In this work we propose improved holographic hard wall (HW) models by the inclusion of anomalous dimensions in the dual operators that describe glueballs inspired by the AdS/CFT correspondence. The anomalous dimensions come from well known semiclassical gauge/string duality analysis showing a dependence with the logarithm of spin $S$ of the boundary states. We show that these logarithm anomalous dimensions of the high spin operators combined with the usual HW model allow us to match the pomeron trajectory and give glueball masses that are better than that of the original HW and soft wall models in comparison with lattice data. We also build up other anomalous HW models considering that the logarithm anomalous dimensions can be approximated by a truncated series of odd powers of the difference $\sqrt{S}-1/\sqrt{S}$. These models also fit the pomeron trajectory and produce good glueball masses. Then, we consider an anomalous dimension that is proportional to $\sqrt{S}$, providing reasonable results. Finally, we propose an asymptotic linear anomalous HW model that effective dimensions for high spins operators are of the form $\mathrm{\Delta }=a\sqrt{S}+b$, where $a$ and $b$ are constants to be fixed by comparison with the soft pomeron trajectory. In this last model, the Regge trajectory is asymptotically linear even for very high spins ($J\sim 100$) matching the soft pomeron trajectory accurately and generates glueball masses with deviations with respect to the lattice data better than the original HW and soft wall models.

We exploit the presence of moduli fields in the ${\mathrm{AdS}}_3\times S^3\times C{Y}_2$, where $C{Y}_2=T^4$ or $K3$, solution to type IIB superstring theory, to construct a $U$-fold solution with geometry ${\mathrm{AdS}}_2\times S^1\times {\mathrm{S}}^3\times C{Y}_2$. This is achieved by giving a nontrivial dependence of the moduli fields in $\mathrm{SO}(4,n)/\mathrm{SO}(4)\times \mathrm{SO}(n)$ ($n=4$ for $C{Y}_2=T^4$ and $n=20$ for $C{Y}_2=K3$), on the coordinate $\eta$ of a compact direction $S^1$ along the boundary of ${\mathrm{AdS}}_3$, so that these scalars, as functions of $\eta$, describe a geodesic on the corresponding moduli space. The backreaction of these evolving scalars on spacetime amounts to a splitting of ${\mathrm{AdS}}_3$ into ${\mathrm{AdS}}_2\times S^1$ with a nontrivial monodromy along $S^1$ defined by the geodesic. Choosing the monodromy matrix in $\mathrm{SO}(4,n;\mathbb{Z})$, this supergravity solution is conjectured to be a consistent superstring background. We generalize this construction starting from an ungauged theory in $D=2d$, $d$ odd, describing scalar fields nonminimally coupled to ($d-1$) forms and featuring solutions with topology ${\mathrm{AdS}}_d\times S^d$, and moduli scalar fields. We show, in this general setting, that giving the moduli fields a geodesic dependence on the $\eta$ coordinate of an $S^1$ at the boundary of ${\mathrm{AdS}}_d$ is sufficient to split this space into ${\mathrm{AdS}}_{d-1}\times S^1$, with a monodromy along $S^1$ defined by the starting and ending points of the geodesic. This mechanism seems to be at work in the known $J$-fold solutions in $D=10$ type IIB theory and hints toward the existence of similar solutions in the type IIB theory compactified on $C{Y}_2$. We argue that the holographic dual theory on these backgrounds is a $1+0$ CFT on an interface in the $1+1$ theory at the boundary of the original ${\mathrm{AdS}}_3$.

In this paper we compute the celestial operator product expansion between two outgoing positive helicity gravitons in the self-dual gravity. It has been shown that the self-dual gravity is a $w_{1+\infty }$-invariant theory whose scattering amplitudes are one-loop exact with all positive helicity gravitons. Celestial $w_{1+\infty }$ symmetry is generated by an infinite tower of (conformally soft) gravitons which are holomorphic conserved currents. We find that at any given order only the descendants of a finite number of $w_{1+\infty }$ currents contribute to the operator product expansion. This is somewhat surprising but, this is consistent with our earlier analysis based on $w_{1+\infty }$ symmetry alone. The phenomenon of truncation also suggests that in some (unknown) formulation the spectrum of conformal dimensions in the dual two dimensional theory can be bounded from below.

