same configuration solves a broad class of algebraic higher-curvature gravity theories. In this sense, the critical flux string and its aligned deformations constitute almost universal solutions.

gr-qc↗

arXiv2026

Static Tidal Perturbations of Relativistic Stars: Corrected Center Expansion and Love Numbers-I

We revisit static tidal perturbations of relativistic stars with emphasis on two technical issues in the standard quadrupolar formulation. First, we derive the regular-center Frobenius expansion of the interior even-parity master function and obtain a corrected subleading coefficient, which differs from the expression commonly used in the literature. Second, we derive the static even-parity master equation on a Schwarzschild-de Sitter background, extending the usual asymptotically flat problem to a two-horizon geometry. To place these results on a common footing, we also show how the general interior even-parity system in Regge-Wheeler gauge reduces to the standard quadrupolar equation used in Love-number calculations. Numerical integrations for polytropic equations of state show that the corrected center coefficient affects only subleading initial data and leaves the extracted Love number $k_2$ unchanged within numerical accuracy. Taken together, these results fix the regular-center input to the standard quadrupolar problem and extend the static even-parity formalism to Schwarzschild-de Sitter backgrounds.

gr-qc↗

arXiv2026

Geometrically Significant Surfaces of Black Holes from a Single Scalar

Black hole spacetimes contain several geometrically distinguished hypersurfaces, including event and Cauchy horizons, stationary-limit surfaces, and curvature singularities. These structures are usually identified by different geometric or causal criteria. We show that, for the Kerr--Newman black hole, the membrane-paradigm pressure of a stretched horizon admits an analytically continued scalar representative whose fully factorized form has zeros, poles, and singular factors aligned with these standard Kerr--Newman loci. Its zeros occur at the outer and inner horizons, its poles occur at the outer and inner stationary-limit surfaces, its higher-order divergence contains the ring-singularity factor, and its large-$r$ behavior records the asymptotic decay of the scalar. The construction is not proposed as a new invariant characterization of the spacetime, nor as a physical extension of the membrane fluid into the black-hole interior. Rather, it gives a compact membrane-pressure-based diagnostic whose analytic structure reorganizes several familiar surfaces of the Kerr--Newman geometry. We also note a secondary, purely algebraic analogy with generalized multi-component van der Waals-type equations of state.

gr-qc↗

arXiv2026

Almost Universal Metrics

A metric is called universal if every symmetric conserved rank-two tensor constructed locally from the metric, the curvature, and covariant derivatives of the curvature is proportional to the metric. Such a metric solves arbitrary metric-based higher-curvature field equations after, at most, a change in the effective cosmological constant. A metric is called almost universal if the same field equations reduce instead to a finite set of algebraic conditions and a single linear scalar equation for a profile function. Universal and almost universal metrics are useful because they keep higher-curvature gravity under analytic control. Plane waves are a well-known example of universal metrics, while the Kerr-Schild-Kundt class of metrics including the $pp$-waves is almost universal. Here, we add a new member to this class of metrics and show that nonzero constant curvature $pp$-wave metrics are also almost universal. They reduce the generic gravity field equations to those of cosmological Einstein-Maxwell theory with null dust. The background of the $pp$-waves has the topology $\mathbb{R}^{1,1}\times S^{2}$ and provides the missing partner to the Nariai metric with ${\rm dS}^{2}\times S^{2}$ and the Bertotti-Robinson metric with ${\rm AdS}^{2}\times S^{2}$ topologies. These quantum-protected metrics are of clear interest. We exemplify our results by using the quadratic and cubic gravity theories.

gr-qc↗

arXiv2026

Can Fractional Time Operators Reproduce Gravitational-Wave Memory? A No-Go Result

We initiate an investigation into whether fractional calculus, with its intrinsic long-tailed memory and nonlocal features, can provide a viable model for gravitational-wave memory effects. We consider two toy constructions: ($i$) a fractional modification of the linearized Einstein field equations using a sequential Caputo operator; and ($ii$) a fractionalized quadrupole formula in which the same operator acts on the source moment. Both constructions yield history-dependent responses with small memory-like offsets. However, in all cases we studied, the signal decays to zero at late times, failing to reproduce the permanent displacement predicted by General Relativity. We showed that, under asymptotic and spatial flatness of spacetime, the solutions of the proposed models decay to zero at late times when the time derivatives of the perturbed metric are temporally localized and bounded at each spatial point. Therefore, our results constitute a no-go demonstration: naive fractionalization is insufficient to model the permanent offset in the metric without explicitly building in flux-balance laws or asymptotic symmetry structure. We argue that any successful model must incorporate fractional kernels directly into the hereditary flux-balance integral of General Relativity while preserving gauge invariance and dimensional consistency. We also discuss possible connections to modified gravity and the absence of memory in spacetime with $D>4$ dimensions.

