A bstract We investigate the interior of AdS black holes under finite shear strain in a class of holographic axion models, which are widely used to describe strongly-coupled systems with broken translations. We demonstrate that the shear anisotropy necessarily eliminates the inner Cauchy horizon, such that the deformed black hole approaches a spacelike singularity. The anisotropic effect induced by the axion fields triggers a collapse of the Einstein-Rosen bridge at the would-be Cauchy horizon, accompanied by a rapid change in the anisotropy of the spatial geometry. In addition, for a power-law axion potential, sufficiently large shear deformations give rise to a domain wall solution that includes a Lifshitz like scaling geometry near the boundary as well as a near horizon Kasner epoch with the Kasner exponents determined by the powers of the potential. Finally, we find that the interior dynamics of black holes generally enter an era described by an anisotropic Kasner universe at later interior time. Depending on the form of the potential, they either tend to stable Kasner universes, or exhibit an endless alternation of different Kasner epochs toward the singularity.

Abstract The formulation of quantum field theory in Minkowski spacetime, which emerges from the unification of special relativity and quantum mechanics, is based on treating time as a parameter, assuming a fixed arrow of time, and requiring that field operators commute for spacelike distances. This procedure is questioned here in the context of quantum field theory in curved spacetime (QFTCS).
In 1935, Einstein and Rosen (ER), in their seminal paper [1] proposed that "a particle in the physical Universe has to be described by mathematical bridges connecting two sheets of spacetime" which involved two arrows of time. Recently proposed direct-sum quantum theory reconciles this ER's vision by introducing geometric superselection sectors associated with the regions of spacetime related by discrete transformations. We further establish that the quantum effects at gravitational horizons involve the physics of quantum inverted harmonic oscillators that have phase space horizons. This new understanding of the ER bridges is not related to classical wormholes, it addresses the original ER puzzle and promises a unitary description of QFTCS, along with observer complementarity. Furthermore, we present compelling evidence for our new understanding of ER bridges in the form of large-scale parity asymmetric features in the cosmic microwave background, which is statistically 650 times stronger than the standard scale-invariant power spectrum from the typical understanding of inflationary quantum fluctuations when compared with the posterior probabilities associated with the model given the data. We finally discuss the implications of this new understanding in combining gravity and quantum mechanics.

Abstract In this manuscript, we investigate the existence of wormhole configurations bounded by fuzzy dark matter halos within the context of the minimal geometric deformation approach to gravitational decoupling. Applying this formalism, we geometrically deform the classical Morris–Thorne wormhole solution and add an extra gravitational source, denoted by $$\Theta _{\mu \nu }$$ Θ μ ν . The Einasto density profile for the dark matter halos is utilized to set up the temporal component of the $$\Theta $$ Θ -sector. We obtain the corresponding shape function from this construction and examine its behavior to make the wormhole configuration traversable. Physical viability of the emergent spacetime is checked with a range of diagnostics. We study energy conditions and present their behavior graphically. To gain a better insight into the internal physical characteristics, we analyze the complexity factor, exoticity parameter, and anisotropy factor, which provide information about the stability and matter content of the configuration. In addition, we perform a cracking analysis to test stability in the presence of perturbations and investigate the causality condition to verify subluminal sound speeds. Our results indicate that the MGD-Einasto model facilitates the realization of wormhole configurations with controlled exotic matter content, forming a promising path for connecting dark matter halo physics to modified gravity solutions.

