Imposing the Petrov-like boundary condition on the hypersurface at finite cutoff, we derive the hydrodynamic equation on the hypersurface from the bulk Einstein equation with electromagnetic field in the near horizon limit. We first get the general framework for spacetime with matter field, and then derive the incompressible Navier-Stokes equations for black holes with electric charge and magnetic charge respectively. Especially, in the magnetic case, the standard magnetohydrodynamic equations will arise due to the existence of the background electromagnetic field on the hypersurface.
We point out that the inequality det E > 0 distinguishes the kinematical phase space of canonical connection gravity from that of a gauge field theory, and characterize the eigenvectors with positive, negative and zero-eigenvalue of the corresponding quantum operator in a lattice-discretized version of the theory. The diagonalization of the operator det E is simplified by classifying its eigenvectors according to the irreducible representations of the octagonal group.
The fluid/gravity correspondence relates solutions of the incompressible Navier-Stokes equation to metrics which solve the Einstein equations. In this paper we extend this duality to a new magnetohydrodynamics/gravity correspondence, which translates solutions of the equations of magnetohydrodynamics (describing charged fluids) into geometries that satisfy the Einstein-Maxwell equations. We present an explicit example of this new correspondence in the context of flat Minkowski space. We show that a perturbative deformation of the Rindler wedge satisfies the Einstein-Maxwell equations provided …
We apply the recently established connection between nonlinear fluid dynamics and AdS gravity to the case of the dyonic black brane in AdS_4. This yields the equations of fluid dynamics for a 2+1 dimensional charged fluid in a background magnetic field. We construct the gravity solution to second order in the derivative expansion. From this we find the fluid dynamical stress tensor and charge current to second and third order in derivatives respectively, along with values for the associated transport coefficients.
The equivalence principle suggests to consider gravity as an infra-red phenomenon, whose effects are visible only outside Einstein's free-falling elevator. By curving spacetime, General Relativity leaves the smallest systems free of classical gravitational effects. However, according to the standard semi-classical treatment, indirect effects of gravity can be experienced inside the elevator through the well-known mechanism of quantum particle production. Here we try a different path than the one historically followed: rather than imposing field quantization on top of a curved manifold, we atte…
Recently it has been shown that imposing Petrov type I condition on the boundary may reduce the Einstein's equation to the Navier-Stokes equation in the non-relativistic and near-horizon limit. In this paper we extend this framework to a spacetime with a cosmological constant. By explicit construction we show that the Navier-Stokes equation can be derived from both black brane background and spatially curved spacetime. We also conjecture that imposing Petrov type I condition on the boundary should be equivalent to the conventional method using the hydrodynamical expansion of the metric in the …
We obtain the static spherically symmetric vacuum solutions of Horava-Lifshitz gravity theory, imposing the detailed balance condition only in the UV limit. We find the solutions in two different coordinate systems, the Painlevé-Gullstrand coordinates and the Poincare coordinates, to examine the consequences of imposing the projectability condition. The solutions in two coordinate systems are distinct due to the non-relativistic nature of the HL gravity. In the Painleve-Gullstrand coordinates complying with the projectability condition, the solution involves an additional integration constant …
We study the nonlinear hydrodynamics of a 2+1 dimensional charged conformal fluid subject to slowly varying external electric and magnetic fields. Following recent work on deriving nonlinear hydrodynamics from gravity, we demonstrate how long wavelength perturbations of the AdS dyonic black brane solution of 4D supergravity are governed by equations equivalent to fluid dynamics equations in the boundary theory. We investigate the implications of $S$-duality for our system, and derive restrictions imposed on the transport coefficients of a generic fluid invariant under the S operation. We also …
We study a large family of metric-affine theories with a projective symmetry, including non-minimally coupled matter fields which respect this invariance. The symmetry is straightforwardly realised by imposing that the connection only enters through the symmetric part of the Ricci tensor, even in the matter sector. We leave the connection completely free (including torsion) and obtain its general solution as the Levi-Civita connection of an auxiliary metric, showing that the torsion only appears as a projective mode. This result justifies the widely used condition of setting vanishing torsion …
Without imposing the trapping boundary conditions and only from within the very definition of area it is shown that the loop quantization of area manifests an unexpected degeneracy in area eigenvalues. This could lead to a deeper understanding of the microscopic description of a quantum black hole. If a certain number of semi-classically expected properties of black holes are imposed on a quantum surface its entropy coincides with the Bekenstein-Hawking entropy.
We study the gravity action built from two gauge fields corresponding to the generators of the conformal group. Starting with the action from which one can obtain Einstein gravity and conformal gravity upon imposing suitable constraints, we keep two independent gauge fields and integrate out the field corresponding to the generator of Lorentz transformations. We identify the two gauge fields with two vierbeins and perturb them around an Anti--de Sitter space. This gives the linearized equations that differ from both, Einstein gravity and conformal gravity linearized equations. We also study th…
General two-dimensional pure dilaton-gravity can be discussed in a unitary way by introducing suitable field redefinitions. The new fields are directly related to the original spacetime geometry and in the canonical picture they generalize the well-known geometrodynamical variables used in the discussion of the vacuum dilatonic black hole. So the model can be quantized using the techniques developed for the latter case. The resulting quantum theory coincides with the quantum theory obtained imposing the Birkhoff theorem at the classical level.