In this paper, we explore the characteristics of reduced density matrix spectra in quantum field theories. Previous studies mainly focus on the function $\mathcal{P}(\lambda )≔{\sum }_i\delta (\lambda -{\lambda }_i)$, where ${\lambda }_i$ denote the eigenvalues of the reduced density matrix. We introduce a series of functions designed to capture the parameter dependencies of these spectra. These functions encompass information regarding the derivatives of eigenvalues concerning the parameters, notably including the function ${\mathcal{P}}_{{\alpha }_J}(\lambda )≔{\sum }_i\frac{\partial {\lambda }_i}{\partial {\alpha }_J}\delta (\lambda -{\lambda }_i)$, where ${\alpha }_J$ denotes the specific parameter. Computation of these functions is achievable through the utilization of Rényi entropy. Intriguingly, we uncover compelling relationships among these functions and demonstrate their utility in constructing the eigenvalues of reduced density matrices for select cases. We perform computations of these functions across several illustrative examples. Especially, we conducted a detailed study of the variations of $\mathcal{P}(\lambda )$ and ${\mathcal{P}}_{{\alpha }_J}(\lambda )$ under general perturbation, elucidating their physical implications. In the context of holographic theory, we ascertain that the zero point of the function ${\mathcal{P}}_{{\alpha }_J}(\lambda )$ possesses universality, determined as ${\lambda }_0=e^{-S}$, where $S$ denotes the entanglement entropy of the reduced density matrix. Furthermore, we exhibit potential applications of these functions in analyzing the properties of entanglement entropy.

We explore the phase structure of quantum chromodynamics (QCD) with two dynamical quark flavors at finite temperature and baryon chemical potential, employing the nonperturbative gauge/gravity duality approach. Our gravitational model is tailored to align with state-of-the-art lattice data regarding the thermal properties of multiflavor QCD. Following a rigorous parameter calibration to match equations of state and the QCD trace anomaly at zero chemical potential derived from cutting-edge lattice QCD simulations, we investigate thermodynamic quantities and order parameters. We predict the location of the critical endpoint (CEP) at $({\mu }_{\mathrm{CEP}},T_{\mathrm{CEP}})=(219,182)\mathrm{MeV}$ at which a line of first-order phase transitions terminate. We compute critical exponents associated with the CEP and find that they almost coincide with the critical exponents of the quantum 3D Ising model.

In this paper, we investigate new integrable extensions of two-center Coulomb systems. We study the most general $n$-dimensional deformation of the two-center problem by adding arbitrary functions supporting second-order commuting conserved quantities. The system is superintegrable for $n>4$ and, for certain choices of the arbitrary functions, reduces to known models previously discovered. Then, based on this extended system, we introduce an additional integrable generalization involving Calogero interactions for $n=3$. In all examples, including the two-center problem, we explicitly present the complete list of Liouville integrals in terms of second-order integrals of motion.

The explicit covariant actions and propagators are given for fields describing particles of all spins and masses, in any spacetime dimension. Massive particles are realized as “dimensionally reduced” massless particles. To obtain compact expressions for the propagators, it was useful to introduce an auxiliary vector coordinate $s^{\mu }$ and consider “hyperfields” that are functions of space $X^{\mu }$ and $s^{\mu }$. The actions and propagators serve as a basic starting point for concrete high spin computations amenable to dimensional regularization, provided that gauge invariant interactions are introduced.

This paper investigates the critical behaviors of the 4-dimensional spinfoam model with cosmological constant for a general 4-dimensional simplicial complex as the discretization of spacetime. We find that, at the semiclassical regime, the spinfoam amplitude is peaked at the real critical points that correspond to zero deficit angles (modulo $4\pi \mathbb{Z}/\gamma$) hinged by internal triangles of the 4-complex. Since the 4-simplices from the model are of constant curvature, the discrete geometry with zero deficit angle manifests a de Sitter (dS) spacetime or an anti–de Sitter (AdS) spacetime depending on the sign of the cosmological constant fixed by the boundary condition. The non-(A)dS spacetimes emerge from the complex critical points by an analytic continuation to complex configurations.

We present a novel asymptotically anti–de Sitter black hole solution with conformally-coupled scalar fields in the first-order formalism of gravity in four dimensions. To do so, we consider a one-parameter extension of conformal transformations by exploiting the fact that the tetrad and spin connection are regarded as independent fields. We solve the field equations analytically and obtain a static black hole solution with nontrivial torsion sourced by the conformal coupling between the scalar field and geometry. The presence of torsion renders the scalar field everywhere regular, while the curvature and torsion singularities coalesce into the origin. We show that this configuration is continuously connected to previously reported solutions in the limit of vanishing torsion and analyze its main properties, focusing on the consequences of the torsional singularity.

The Einstein equivalence principle in general relativity allows us to interpret accelerating black holes as a black hole immersed into the gravitational field of a larger companion black hole. Indeed it is demonstrated that C-metrics can be obtained as a limit of a binary system where one of the black holes grows indefinitely large, becoming a Rindler horizon. When the bigger black hole, before the limiting process, is of Schwarzschild type we recover usual accelerating black holes belonging to the Plebanski-Demianski class, thus type D. Whether the greater black hole carries some extra features, such as electric charges or rotations, we get generalized accelerating black holes which belong to a more general class, the type I. In that case the background has a richer structure, reminiscent of the physical features of the inflated companion, with respect to the standard Rindler spacetime. This insight allow us to build a general type D metric, describing an accelerating Kerr-NUT black black hole. It has well defined limits to all the type-D black holes of general relativity, including the elusive (type-D) accelerating Taub-NUT spacetime. Extension to the presence of the cosmological constant is also provided.