Abstract In this manuscript, the properties of topologically charged Morris–Thorne wormholes (WHs) are investigated within the framework of gravity, which modifies general relativity by introducing a generic function of Ricci scalar . The study primarily focuses on how different choices of shape functions influence the physical characteristics of WH models under consideration. To explore the viability of such WHs, the field equations in gravity are solved by considering an anisotropic energy‐momentum tensor (EMT). A key aspect of this investigation is the analysis of the matter content supporting these WHs, particularly whether it satisfies or violates the classical energy conditions, such as the Null, Weak, and Strong Energy Conditions. Unlike traditional WH solutions, which often require exotic matter with negative energy density, this study aims to examine the possibility of sustaining these structures with non‐exotic matter. Also, the influence of the global monopole charge are explored and the correction terms arising from modifications on the energy conditions, providing insights into their role in determining the physical plausibility of these WHs. The repulsive or attractive nature of the WHs is assessed by calculating the anisotropy parameter, which measures the deviation from isotropic pressure conditions. The results indicate that the global monopole parameter and the modifications introduced by gravity significantly affect the energy conditions, thereby controlling the physical viability of these WHs. This study contributes to a deeper understanding of traversable WHs in alternative gravity theories, potentially offering new avenues for theoretical and astrophysical research into exotic spacetime structures.

We show that non-minimal coupling between matter and geometry can indeed help in constructing stable, traversable, wormholes (WHs) without requiring exotic matter under certain conditions. In models like f(𝒬,𝒯) = 𝒬 + β𝒯 gravity, where 𝒬 is the non-metricity scalar, and 𝒯 is the trace of the energy-momentum tensor, the coupling between matter and geometry introduces additional degrees of freedom in terms of the parameter β. These can mimic the effects of exotic matter or even replace it entirely under specific parameter choice. The analysis involves deriving WH shape functions based on two dark matter (DM) density profiles: a solitonic core at the center of DM halos, and the outer halo follows the universal Navarro-Frenk-White (NFW) density profile of cold DM (CDM). The WH solutions derived in these models satisfy important geometric conditions like: flaring-out condition (necessary for traversability) and asymptotic flatness condition. For large positive coupling parameter, the null energy condition (NEC) can be satisfied at the WH throat, meaning exotic matter is not needed, while the WH is no longer Lorentzian and the flaring-out condition is broken. However, for large negative coupling parameter, the NEC can be satisfied, allowing for healthy WHs without exotic matter, provided the coupling strength remains within certain bounds. In the latter case, the NEC is broken only effectively. We investigate the stability of the obtained WH solutions by virtue of a modified version of Tolman-Oppenheimer-Volkoff (TOV) equation, which includes a new force due to matter-geometry non-minimal, showing that these WHs can be dynamically stable.

Abstract We extend the notion of chord number in the strict large N double-scaled Sachdev-Ye-Kitaev (DSSYK) model to the corresponding finite N ETH matrix model. The chord number in the strict large N DSSYK model is known to correspond to the discrete length of the Einstein-Rosen bridge in the gravity dual, which reduces to the renormalized geodesic length in JT gravity at weak coupling. At finite N, these chord number states form an over-complete basis of the non-perturbative Hilbert space, as the structure of the inner product gets significantly modified due to the Cayley-Hamilton theorem: There are infinitely many null states. In this paper, by considering “EFT for gravitational observables” or a version of “non-isometric code”, we construct a family of chord number operators at finite N. While the constructed chord number operator depends on the reference chord number state, it realizes approximate q-deformed oscillator algebra and reproduces semiclassical bulk geometry around the reference state. As a special case, we will show that when the reference is chosen to be the chord number zero state, the chord number operator precisely matches with the Krylov state complexity, leading to the “ramp-slope-plateau” behavior at late times, implying the formation of “gray hole”.

In holographic quantum gravity, Euclidean pieces of the spacetime appear in the large N limit as representing semi-classical states of the theory. In this paper, we argue that the duals of entangled states are spacetime geometries that contain Euclidean regions in order to preserve classical connectivity. Thereby, the proposal is to extend the ER-EPR conjecture to regimes whether wormholes (Einstein–Rosen bridges) become unstable but the entangled structure of the dual state persists.

