Pure Gravity Research Articles

Finiteness of quantum gravity with matter on a PL spacetime

We study the convergence of the path integral (PI) for general relativity with matter on a picewise linear (PL) spacetime that corresponds to a triangulation of a smooth manifold by using a PI measure that renders the pure gravity PI finite. This measure depends on a parameter p, and in the case when the matter content is just scalar fields, we show that the PI is absolutely convergent for 0,5 and not more than two scalar fields. In the case of Yang–Mills (YM) fields, we show that the PI is absolutely convergent for the U(1) group and 0,5. In the case of Dirac fermions, we show that the PI is absolutely convergent for any number of fermions and a sufficiently large p. When the matter content is given by scalars, YM fields and fermions, as in the case of the standard model (SM), we show that the PI is absolutely convergent for 52,5. Hence one can construct a finite quantum gravity theory on a PL spacetime such that the classical limit is general relativity coupled to the SM.

Gauge-Invariant Double Copies via Recursion Relations.

We prove by construction that all tree-level amplitudes in pure (super)gravity can be expressed as termwise, gauge-invariant double copies of those of pure (super-)Yang-Mills obtained via on-shell recursion. These representations are far from unique: varying the recursive scheme leads to a wide variety of distinct but equally valid representations of gravitational amplitudes, all realized as double copies.

Closed Timelike Curves Induced by a Buchdahl-Inspired Vacuum Spacetime in R2 Gravity

The recently obtained special Buchdahl-inspired metric Phys. Rev. D 107, 104008 (2023) describes asymptotically flat spacetimes in pure Ricci-squared gravity. The metric depends on a new (Buchdahl) parameter k˜ of higher-derivative characteristic, and reduces to the Schwarzschild metric, for k˜=0. For the case k˜∈(−1,0), it was shown that it describes a traversable Morris–Thorne–Buchdahl (MTB) wormhole Eur. Phys. J. C 83, 626 (2023), where the weak energy condition is formally violated. In this paper, we briefly review the special Buchdahl-inspired metric, with focuses on the construction of the Kruskal–Szekeres (KS) diagram and the situation for a wormhole to emerge. Interestingly, the MTB wormhole structure appears to permit the formation of closed timelike curves (CTCs). More specifically, a CTC straddles the throat, comprising of two segments positioned in opposite quadrants of the KS diagram. The closed timelike loop thus passes through the wormhole throat twice, causing two reversals in the time direction experienced by the (timelike) traveller on the CTC. The key to constructing a CTC lies in identifying any given pair of antipodal points (T,X) and (−T,−X) on the wormhole throat in the KS diagram as corresponding to the same spacetime event. It is interesting to note that the Campanelli–Lousto metric in Brans–Dicke gravity is known to support two-way traversable wormholes, and the formation of the CTCs presented herein is equally applicable to the Campanelli–Lousto solution.

Conformal hairy black holes of quartic quasi-topological gravity with power-Yang–Mills source

We study higher dimensional hairy black holes of quartic quasi-topological gravity in the framework of non-abelian power-Yang–Mills theory. It is shown that real solutions of the gravitational field equations exist only for positive values of quartic quasi-topological coefficient. Depending on the values of the mass, conformal coupling constants, quasi-topological coefficients, Yang–Mills magnetic charge, and nonlinearity parameter, they can be interpreted as black holes with one horizon, at most three horizons and naked singularity. It is also shown that the solution associated with these black holes has an essential curvature singularity at the centre r=0. Thermodynamic and conserved quantities for these hairy black holes are computed and we show that the first law has been verified. We also check thermodynamic stability in both canonical and grand canonical ensembles. In addition to this, we also formulate new power-Yang–Mills hairy black hole solutions in pure quasi-topological gravity. The physical and thermodynamic properties of these black holes are discussed as well. It is concluded that unlike Yang–Mills black holes without scalar hair there exist stability regions for the power-Yang–Mills hairy black holes in grand canonical ensemble. Finally, we discuss the thermodynamics of horizon flat power-Yang–Mills rotating black branes and analyze their thermodynamic and conserved quantities by using the counter-term method inspired by AdS/CFT correspondence.

On-shell operator construction in the effective field theory of gravity

We construct the on-shell amplitude basis and the corresponding effective operators for generic modified gravity theory, such as pure gravity with higher derivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking the Weyl tensor as the building block, we utilize the Young tensor technique to obtain independent operators, without equation of motion and total derivative redundancies. We update our algorithm and vastly increase the speed for finding the monomial basis (m-basis) of effective operators expressed in terms of Weyl tensors with Lorentz indices, the familiar form for the General Relativity community. Finally, we obtain the complete and independent amplitude and operator basis for GRSMEFT and GRLEFT up to mass dimension 10.