The memory effect in gravitational wave (GW) signals is the phenomenon, wherein the relative position of two inertial GW detectors undergoes a permanent displacement owing to the passage of GWs through them. Measurement of the memory signal is an important target for future observations as it establishes a connection between observations with field-theoretic results like the soft-graviton theorems. Theoretically, the memory signal is predicted at the leading order quadrupole formula for sources like binaries in hyperbolic orbits. This can be in the realm of observations by Advanced LIGO, Einstein-Telescope, or LISA for black holes with masses $\sim O({10}^3{M}_{\odot })$ scattered by the supermassive black hole at the galactic center. Apart from the direct memory component there is a nonlinear memory signal in the secondary GW emitted from the primary GW chirp-signals emitted by coalescing binaries. In this paper, we compute the gravitational wave signals and their energy spectrum using the field-theoretic method by computing the scattering amplitudes for eccentric elliptical and hyperbolic binary orbits. The field theoretic calculation gives us the gravitational waveforms of linear and nonlinear memory signals directly in the frequency space. The frequency domain templates are useful for extracting signals from the data. We compare our results with other calculations of linear and nonlinear memory signals in literature and point out novel features we find in our calculations like the presence of $\log (\omega )$ terms in the linear memory from hyperbolic orbits.

Brans-Dicke (BD) theory is one of the simplest scalar-tensor theories, with potential applications in dark matter, dark energy, inflation, and primordial nucleosynthesis. The strongest constraint on the BD coupling constant is provided by the Cassini measurement of the Shapiro time delay in the Solar System. Constraints from gravitational wave (GW) events are subject to asymmetric binaries. The third Gravitational-Wave Transient Catalog (GWTC) reports a neutron star-black hole (NSBH) merger event, GW200115, making it possible to constrain BD by GW. With the aid of this source and Bayesian Markov-chain Monte Carlo (MCMC) analyses, we derive a 90% credible lower bound on the modified parameter of scalar-tensor theories as ${\phi }_{-2}>-7.94\times {10}^{-4}$ by using dominant-mode correction. Specific to BD theory, we have the constraint ${\omega }_{\mathrm{BD}}>4.75$. Asymmetric binary systems usually have a significant mass ratio; in such cases, higher harmonic modes cannot be neglected. Our work considers higher harmonic corrections from scalar-tensor theories and provides a tighter constraint of ${\phi }_{-2}>-7.59\times {10}^{-4}$. Transitioning to BD theory, the constraint is ${\omega }_{\mathrm{BD}}>5.06$, with a 6.5% improvement. We also consider a plausible NSBH event, GW190814, which is a highly unequal mass ratio source that exhibits strong evidence for higher-order multipoles. We obtain poorly converged results when using the dominant mode, while getting a constraint of ${\phi }_{-2}>-6.60\times {10}^{-4}$ on scalar-tensor theories when including the higher harmonic modes. This suggests that the difference between the dominant mode and higher modes has a significant impact on our analysis. Furthermore, treating this suspected event as an NSBH event, we find ${\omega }_{\mathrm{BD}}>6.12$ when including the higher harmonic modes. Combining GW200115 and GW190814 and including higher modes, the constraint is improved to ${\omega }_{\mathrm{BD}}>110.55$. This is currently the strongest constraint utilizing GWs, contingent upon GW190814 being an NSBH event. Additionally, we take into account a BD-like theory, known as screened modified gravity, and investigate the coupling constant constraints, both with and without higher-mode corrections, by using data from both GW200115 and GW190814.

Zermelo navigation is not only a fundamental tool in Finsler geometry but also a fundamental approach to the geometrization of dynamics in physics. In this paper, we consider the Zermelo navigation problem on optical Riemannian space and, via Zermelo/Randers/spacetime triangle, and explore the generation of new spacetimes from preexisting ones. Whether the Randers metric has reversible geodesics corresponds to the presence of time-reversal symmetry in the generated spacetime. In cases where the Randers metric has reversible geodesics, we utilize a radial vector field to generate new static spacetimes from existing ones. For example, we can generate Schwarzschild, Rindler, de Sitter, and Schwarzschild-de Sitter spacetimes from flat spacetime. In fact, the Zermelo navigation method allows for the derivation of a variety of static spacetimes from flat spacetime. For multiparameter spacetimes, they can be generated through various navigation paths. However, for some spacetimes, not all navigation paths may exist. In the second scenario, when the Randers metric does not have reversible geodesics, we employ a rotational vector field to transform nonflat static metrics into slowly rotating spacetimes. Alternatively, using a mixed vector field, we generate slowly rotating spacetimes starting from flat spacetime. We provide examples of generating Kerr spacetimes and Kerr-de Sitter spacetimes.