We present a quantitative holographic relation between a microscopic measure of randomness and the geometric length of the wormhole in the black hole interior. To this end, we perturb an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. We use the random circuit to prepare ensembles of states of the black hole whose semiclassical duals contain Einstein-Rosen (ER) caterpillars: Long cylindrical wormholes with large numbers of matter inhomogeneities, of linearly growing length with the circuit time. In this setup, we show semiclassically that the ensemble of ER caterpillars of average length k\ell_{\Delta}kℓΔ and matter correlation scale \ell_{\Delta}ℓΔ forms an approximate quantum state kk-design of the black hole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. We comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.

Abstract In this paper, we analyze the properties of wormhole (WH) solutions within the framework of modified f ( R , L m ) gravity. The shape function and redshift function are essential components in the modeling of wormholes, as they dictate the wormhole’s metrics and characteristics. Our study sheds light on how the features of f ( R , L m ) gravity interact with gravitational effects, offering insights into possible wormhole configurations. We also investigate the behavior of energy conditions, the fundamental properties of wormholes, and their embedding diagrams. The stability of the WH solutions is further assessed using the Tolman-Oppenheimer-Volkoff (TOV) equation, which confirms that the solutions meet the equilibrium criteria. Additionally, the volume integral quantifier (VIQ) is discussed to understand the amount of exotic matter required around the wormhole throat. The increasing nature of the active gravitational mass supports the physical viability of the WH solutions. We also explore the complexity factor and sound speed associated with the WH solutions. Overall, our findings contribute to the broader discussion on alternative theories of gravity and the nature of exotic spacetime geometries.

Circuit complexity, defined as the minimum circuit size required for implementing a particular Boolean computation, is a foundational concept in computer science. Determining circuit complexity is believed to be a hard computational problem. Recently, in the context of black holes, circuit complexity has been promoted to a physical property, wherein the growth of complexity is reflected in the time evolution of the Einstein-Rosen bridge ("wormhole") connecting the two sides of an anti-de Sitter "eternal" black hole. Here, we are motivated by an independent set of considerations and explore links between complexity and thermodynamics for functionally equivalent circuits, making the physics-inspired approach relevant to real computational problems, for which functionality is the key element of interest. In particular, our thermodynamic framework provides an alternative perspective on the obfuscation of programs of arbitrary length-an important problem in cryptography-as thermalization through recursive mixing of neighboring sections of a circuit, which can be viewed as the mixing of two containers with "gases of gates." This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits of same size and functionality that cannot be connected via a polynomial number of local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide, a statement that implies the collapse of the polynomial hierarchy of computational complexity theory to its first level.

In this study, we explore the geometric features of a charged traversable wormhole (WH) in the realm of [Formula: see text] gravity with strange quark matter. We developed the field equations for Morris–Thorne-type charged WH metric with anisotropic fluid distribution and obtained the corresponding WH results for two kinds of shape functions. To visualize the proper shape of the WH, we depicted three-dimensional and two-dimensional embedding portraits for the chosen values of both [Formula: see text] and [Formula: see text] at the throat radius [Formula: see text]. In addition, all necessary needs to build a WH shape are analyzed for the considering shape functions. Next, we analyze the energy conditions together with the MIT bag model, for different values of free parameters for both cases. It is observed that in both cases, all the energy conditions are violated in different regions of the WH spacetime, corresponding to some ranges of model parameters. The violation of the null energy condition (NEC) confirms the existence of exotic matter inside the WH throat. On the other hand, the validity of energy conditions predicts a fabric of stable traversable WHs. For both cases, the equilibrium configuration is analyzed through the TOV equation showing the stability of considering solutions.

In this work, we investigate a traversable wormhole in general relativity (GR) with a cosmological constant ([Formula: see text]). As a shape function plays a crucial role in the construction of wormhole solutions, we apply the Karmarkar condition to find the wormhole shape function (WSF). The derived WSF creates wormhole geometry that connects two asymptotically flat surfaces in spacetime and meets all the required criteria. We use various graphs to analyze the energy conditions (ECs) and the anisotropic parameter ([Formula: see text]). Furthermore, we employ the causality and Herrera cracking methods to determine the wormhole’s stability and conclude that all essential criteria are met. Hence, GR provides a stable, traversable wormhole solution that can be sustained in the presence of non-exotic matter by introducing a cosmological constant.