Covariant generalized conserved charges of General Relativity

Motivated by the current research of generalized symmetries and the construction of conserved charges in pure Einstein gravity linearized over Minkowski spacetime in Cartesian coordinates, we investigate, from a purely classical point of view, the construction of these charges in a coordinate- and frame-independent language in order to generalize them further. We show that all the charges constructed in that context are associated to the conformal Killing-Yano 2-forms of Minkowski spacetime. Furthermore, we prove that those associated to closed conformal Killing-Yano 2-forms are identical to the charges constructed by Kastor and Traschen for their dual Killing-Yano (d − 2)-forms. We discuss the number of independent and non-trivial gravitational charges that can be constructed in this way.

Quantum exponentials for the modular double and applications in gravity models

In this note, we propose a decomposition of the quantum matrix group SLq+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{SL}}_q^{+} $$\\end{document}(2, ℝ) as (deformed) exponentiation of the quantum algebra generators of Faddeev’s modular double of Uq(sl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{sl} $$\\end{document}(2, ℝ)). The formula is checked by relating hyperbolic representation matrices with the Whittaker function. We interpret (or derive) it in terms of Hopf duality, and use it to explicitly construct the regular representation of the modular double, leading to the Casimir and its modular dual as the analogue of the Laplacian on the quantum group manifold. This description is important for both 2d Liouville gravity, and 3d pure gravity, since both are governed by this algebraic structure. This result builds towards a q-BF formulation of the amplitudes of both of these gravitational models.

More on pure gravity with a negative cosmological constant

We identify an ambiguity in the Chern-Simons formulation of three-dimensional gravity with negative cosmological constant that originates in an outer automorphism of the Lie algebra sl\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathfrak{sl} $$\\end{document}(2, ℝ). It has important consequences for the stability of the theory in a space-time with boundary. We revisit the classical equivalence of three-dimensional gravity with a boundary Liouville theory both on and off the mass shell. Moreover, we provide further details on the quantum equivalence, the gauge symmetry that renders the spectrum diagonal, as well as the relation between asymptotically AdS3 metrics and polar boundary conditions. We thus set the proposal that the Liouville conformal field theory serves as a definition of a unitary theory of pure gravity in three dimensions with negative cosmological constant on a more stable footing.

Pure gravity traveling quasi‐periodic water waves with constant vorticity

AbstractWe prove the existence of small amplitude time quasi‐periodic solutions of the pure gravity water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom delimited by a space periodic free interface. Using a Nash‐Moser implicit function iterative scheme we construct traveling nonlinear waves which pass through each other slightly deforming and retaining forever a quasiperiodic structure. These solutions exist for any fixed value of depth and gravity and restricting the vorticity parameter to a Borel set of asymptotically full Lebesgue measure.

Gaussian regular black holes in pure quadratic gravity

Gaussian regular black holes in pure quadratic gravity

Holography for bulk states in 3D quantum gravity

In this work we discuss the holographic description of states in the Hilbert space of (2+1)-dimensional quantum gravity, living on a time slice in the bulk. We focus on pure gravity coupled to pointlike sources for heavy spinning particles. We develop a formulation where the equations for the backreacted metric reduce to two decoupled Liouville equations with delta-function sources under pseudosphere boundary conditions. We show that both the semiclassical wavefunction and the gravity solution are determined by a universal object, namely a classical Virasoro vacuum block on the sphere. In doing so we derive a version of Polyakov’s conjecture, as well as an existence criterion, for classical Liouville theory on the pseudosphere. We also discuss how some of these results are modified when considering closed universes with compact spatial slices.

A proposal for 3d quantum gravity and its bulk factorization

Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a q-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. In the conventional Chern-Simons description, these black holes correspond to Wilson lines in representations of PSL(2, ℝ) ⨂ PSL(2, ℝ). We show that the correct calculation of gravitational entropy suggests we should interpret the bulk theory as an extended topological quantum field theory associated to the quantum semi-group {textrm{SL}}_q^{+}left(2,mathbb{R}right)bigotimes {textrm{SL}}_q^{+}left(2,mathbb{R}right) . Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime.

Higher derivative contributions to black hole thermodynamics at NNLO

In an effective theory of gravity, thermodynamic quantities of black holes receive corrections from the infinite series of higher derivative terms. At the next to leading order, these can be obtained by using only the leading order solution. In this paper, we push forward this property to the next to next to leading order. We propose a formula which yields the Euclidean action of asymptotically flat black holes at the next to next to leading order using only the solution up to and including the next to leading order. Other conserved quantities are derived from the Euclidean action via standard thermodynamic relation. We verify our formula in examples of D-dimensional pure gravity and Einstein-Maxwell theory extended by 4- and 6-derivative terms. Based on our formula, we also prove that for asymptotically flat black holes, the physical quantities are invariant under field redefinitions.

Von Neumann algebras in JT gravity

We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II∞ factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit. We comment on how the factorization problem differs between pure JT gravity and JT gravity with matter.