We show that a globally hyperbolic spacetime containing a trapped surface and satisfying the strong energy condition and a condition on certain radial tidal forces must be timelike geodesically incomplete. This constitutes a “timelike” version of Penrose’s celebrated singularity theorem. Recall that the latter concludes that certain spacetimes are null incomplete, providing the first theoretical evidence that black holes actually exist in our Universe. By concluding timelike instead of null incompleteness, we obtain, at the expense of stronger assumptions, a clearer physical interpretation and the existence of an event horizon.

We propose a new $\overline{\mu }$-scheme Hamiltonian effective dynamics in the spherical symmetric spacetime which is generally covariant as derived from a covariant Lagrangian. The Lagrangian belongs to the class of extended mimetic gravity Lagrangians in four dimensions. We apply the effective dynamics to both cosmology and black hole. The effective dynamics reproduces the nonsingular loop-quantum-cosmology effective dynamics. From the effective dynamics, we obtain the nonsingular black hole solution, which has a killing symmetry in addition to the spherical symmetry and reduces to the Schwarzschild geometry asymptotically near the infinity. The black hole spacetime resolves the classical singularity and approaches asymptotically the Nariai geometry ${\mathrm{dS}}_2\times S^2$ at the future infinity in the interior of the black hole. The resulting black hole spacetime has the complete future null infinity ${ℐ}^{+}$. Thanks to the general covariance, the effective dynamics can be reformulated in the light cone gauge.

Two novel topological black hole exact solutions with unusual shapes of horizons in the simplest holographic axions model, the four-dimensional Einstein-Maxwell-axions theory, are constructed. We draw embedding diagrams in various situations to display unusual shapes of novel black holes. To understand their thermodynamics from the quasilocal aspect, we rederive the unified first law and the Misner-Sharp mass from the Einstein equation for the spacetime as a warped product ${\overline{\mathcal{M}}}_{(2)}\times {\widehat{\mathcal{M}}}_{(D-2)}$. The Ricci scalar $\widehat{R}$ of the submanifold ${\widehat{\mathcal{M}}}_{(D-2)}$ can be a nonconstant. We further improve the thermodynamics method based on the unified first law. Such a method simplifies constructing solutions and hints at generalization to higher dimensions. Moreover, we apply the unified first law to discuss black hole thermodynamics.

Perturbation theory of vacuum spherically-symmetric spacetimes (including the cosmological constant) has greatly contributed to the understanding of black holes, relativistic compact stars, and even inhomogeneous cosmological models. The perturbative equations can be decoupled in terms of (gauge-invariant) master functions satisfying $1+1$ wave equations. In this work, building on previous work on the structure of the space of master functions and equations, we study the reconstruction of the metric perturbations in terms of the master functions. To that end, we consider the general situation in which the perturbations are driven by an arbitrary energy-momentum tensor. Then, we perform the metric reconstruction in a completely general perturbative gauge. In doing so, we investigate the role of Darboux transformations and Darboux covariance, responsible for the isospectrality between odd and even parity in the absence of matter sources, and also of the physical equivalence between the descriptions based on all the possible master equations. We also show that the metric reconstruction can be carried out in terms of any of the possible master functions and that the expressions admit an explicitly covariant form.

We revise the work of Scholtz, Flandera, and Gürlebeck [Phys. Rev. D 96, 064024 (2017)]. We cast the Kerr metric explicitly in the form suitable for the framework of isolated horizons. We proceed in a geometrical fashion and are capable to provide the results in a compact closed manner, without any unevaluated integrals. We also discuss the uniqueness and drawbacks of this construction. We suggest a new vector field to generate the null geodesic foliation.

While nonrotating black-hole solutions are well known in Einstein–æther gravity, no axisymmetric solutions endowed with Killing horizons have been so far found outside of the slowly rotating limit. Here we show that the Kerr spacetime is also an exact vacuum solution of Einstein–æther gravity in a phenomenologically viable corner of the parameter space; the corresponding æther flow is characterized by a vanishing expansion. Such a solution displays all the characteristic features of the Kerr metric (inner and outer horizons, ergoregion, etc.) with the remarkable exception of the causality-violating region in proximity of the ring singularity. However, due to the associated æther flow, it is endowed with a special surface, inside the Killing horizon, which exhibits many features normally related to the universal horizon of the nonrotating solutions—to which it tends in the limit of zero angular momentum. Hence, these Kerr black holes are very good mimickers of their general relativistic counterparts while sporting important differences and specific structures. As such, they appear particularly well-suited candidates for future phenomenological studies.