gr-qc↗

arXiv2026

Geometry is Wavy: Curvature Wave Equations for Generic Affine Connections

Geometry is wavy: even at the purely geometric level (no particular theory chosen), curvature satisfies a covariant quasilinear wave equation. In Riemannian geometry equipped with the Levi-Civita connection, the Riemann curvature tensor obeys a wave equation of the schematic form \[ \Box Riem=\mathcal{Q}(Riem,Riem), \] where $\mathcal{Q}(Riem,Riem)$ denotes the terms quadratic in the curvature arising from the Bianchi identities. In this work, we generalize this curvature wave equation to spacetimes endowed with a generic affine connection possessing torsion and nonmetricity. Working within the metric-affine framework, we derive the corresponding wave equation for the Riemann tensor and analyze its structure in several geometrically and physically distinguished settings, including Einstein spaces, teleparallel gravity, and Einstein-Cartan theory.

gr-qc↗

arXiv2025

A Universal Smarr Formula via Coupling Constants

In gravitational theories containing matter fields and higher-derivative corrections, the standard Smarr formula often fails unless all dimensionful couplings are incorporated consistently. Traditionally, parameters such as the cosmological constant or the coefficients of higher-derivative terms are regarded as immutable features of the theory and therefore excluded from the thermodynamic phase space. In our recent work, we developed a fully general framework that promotes every such coupling to a dynamical, freely varying parameter of black hole solutions. This is accomplished by introducing, for each coupling, an auxiliary scalar and gauge field, through which the coupling appears as a conserved charge associated with the global sector of an emergent gauge symmetry. The corresponding conjugate variables naturally arise as electric potentials evaluated at the black hole horizon. As a result, the first law and the Smarr relation acquire additional, systematically determined contributions, yielding a consistent and universal extension of black hole thermodynamics. We illustrate the validity of this construction by revisiting several black hole examples in the literature where the Smarr formula remains inconsistent even after treating the cosmological constant as a thermodynamic variable. Our analysis shows that only by including all dimensionful couplings in this generalized manner can one obtain an internally consistent Smarr relation, thereby providing the foundation for a truly universal formulation of black hole thermodynamics.

gr-qc↗

arXiv2025

Instability and Information Production Around Kerr Black Holes: Effects on Entropy and the Shadow

Massless or massive particles in unstable orbits around a Kerr black hole exhibit exponentially unstable motion when perturbed. They either plunge into the black hole or escape to infinity after making some oscillations around the equatorial plane. This exponentially unstable motion causes information production. In the case of the photons that escape to infinity, it was recently suggested that this information can be used to resolve the subring structure of the shadow image and obtain more precise data about the black hole mass and spin. Here, we extend this method to obtain more precise results by including th non-equatorial contributions to the Lyapunov exponents. For massive particles plunging into the Kerr black hole, we show that the associated Kolmogorov-Sinai entropy derived from the Lyapunov exponents can be interpreted in the context of black hole thermodynamics and obeys Bekenstein's bound on the entropy of a physical system. Thus, the perturbed unstable orbits, either ending inside the black hole or at the observer's screen, have physical consequences.

gr-qc↗

arXiv2025

Perturbative Analytical Construction of Bowen-York Initial Data for Binary Black Holes up to Third Order in Spin and Linear Momentum

We analytically construct initial data for binary black hole systems by solving the Einstein constraint equations within the Bowen-York framework. Allowing for arbitrarily oriented linear momenta and spins, we obtain a perturbative solution of the vacuum Hamiltonian constraint up to third order in the source parameters. Our solution explicitly incorporates the system's binary nature via position-weighted multipole moments. The momentum constraints are solved exactly, while the conformal factor is determined analytically. Using the resulting initial data, we compute the ADM energy, linear and angular momenta, and the irreducible mass. We also determine the shape of the apparent horizon and show that it is geometrically consistent with the inner-end regularity. The resulting expressions are written in a manifestly tensorial form and provide an analytic benchmark for numerical-relativity calculations within the perturbative far-zone regime considered here.

