Two-dimensional Gravity Models Research Articles

Gravitating kinks with asymptotically flat metrics

In this work, we consider a two-dimensional (2D) dilaton gravity model where the dilaton kinetic term is modified by an additional derivative coupling term . In the case with a canonical scalar matter field, the field equations of this model have a simple first-order formalism, from which exact static kink solutions can be constructed. The novelty of these solutions is that the corresponding metric can be asymptotically flat rather than asymptotically anti-de Sitter. The linear stability and the localization of scalar matter fields are also studied. It was found that the solutions are stable against small linear perturbations, and the localization of scalar matter fields can be realized by introducing scalar-kink interactions.

Kink solutions in generalized 2D dilaton gravity

We study static kink solutions in a generalized two-dimensional dilaton gravity model, where the kinetic term of the dilaton is generalized to be an arbitrary function of the canonical one X=−12(∇φ)2, say F(X), and the kink is generated by a canonical scalar matter field ϕ. It is found that for arbitrary F(X), the background field equations have a simple first-order formalism, and the linear perturbation equation can always be written as a Schrödinger-like equation with factorizable Hamiltonian operator. After choosing appropriate F(X) and superpotential, we obtain a sine-Gordon type kink solution with pure AdS2 metric. The linear perturbation issue of this solution becomes an exactly solvable conformal quantum mechanics problem, if one of the model parameter takes a critical value.

Investigation into a deep-rooted crustal framework deduced from potential field data in Cretaceous and Tertiary strata, Sokoto Basin NW, Nigeria

The Paleocene sediments from the Sokoto Group, which comprises of the Gamba, Dange, and Kalambaina formations, were covered by Maastrichtian sediments from the Rima Group, which includes the Wurno, Dukamaje, and Taloka formations. High-resolution aeromagnetic and satellite gravity measurements were used to study these sediments. The aforementioned strata correspond to the Cretaceous and Tertiary strata in this research area and are situated in the south-eastern part of the Iullemmeden Basin. Our aim is to determine and explain the horizontal variation in density and magnetization using the whole regional satellite gravity and aeromagnetic data. The deeper magnetic and density sources were scanned using a two-dimensional (2D) radially averaged power spectrum analysis to produce the NE to SW and E to W trending models for the Moho, lower, and upper lithosphere under the study area. The results were further assessed using upward continuation, derivative analysis, and two-dimensional gravity and magnetic modeling. Numerous important structural trends (i.e., NE-SW, E-W & ENE-WSW), have been identified as a result of the vertical gradients for the potential field data. Spectral analysis and Euler deconvolution can be used to calculate the depths to the lower and upper mantle crust boundaries as well as the depth to Moho. The findings of a qualitative analysis point to an intrusion of the Gundumi and Illo Formations that has a northeast orientation as the primary cause of the significant gravitational and magnetic interaction. The differences in the deep-seated crustal structures and mineralized anomalous bodies with depth were visible on anomaly maps with an upward continuation of 5 km, 7 km, 20 km, and 30 km. Quantitatively, the 2D regional models along the selected profiles (L1, L2, L4, L6 and L7) display a typical lithostratigraphic succession of the Gundumi and Illo Formation (Continental Intercalaire, CI) type of crust, which is subdivided into the lower and upper mantle crust as well as the Moho. The sediment thickness by surface depth ranges from ∼4.06 km and ∼23.31 km. The Moho interface, lower and upper mantle crusts, and magnetic crust are all located at depths of around ∼10.23 km. The distance between the local models of the foundation rocks to the north and south of the Sokoto Group was approximately ∼6 to ∼8 km and ∼4.5 km, respectively.

The crustal structure of the western Amundsen Basin, Arctic Ocean, derived from seismic refraction/wide-angle reflection data

SUMMARY Two geophysical expeditions (LOMROG II and III) were carried out in 2009 and 2012 to acquire seismic data in the western Amundsen Basin in the Arctic Ocean, a basin formed by ultraslow seafloor spreading at the Gakkel Ridge. Previous studies show alternating magmatic and amagmatic segments at the ridge but it is unclear if such segmentation persisted throughout the entire opening history of the basin. The seismic refraction data were used to develop P-wave velocity models down to the uppermost mantle using forward modelling of traveltimes. The coincident seismic reflection data were used to constrain the geometry of the sedimentary layers and for characterizing the acoustic basement. 2-D gravity modelling was used to determine the Moho depth in areas when data quality was insufficient to resolve a Moho reflection. The models distinguish three different basement types: oceanic crust with layers 2 and 3, oceanic crust that is lacking a layer 3 and exhumed and serpentinized mantle. The maximum observed crustal thickness is 6 km. Areas with thin crust (<3 km) may be underlain by partially serpentinized mantle. Where exhumed mantle is observed, a serpentinization front separates highly serpentinized mantle at the top from partially serpentinized mantle below. The presence of oceanic crust off-axis of the presently amagmatic sector of the Gakkel Ridge indicates that there is both a spatial and temporal variation of crustal accretion processes at the ridge.