Abstract We analyze the correlation function in Jackiw–Teitelboim gravity using three approaches: by summing over all geodesics connecting boundary operators, integrating over the region of moduli space determined by the “no-shortcut condition,” and using the formula for the universal spectral density correlation in the $\tau$-scaling limit. We find that the behaviors of the three results coincide at late times: they all exhibit a “ramp” instead of permanent decay. Using the third approach we also confirm that the “plateau” appears after $T_H=2\pi e^{S_0}\widehat{\rho }_0(E)$. Overall, our results are consistent with the spectral form factor analysis. We also calculate the Einstein–Rosen bridge length $\langle \ell (T) \rangle$ using the three approaches and find that the results are in good agreement with each other. We also find that the $\langle \ell (T) \rangle$ grows as a cubic function in $T$ due to the contribution from geometry including one observable baby universe, and converges to a constant after $T=T_H$. For the geometry with one baby universe, we compute the size $\langle b(T) \rangle$ of the baby universe and find that it is of the same order as $\langle \ell (T) \rangle$. This result is consistent with the baby universe emission mechanism previously claimed.

We investigate the gravitational dual of a fermionic field theory at finite temperature and charge density in two spatial dimensions, subject to a deformation by a relevant scalar operator. This makes a (3 + 1)-dimensional Einstein-Maxwell system coupled to a free fermion fluid, known as an electron cloud, undergo a holographic renormalization group flow. The inner (Cauchy) horizon is destroyed and the near-singularity metric instead adopts the form of a positive-pt Kasner cosmology, signaling the collapse of the Einstein-Rosen bridge. Previous studies have suggested that this collapse hinders direct probing of the singularity. Nonetheless, we propose and compute several CFT observables that characterize the interior and near-singularity geometries. These include the thermal a-function, which decays with a specific power of pt as nearly all CFT degrees of freedom are integrated out, and two-point correlators for neutral and charged operators, with the latter directly probing the singularity despite the positive-pt. We also calculate characteristic velocities related to entanglement and complexity growth in the time-evolved thermofield double state, as well as the butterfly effect indicative of operator spreading. Notably, the deformed electron cloud features a Lifshitz IR fixed point and an additional Kasner trans-IR fixed point, absent in neutral RG flows.

Abstract Many papers on modified gravity theories (MGTs), and metric‐affine geometry have been published. New classes of black hole (BH), wormhole (WH), and cosmological solutions involving nonmetricity and torsion fields were constructed. Nevertheless, the fundamental problems of formulating nonmetric Einstein–Dirac–Maxwell (EDM), equations, and study of important nonmetric gravitational, electromagnetic and fermion effects, have not been solved in MGTs. The main goal of this work is to elaborate on a model of nonmetric EDM theory as a generalization of f(Q) gravity. The authors developed anholonomic frame and connection deformation method which allowed authors to decouple in general form and integrate nonmetric gravitational and matter fields equations. New classes of generated quasi‐stationary solutions are defined by effective sources with Dirac and Maxwell fields, nonmetricity and torsion fields, and generating functions depending, in general, on all space‐time coordinates. For respective nonholonomic parameterizations, such solutions describe nonmetric EDM deformations of BH and cosmological metrics. Variants of nonmetric BH, WH, and toroid solutions with locally anisotropic polarizations of the gravitational vacuum and masses of fermions, and effective electromagnetic sources, are constructed and analyzed. Such nonmetric deformed physical objects cannot be characterized in the framework of the Bekenstein–Hawking paradigm if certain effective horizon/holographic configurations are not involved. It is shown how to define and compute other types of nonmetric geometric thermodynamic variables using generalizations of the concept of G. Perelman W‐entropy.