gr-qc↗

arXiv2025

Fluid-membrane Descriptions of Various Black Holes

The membrane paradigm of black holes is an effective theory that replaces the event horizon with a fictitious yet tangible fluid. It has provided us with valuable insights, especially in understanding the environment of black holes. The paradigm establishes a fluid/gravity correspondence that allows the computation of the thermal properties of the black hole in terms of the transport coefficients of the fluid. Recently, we showed that this is a van der Waals-type fluid for Kerr and especially for Johannsen-Psaltis black holes. Here, we use the paradigm to study the properties of various black holes in different dimensions to test the predictive capacity of effective theory. Among these, for the BTZ black holes, the paradigm gives a physical bulk viscosity, unlike the generic examples, for which the paradigm works with a negative bulk viscosity. For Lorentz-violating black holes, we demonstrate that the parameter for Lorentz violation is seen as a hair under the paradigm, which shifts the ergoregion where the fluid pressure diverges. It might have a consequence for black hole jets. For asymptotically safe quantum-corrected black holes, the paradigm detects the final state of evaporation, i.e., a remnant with a correct value for the mass that still has an event horizon. Finally, we check the paradigm with stringy black holes that have dilatonic and axionic charges, and the fluid produces the known results.

gr-qc↗

arXiv2025

Physical Interpretations of Integration Constants and Large Gauge Effects in Flat and AdS Spacetimes

As in other partial differential equations, one ends up with some arbitrary constants or arbitrary functions when one integrates Einstein's equations, or more generally field equations of any other gravity. Interpretation of these arbitrary constants and functions as some physical quantities that can, in principle, be measured is a non-trivial matter. Concentrating on the case of constants, one usually identifies them as conserved mass, momentum, angular momentum, center of mass, or some other hairs of the solution. This can be done via the Arnowitt-Deser-Misner (ADM)-type construction based on pure geometry, and the solution is typically a black hole. Hence, one talks about the black hole mass and angular momentum, etc. Here we show that there are several misunderstandings: First of all, the physical interpretation of the constants of a given geometry depends not only on pure geometry, i.e. the metric, but also on the theory under consideration. This becomes quite important, especially when there is a cosmological constant. Secondly, one usually assigns the maximally symmetric spacetime, say the flat or the (anti)-de Sitter spacetime, to have zero mass and angular momentum and linear momentum. This declares the maximally symmetric spacetime to be the vacuum of the theory, but such an assignment depends on the coordinates in the ADM-type constructions and their extensions: in fact, one can introduce large gauge transformations (new coordinates) which map, say, the flat spacetime to flat spacetime but the resultant flat spacetime can have a nontrivial mass and angular momentum, if the new coordinates are such that the metric components do not decay properly. These issues, which are often overlooked, will be examined in detail, and a resolution, via the use of a divergence-free rank $(0,4)$-tensor, will be shown for the case of anti-de Sitter spacetimes.

gr-qc↗

arXiv2025

Consistency Problems of Conformal Killing Gravity

We show that gravity field equations based on a tensor with rank greater than 2 have consistency problems in the sense that integration constants in the solutions, such as the parameter $m$ in the Schwarzschild metric, do not allow for an interpretation in terms of conserved quantities in the theory. The recently introduced Conformal Killing Gravity, an interesting extension of General Relativity that inherits all the solutions of the latter, and defined with a rank-3 tensor field equation that does not arise from a diffeomorphism-invariant action, is plagued with this problem. In this theory, it is not clear at all how one can define the energy and angular momentum for black hole solutions, or define the analogues of the formulas, such as the quadrupole formula, in the weak field limit for gravitational waves emitted by compact sources.

gr-qc↗

arXiv2025

Vanishing of Conserved Charges in Cotton Gravity

Cotton gravity was recently introduced as a higher derivative extension of General Relativity. The field equations of the theory involve the rank-3 Cotton tensor. Here we show that all solutions of the theory, including the black holes, have vanishing conserved charges, i.e. mass and angular momentum. This result implies that either the theory is unphysical since all the black holes carry the charges of the vacuum and can be created at no energy cost, or the theory has confinement of mass/energy and all other conserved quantities.

gr-qc↗

arXiv2024

Anomaly Induced Inflation in the Minimal Quartic Extension of Einstein's Gravity

A particular extension of Einstein's General Relativity up to and including quartic terms in the curvature tensor is minimal in the sense that it has a unique maximally symmetric vacuum and only a massless spin-2 excitation in its spectrum around the vacuum. We study the inflation phase of the universe in this minimal quartic extension of Einstein's gravity in the presence of trace anomaly terms coming from the Standard Model fields and the fields of the Minimal Supersymmetric Standard Model. We show that the theory allows a quasi-de Sitter phase with sufficient $e$-foldings.

gr-qc↗