Critical JT gravity

In this paper, we investigate a critical behavior of JT gravity, a model of two-dimensional quantum gravity on constant negatively curved spacetimes. Our approach involves using techniques from random maps to investigate the generating function of Weil-Petersson volumes, which count random hyperbolic surfaces with defects. The defects are weighted geodesic boundaries, and criticality is reached by tuning the weights to the regime where macroscopic holes emerge in the hyperbolic surface, namely non-generic criticality. We analyze the impact of this critical regime on some universal features, such as its density of states. We present a family of models that interpolates between systems with ρ0(E) ~ sqrt{E-{E}_0} and ρ0(E) ~ (E − E0)3/2, which are commonly found in models of JT gravity coupled to dynamical end-of-the-world and FZZT branes, and give a precise definition of what this phase transition means from the random geometry point of view.

An outsider’s perspective on information recovery in de Sitter space

Entanglement islands play a crucial role in our understanding of how Hawking radiation encodes information in a black hole, but their relevance in cosmological spacetimes is less clear. In this paper, we continue our investigation of information recovery in de Sitter space and construct a two-dimensional model of gravity containing a domain wall that interpolates between de Sitter space and Rindler space. The Rindler wedges introduce weakly-gravitating asymptotic regions from which de Sitter space can be probed, yielding an outside perspective of the cosmological horizon. In contrast to earlier works, backreaction effects are under control by considering a quantum state that only breaks the thermal equilibrium of the Bunch-Davies state for a finite time. This allows information to be decoded from the Gibbons-Hawking radiation in a controlled fashion.

Non-Abelian Gauge Theories with Composite Fields in the Background Field Method

Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green’s functions for a Yang–Mills theory with composite and background fields are introduced, including the generating functional of vertex Green’s functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and employed on a systematic basis. On the one hand, this involves the consideration of (modified) Ward identities with a field-dependent anticommuting parameter, also depending on a non-trivial background. On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov–Zwanziger theory, including the case of a local BRST-invariant horizon, and also by the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion.

Marine Geophysical Data and Its Application to Assessment of Crustal Structure along the Northern Egyptian Passive Continental Margin

The Egyptian passive continental margin is considered a remarkable geologic setting, in addition to being an occupation and manufacturing locality in north Egypt. This work used accessible potential field data, such as marine gravity data, to provide a wider vision of the potential field of the area under investigation. The results of the two-dimensional (2D) gravity modelling revealed a good agreement between the modelled gravity and observed gravity fields, including known regional structures found in the investigated area. The findings revealed that crustal modelling was affected by the tectonic structure and the huge thickness of sedimentary layers, which act as barriers to the crystal crust. The results revealed that the crustal thickness and density are spread among the deposited layer and the inferior mantle in the Moho range. Furthermore, it was found that the basement extent lies nearly 6–9 km lower in the northern Egyptian coastline to approximately 13 km under the Herodotus abyssal plain. Moreover, it was shown that the thickness of the sedimentary layers deposit increases near the East Mediterranean Ridge.

Color decorations of Jackiw-Teitelboim gravity

We introduce the colored version of Jackiw-Teitelboim (JT) gravity which is the two-dimensional dilaton gravity model with matrix-valued fields. It is straightforwardly formulated in terms of BF action with su(N, N) gauge algebra so that the standard JT gravity is embedded as su(1, 1) ⊂ su(N, N) subsector. We also elaborate on the respective metric formulation which is shown to involve the JT fields plus su(N) non-Abelian fields as well as su(N)-matrix valued metric and dilaton fields. Their interactions are governed by minimal couplings and potential terms of cubic and quartic orders involving derivatives.

The volume of the black hole interior at late times

Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior and study it at arbitrarily late times for black holes in various models of two-dimensional gravity. Because of a novel universal cancellation between the contributions of the semi-classical black hole spectrum and some of its non-perturbative corrections, we find that, after a linear growth at early times, the length of the interior saturates at a time, and towards a value, that is exponentially large in the entropy of the black hole. This provides a non-perturbative test of the complexity equals volume proposal since complexity is also expected to plateau at the same value and at the same time.