A spinorial double copy for mathcal{N} = 0 supergravity

The Weyl double copy is a formula relating solutions of scalar, gauge and gravity theories, and is related to the BCJ double copy for scattering amplitudes. The latter relates Yang-Mills theory to mathcal{N} = 0 supergravity, where an axion and dilaton are present in addition to the graviton. However, the traditional Weyl double copy applies only to pure gravity solutions, such that it remains to be seen whether or not it can be extended to the full spectrum of mathcal{N} = 0 supergravity. We examine this question using recently developed twistor methods, showing that some sort of double copy formula for mathcal{N} = 0 supergravity is indeed possible for certain solutions. However, it differs both from the traditional Weyl double copy form, and recent conjectures aimed at generalising the Weyl double copy to non-vacuum solutions.

DeWitt Boundary Condition in One-Loop Quantum Cosmology

DeWitt’s suggestion that the wave function of the universe should vanish at the classical Big Bang singularity is considered here within the framework of one-loop quantum cosmology. For pure gravity at one loop about a flat four-dimensional background bounded by a 3-sphere, three choices of boundary conditions are considered: vanishing of the linearized magnetic curvature when only transverse-traceless gravitational modes are quantized; a one-parameter family of mixed boundary conditions for gravitational and ghost modes; and diffeomorphism-invariant boundary conditions for metric perturbations and ghost modes. A positive ζ(0) value in these cases ensures that, when the three-sphere boundary approaches zero, the resulting one-loop wave function approaches zero. This property may be interpreted by saying that, in the limit of small three-geometry, the resulting one-loop wave function describes a singularity-free universe. This property holds for one-loop functional integrals, which are not necessarily equivalent to solutions of the quantum constraint equations.

A modification to the Schrödinger equation for broader bandwidth gravity-capillary waves on deep water with depth-uniform current

We derive a nonlinear Schrödinger equation for the propagation of the three-dimensional broader bandwidth gravity-capillary waves including the effect of depth-uniform current. In this derivation, the restriction of narrow bandwidth constraint is extended, so that this equation will be more appropriate for application to a realistic sea wave spectrum. From this equation, an instability condition is obtained and then instability regions in the perturbed wavenumber space for a uniform wave train are drawn, which are in good agreement with the exact numerical results. As it turns out, the corrections to the stability properties that occur at the fourth-order term arise from an interaction between the mean flow and the frequency-dispersion term. Since the frequency-dispersion term, in the absence of depth-uniform current, for pure capillary waves is of opposite sign for pure gravity waves, so too are the corrections to the instability properties. doi: 10.1017/S1446181123000020

Rational wavefunctions in de Sitter spacetime

The Bootstrap approach to calculating cosmological correlators relies on a well motivated ansatz. It is typical in the literature to assume that correlators are rational functions as this greatly increases our constraining power. However, this has only previously been demonstrated for some specific theories. In this paper we find a set of assumptions which we prove are sufficient to ensure that the wavefunction coefficients are rational. As a corollary of this we generalise the manifestly local test to higher dimensions. This result greatly reduces the allowed space of functions that wavefunction coefficients can take in both the Effective Field Theory of Inflation and Pure Gravity models and is thus a key ingredient in the Cosmological Bootstrap program.

Seeking for resonances in unitarized one-loop graviton-graviton scattering

Some effective field theories exhibit dynamical resonances that, when properly included, mitigate their bad behavior at high energies. Unitarization of the partial wave amplitudes is the preferred method to unveil such resonances. Interpreting the Einstein-Hilbert theory in the spirit of effective Lagrangians, we implement the inverse amplitude method and unitarize the one-loop level graviton-graviton scattering in pure gravity. Due to the presence of infrared divergences, the analysis requires a careful treatment of the infrared region and the introduction of infrared regulators, carefully selected in order to fulfill perturbative unitarity.

Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields

Einstein gravity minimally coupled to a scalar field with a two-parameter Higgs-like self-interaction in three spacetime dimensions is recast in terms of a Chern-Simons form for the algebra g+ ⊕ g− where, depending on the sign of the self-interaction couplings, g± can be so(2, 2), so(3, 1) or iso(2, 1). The field equations can then be expressed through the field strength of non-flat composite gauge fields, and conserved charges are readily obtained from boundary terms in the action that agree with those of standard Chern-Simons theory for pure gravity, but with non-flat connections. Regularity of the fields then amounts to requiring the holonomy of the connections along contractible cycles to be trivial. These conditions are automatically fulfilled for the scalar soliton and allow to recover the Hawking temperature and chemical potential in the case of the rotating hairy black holes presented here, whose entropy can also be obtained by the same formula that holds in the case of a pure Chern-Simons theory. In the conformal (Jordan) frame the theory is described by General Relativity with cosmological constant conformally coupled to a self-interacting scalar field, and its formulation in terms of a Chern-Simons form for suitably composite gauge fields is also briefly addressed.