This study examines the physical and geometrical implications of the vector field [Formula: see text] within the Finsler–Randers metric framework, particularly in the context of Wormhole (WH) geometry. By introducing a non-vanishing vector field with a vanishing covariant derivative to the Finsler manifold via osculation, we derived new Finsler metrics specifically adapted for WH structures. This approach alters traditional geometric interpretations by incorporating direction-dependent variables ([Formula: see text]), which significantly influence the redshift and shape functions of WHs. The resulting differential equations reveal how these modifications impact the geometry and offer new insights into the stability and properties of WHs. In Case 1, both constant and dynamic redshift functions showed how the vector field affects gravitational redshift and energy conditions, crucial for WH stability and traversability, through the parameter [Formula: see text]. In Case 2, the focus was on the vector field impact on the WH geometry emphasizing its role in defining the spatial structure and throat. Additionally, we explored different models under constant and variable equation of state parameters, [Formula: see text], leading to new shape functions that highlight the unique characteristics of WHs in a Finslerian background.

In a brane-world context in which our universe would be a four-dimensional brane embedded into a five-dimensional spacetime or bulk, wormhole geometries are induced on branes. In this article, the Morris–Thorne wormhole and the Molina–Neves wormhole are obtained on the brane using the Nakas–Kanti approach, which starts from a regular five-dimensional spacetime to obtain known black hole and wormhole solutions on the four-dimensional brane. From the bulk perspective, these wormholes are five-dimensional solutions supported by an exotic fluid, but from the brane perspective, such objects are wormholes not supported by any fields or particles that live on the four-dimensional spacetime. Thus, the cause of these wormholes is the bulk influence on the brane.

In this study, we explore the behavior of a Morris–Thorne wormhole under the influence of a Ricci soliton vector field. We derive the expressions for the four components of the vector field in this context and determine the corresponding shape function. Our analysis shows that the wormhole solution satisfies all the criteria for a traversable wormhole. Notably, we identify a negative trend in the null energy condition near the wormhole’s throat. To provide further insight, we present an embedding diagram depicting the wormhole’s geometry. Additionally, we evaluate its stability using the Tolman–Oppenheimer–Volkoff (TOV) equation and calculate the required exotic matter through the Volume Integral Quantifier.

This work aims to explore the possibility of wormholes (WHs) fenced by fuzzy Dark Matter (FDM) haloes relying on the Einasto density profile (EDP). The research explains how combining the EDP with an anisotropic stress-energy momentum tensor leads to the formation of WH solutions corresponding to different Einasto index values. We have investigated the existence of fuzzy WHs and developed the shape function for them. An analysis is conducted on the active gravitational mass and the lodging diagrams for a certain form of the shape function. Additionally, we have also examined the exotic matter’s breach of the null energy conditions, the equilibrium conditions, and the complexity factor associated with the fuzzy WHs.

In the conventional method of studying wormhole (WH) geometry, traversability requires the presence of exotic matter, which also provides negative gravity effects to keep the wormhole throat open. In de Rham–Gabadadze–Tolley (dRGT) massive gravity theory, we produce two types of WH solutions in our present paper. We obtain the field equations for exact WH solutions by selecting a static and spherically symmetric metric for the background geometry. We derive the WH geometry completely for the two different choices of redshift functions. The obtained WH solutions violate all the energy conditions, including the null energy condition (NEC). Various plots are used to illustrate the behavior of the wormhole for a suitable range of m2c1, where m is the graviton mass. It is observed that the photon deflection angle becomes negative for all values of m2c1 as a result of the repulsive action of gravity. It is also shown that the repulsive impact of massive gravitons pushes the spacetime geometry so strongly that the asymptotic flatness is affected. The volume integral quantifier (VIQ) is computed to determine the amounts of matter that violate the null energy condition. The complexity factor of the proposed model is also discussed.