Delineation of structural and tectonic features in the Mahanadi basin, eastern India: New insights from remote sensing and land gravity data

• An integrated analysis (ALOS PALSAR , SRTM-DEM, and Ground Gravity data) is performed to delineate the structural and tectonic framework at the Mahanadi graben , India. • The 2-D gravity model incorporates the rifting model of the basin formation along the preexisting basement shear zones. • The structural trends with pronounced geomorphic expressions represent the reactivated structures formed under the evolving stress regimes of the Mahanadi graben. During Gondwana dispersal, the Mahanadi basin experienced rifting and reactivation of preexisting structures, causing terrain deformation with faulting. The landform around Proterozoic Sukinda Thrust in the Mahanadi basin provides an opportunity to map the geomorphic expressions and correlate them with the tectonics of the graben using remote sensing images, digital elevation model, and gravity data. The subsurface extensions of the identified structures using SAR data and relief image analysis are modeled with the Bouguer gravity anomaly. The mapped tectonic features correlate well with the gravity gradient trends in residual gravity anomalies. The E-W and NW-SE trending residual gravity lineaments match well with the mapped faults and suggest their extension within the shallow crust. The two-dimensional (2-D) gravity model realistically constrains the subsurface geology, and by incorporating other published data, we suggest that the Gondwana rifting had reactivated the preexisting shear zones in the cratonic basement down to a depth of ∼ 5 km and subsequently deposited sediments into the fault-bound shallow basin of the Mahanadi graben.

Replica wormholes from Liouville theory

The replica wormholes are a key to the existence of the islands that play a central role in a recent proposal for the resolution of the black hole information paradox. In this paper, we study the replica wormholes in the JT gravity, a model of two-dimensional quantum gravity coupled to a non-dynamical dilaton, by making use of the 2d conformal field theory (CFT) description, namely, the Liouville theory coupled to the (2, p) minimal matter in the p → ∞ limit. In the Liouville CFT description, the replica wormholes are created by the twist operators and the gravitational part of the bulk entanglement entropy can be reproduced from the twist operator correlators. We propose the precise dictionary and show how this correspondence works in detail.

A new basin depth map of the fault-bound Wellington CBD based on residual gravity anomalies

ABSTRACT A new basin depth map for the Wellington Central Business District shows a maximum depth of 540 m near the Wellington Stadium. Our new basin geometry constraints are from a residual gravity anomaly study, based on ∼600 new gravity observations. Residual gravity anomalies are as large as −6.2 mGal with uncertainties <0.1 mGal. Two-dimensional gravity models constrained by boreholes that intersect basement are used to generate the basin depth map. Our maximum depth is twice that previously estimated from other geological and geophysical criteria. An onshore extension of the recently discovered Aotea Fault on the western side of Mt Victoria, is also interpreted from the gravity data. A maximum basement offset of up to 130 m and gravity anomaly gradients up to 8 mGal/km are observed across the fault. A secondary splay off the main Aotea Fault is identified in the NW corner of Mt Victoria, and a possible extension to the Lambton Fault is identified beneath the Wellington Railway Station. This new basin depth and fault trace data provide valuable constraints to models of seismic hazard assessment for Wellington City.

K-field kinks in two-dimensional dilaton gravity

In this work, kinks with non-canonical kinetic energy terms are studied in a type of two-dimensional dilaton gravity model. The linear stability issue is generally discussed for arbitrary static solutions, and the stability criteria are obtained. As an explicit example, a model with cuscuton term is studied. After rewriting the equations of motion into simpler first-order formalism and choosing a polynomial superpotential, an exact self-gravitating kink solution is obtained. The impacts of the cuscuton term are discussed.

Approximate Killing symmetries in non-perturbative quantum gravity

We study the notion of approximate Killing vector fields in several toy models of non-perturbative two-dimensional quantum gravity. Using the framework of discrete exterior calculus, we show how to formulate quantum observables related to such approximate Killing vector fields. Using these methods, we aim to investigate symmetry properties of the space–time geometry produced by the quantum gravitational model at hand. Since we expect quantum fluctuations to dominate at small scales, our goal is to construct a scale-dependent notion of symmetry that might be used to determine whether the emergent (semi-)classical geometry admits any approximate Killing symmetries. We have evaluated one particular choice of such an observable on three ensembles of discrete geometry. We find that the method is useful in the setting where fluctuations are small, but that more work is needed before these ideas can be applied in the deep quantum regime.

