Quantum corrections to the area law are applied routinely to black holes coupled to nonlinear electrodynamics, almost always with a free coefficient and an unstated prescription for the temperature. We ask what they actually determine for the Einstein–Euler–Heisenberg black hole in anti-de Sitter space. At fixed geometric temperature a logarithmic correction rescales the heat capacity by [Formula: see text], leaving the divergence locus and the critical point exactly invariant; imposing the first law instead rescales the temperature and displaces them. In either case the coexistence line of the first order transition moves, by an amount we obtain in closed form: the correction reorganises the phase diagram without generating new critical behaviour. Nor is the coefficient free, being fixed by Gaussian fluctuations wherever the canonical ensemble exists and meaningless where it does not. Near extremality the area law is no longer the right organising principle. We obtain the Schwarzian coupling of the AdS[Formula: see text] throat and the gap scale it sets, which vacuum polarisation lowers, and there the correction is logarithmic in [Formula: see text] with a coefficient fixed by the one loop measure. Vacuum polarisation also raises the extremal ratio of charge to mass, as the weak gravity conjecture requires, with a sign inherited from one loop positivity. Finally, the branch of small horizons on which corrected heat capacities are conventionally plotted lies at [Formula: see text] in Heaviside–Lorentz units, independent of charge and mass, where the effective Lagrangian has already failed.
This paper investigates the fundamental ℓ = 2 quasinormal mode (QNM) frequencies and the corresponding ℓ = 2 partial-wave greybody factors of static, spherically symmetric black holes in a background spacetime whose metric depends on both the Kalb–Ramond (KR) field parameter τ (inducing spontaneous Lorentz symmetry breaking, LSB) and the perfect-fluid dark matter (PFDM) parameter ζ/M. We adopt the observationally motivated 1σ bounds on the LSB parameter τ and PFDM parameter ζ/M obtained from the M87* shadow analysis of Ref.[1]. Combining the sixthorder WKB approximation with time-domain numerical integration, we calculate the fundamental ℓ = 2 QNM frequencies of scalar and electromagnetic test fields in this spacetime. Numerical results show that both the real part and the absolute value of the imaginary part of the fundamental ℓ = 2 QNM frequencies increase monotonically with the growth of τ and ζ/M. Furthermore, the ℓ = 2 partial transmission probabilities computed for the scalar and electromagnetic perturbations show that the transmission probability decreases monotonically with increasing τ or ζ/M. This suppression is primarily due to the increase of the effective potential barrier. This work constructs a self-consistent physical picture describing how the background geometry, which depends on both τ and ζ/M, shapes the fundamental ℓ = 2 QNM frequencies and the associated greybody factors of the black hole.
The local Gribov–Zwanziger action carries auxiliary fields with two adjoint labels, while Gribov’s second-order no-pole condition involves a single one. We show that the map [Formula: see text] is the projector onto the antisymmetric adjoint channel of [Formula: see text], and that the resulting one-index localization reproduces the Gribov gluon propagator exactly at bilinear order, with [Formula: see text]. Beyond this order the two localizations differ by fixed coefficients within the ring generated by [Formula: see text], [Formula: see text] and [Formula: see text], and the one-index functional departs from Zwanziger’s horizon function, hence from the exact no-pole condition, at cubic order. The difference of the two actions is BRST-exact in the extended theory in which the soft breaking is promoted to a doublet of sources, and in the physical limit its effect is governed by an explicit Ward identity. We classify the two-loop vacuum contributions with the complete propagator matrix, and we derive the Ward identities and admissible counterterms of the one-index action, finding one direction outside the action which decouples from all Green functions without external [Formula: see text] legs.
We present a systematic asymptotic small-[Formula: see text] expansion of the Liouville DOZZ three-point structure constant in the light-operator regime [Formula: see text] in the limit [Formula: see text]. In this limit the DOZZ structure constant admits the asymptotic representation [Formula: see text] where [Formula: see text] is an explicitly determined prefactor. Using Thorn’s asymptotic expansion of the [Formula: see text]-function, we derive explicit closed-form expressions for the first coefficients [Formula: see text] and show that they form a symmetric polynomial structure in the variables [Formula: see text]. The resulting asymptotic expansion provides explicit finite-[Formula: see text] corrections to the leading light-limit Liouville three-point data and furnishes a practical framework for applications in celestial holography. In particular, it provides Liouville data relevant for a perturbative program aimed at studying finite-[Formula: see text] corrections to celestial Yang–Mills amplitudes. Finally, we formulate such a perturbative Liouville framework and discuss several directions for its future development.
This paper examines charged anisotropic compact star structures under modified Rastall [Formula: see text] gravity, where [Formula: see text] is the non-metricity scalar. The Karmarkar condition establishes a particular relationship between the metric potentials, making it easier to develop precise solutions to the relevant field equations. Two different methods are used to analyze the behavior of the [Formula: see text] function. To determine the form of [Formula: see text], a hybrid linear equation of state is used in the first method. In the second, [Formula: see text] is kept in the same hybrid form, but [Formula: see text] is given a logarithmic expression. Various gravitational models with hybrid, power-law and exponential forms are examined by changing the parameters [Formula: see text] and [Formula: see text]. The physical plausibility of the obtained configurations is examined using the observed mass and radius measurements of PSR J1614-2230 and PSR J0740+6620. The observational uncertainties are propagated to the derived compactness quantities, while the model parameters are explored within physically viable ranges. A quantitative comparison of the charged and uncharged limits shows that the representative electric charge produces small but non-zero modifications in the surface properties. The resulting configurations satisfy the required physical acceptability and stability conditions.