Geometry of the Bushveld Complex from 3D potential field modelling

A full three-dimensional (3D) potential field model of the central and southern Bushveld Complex reveals information about the Complex in areas obscured by younger geological cover. Previously, two-dimensional gravity models and a few magnetic models limited to certain sections of the Bushveld Complex have been used to propose geometries for the Rustenburg Layered Suite, especially in the western and eastern lobes. These models were often used to support different emplacement models. Although these models provided valuable information, two-and-a-half-dimensional (2.5D) potential field modelling is not well suited to modelling complex 3D geology. Also, in most cases, only the magnetic or gravity data were modelled, but jointly modelling both data sets better constrains the results, as was shown recently for a 3D model of the northern lobe. Joint 3D modelling of regional gravity and magnetic data combined with published crustal thickness models derived from broadband seismic tomography studies and constrained by density and susceptibility data, geologic mapping, boreholes and seismic reflection data were used to create a 3D model of the central and southeastern sections of the Bushveld Complex, as well as the southern part of the northern lobe. The model shows a complex geometry with thick continuous Rustenburg Layered Suite S in most of the western and southeastern lobes, but less continuous Rustenburg Layered Suite in the eastern lobe. Large domes or thick granites and granophyre in the latter interrupt the continuity of the Rustenburg Layered Suite and the western and eastern lobes are strictly speaking only partially connected in places. However, they are not separate intrusions, but one disconnected by pre-existing and synmagmatic updoming. Three possible feeders were modelled in the northern, western, and south-eastern lobes.

Excitation spectra of quantum matter without quasiparticles. II. Random t−J models

We present numerical solutions of the spectral functions of $t$-$J$ models with random and all-to-all exchange and global SU($M$) spin rotation symmetry. The solutions are obtained from the saddle-point equations of the large volume limit, followed by the large $M$ limit. These saddle point equations involve Green's functions for fractionalized spinons and holons carrying emergent U(1) gauge charges, obeying relations similar to those of the Sachdev-Ye-Kitaev (SYK) models. The low frequency spectral functions are compared with an analytic analysis of the operator scaling dimensions, with good agreement. We also compute the low frequency and temperature behavior of gauge-invariant observables: the electron Green's function, the local spin susceptibility and the optical conductivity; along with the temperature dependence of the d.c. resistivity. The time reparameterization soft mode (equivalent to the boundary graviton in holographically dual models of two-dimensional quantum gravity) makes important contributions to all observables, and provides a linear-in-temperature contribution to the d.c. resistivity.

Wormholes, a fluctuating cosmological constant and the Coleman mechanism

We show that in a two-dimensional model of quantum gravity the summation over all possible wormhole configurations leads to a kind of Coleman mechanism where the cosmological constant plays no role for large universes. Observers who are unable to observe the change in topology will naturally interpret the measurements of the size of the universe as being caused by a fluctuating cosmological constant, rather than fluctuating topology of spacetime.

Scalar perturbations of black holes in Jackiw-Teitelboim gravity

We study linear scalar perturbations of black holes in two-dimensional (2D) gravity models with a particular emphasis on Jackiw-Teitelboim (JT) gravity. We obtain an exact expression of the quasinormal mode frequencies for single horizon black holes in JT gravity and then verify it numerically using the Horowitz-Hubeny method. For a 2D Reissner-Nordstr\"om like solution, we find that the massless scalar wave equation reduces to the confluent Heun equation using which we calculate the Hawking spectra. Finally, we consider the dimensionally reduced Ba\~nados-Teitelboim-Zanelli (BTZ) black hole and obtain the exterior and interior quasinormal modes. The dynamics of a scalar field near the Cauchy horizon mimics the behavior of the same for the usual BTZ black hole, indicating a possible violation of the strong cosmic censorship conjecture in the near extreme limit. However, quantum effects seem to rescue strong cosmic censorship.

Quantum fields, geometric fluctuations, and the structure of spacetime

Quantum fluctuations of the vacuum stress-energy tensor are highly non-Gaussian, and can have unexpectedly large effects on spacetime geometry. In this paper, we study a two-dimensional dilaton gravity model coupled to a conformal field, in which the distribution of vacuum fluctuations is well understood. In this model, the fluctuations of the matter field are responsible for the fluctuations of the geometry itself. By analyzing the geodesic deviation in this model, we show that a pencil of massive particles propagating on this fuzzy spacetime eventually converges and collapses. This is consistent with our earlier analysis of null geodesics in [Phys. Rev. Lett.\ 107, 021303 (2011)].