We consider an $O(d,d;\mathbb{Z})$ invariant massive deformation of double field theory at the level of free theory. We study Kaluza-Klein reduction on $R^{1,n-1} \times T^{d}$ and derive the diagonalized second order action for each helicity mode. Imposing the absence of ghosts and tachyons, we obtain a class of consistency conditions which include the well known weak constraint in double field theory as a special case. Consequently, we find two-parameter sets of $O(d,d;\mathbb{Z})$ invariant Fierz-Pauli massive gravity theories.
Previously it has been shown that imposing a Petrov-like boundary condition on a hypersurface may reduce the Einstein equation to the incompressible Navier-Stokes equation, but all these correspondences are established in the near horizon limit. In this note, we remark that this strategy can be extended to an arbitrary finite cutoff surface which is spatially flat, and the Navier-Stokes equation is obtained by employing a non-relativistic long-wavelength limit.
We derive the the Barrett-Crane spin foam model for Euclidean 4 dimensional quantum gravity from a discretized BF theory, imposing the constraints that reduce it to gravity at the quantum level. We obtain in this way a precise prescription of the form of the Barrett-Crane state sum, in the general case of an arbitrary manifold with boundary. In particular we derive the amplitude for the edges of the spin foam from a natural procedure of gluing different 4-simplices along a common tetrahedron. The generalization of our results to higher dimensions is also shown.
We consider the quantization of matter fields in a background described by the teleparallel equivalent to general relativity. The presence of local Lorentz and gauge symmetries gives rise to different coupling prescriptions, which we analyse separately. As expected, quantum matter fields produce divergences that cannot be absorbed by terms in the background action of teleparallel equivalent to general relativity. Nonetheless, the formulation of teleparallel gravity allows one to find out the source of the problem. By imposing local Lorentz invariance after quantization, we show that a modified…
The action principle of the BF type introduced by Capovilla, Montesinos, Prieto, and Rojas (CMPR) which describes general relativity with Immirzi parameter is modified in order to allow the inclusion of the cosmological constant. The resulting action principle is on the same footing as the original Plebanski action in the sense that the equations of motion coming from the new action principle are equivalent to the Holst action principle plus a cosmological constant without the need of imposing additional restrictions on the fields. We consider this result a relevant step towards the coupling o…
We calculate the shear viscosity of field theories with gravity duals of Gauss-Bonnet gravity with a non-trivial dilaton using AdS/CFT. We find that the dilaton filed has a non-trivial contribution to the ratio of shear viscosity over entropy density and after imposing causal constraint for the boundary field theory, the new lower bound $4/25π$, obtained from pure Gauss-Bonnet gravity, may have a small violation.
We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the cosmological context assuming weak gravity. The two formulations are made for a general scalar field with general $f(ϕ)$-coupling, and an axion as a massive scalar field with $ϕ^2$-coupling, with the helical electromagnetic field. The $α$-dynamo term appears naturally from the helical coupling in the MHD formulation. In the presence of the electromagnetic coupling, however, the Schrödinger and hydrodynamic formulations of the coherently oscillating axion are {\it not} available for the conventional $ϕ$ coupling; instead, …
We discuss the $(2+1)$-dimensional parity violating charged fluid on a finite cutoff surface $Σ_c$, dual to the nondynamical and dynamical Chern-Simons (CS) modified gravities. Using nonrelativistic long-wavelength expansion method, the field equations are solved up to $\mathcal{O}(ε^2)$ in the nondynamical model. It is shown that there exists nonvortical dual fluid with shear viscosity $η$ and Hall viscosity $η_A$ on the cutoff surface $Σ_c$. The ratio of shear viscosity over entropy density $η/s$ of the fluid takes the universal value $1/{4π}$, while the ratio of Hall viscosity over entropy …
Cosmography is an ideal tool to investigate the cosmic expansion history of the Universe in a model-independent way. The equations of motion in modified theories of gravity are usually very complicated; cosmography may select practical models without imposing arbitrary choices a priori. We use the model-independent way to derive $f(z)$ and its derivatives up to fourth order in terms of measurable cosmographic parameters. We then fit those functions into the luminosity distance directly. We perform the MCMC analysis by considering three different sets of cosmographic functions. Using the larges…
It is shown that the Callan-Giddings-Harvey-Strominger theory on the cylinder can be consistently quantized (using Dirac's approach) without imposing any constraints on the sign of the gravitational coupling constant or the sign (or value) of the cosmological constant. The quantum constraints in terms of the original geometrical variables are also derived.
Inspired by the general relation between the boundary global symmetry and the bulk gauge symmetry in AdS/CFT, we reformulate the $d+1$ dimensional AdS gravity theory as a $SO(2,d)$ gauge theory. In this formalism, the pull back of the bulk equation of motion onto a co-dimension one hypersurface $Σ$ can be naturally related to the $SO(2,d)$ conservation law under a local energy scale in the dual CFT. The consistency of CFT requires that the $SO(2,d)$ covariant anomaly vanishes at arbitrary scale. After imposing a covariant area law as the renormalization condition, the vanishing of $SO(2,d)$ an…
We construct a two-dimensional action principle invariant under a spin-three extension of BMS$_3$ group. Such a theory is obtained through a reduction of Chern-Simons action with a boundary. This procedure is carried out by imposing a set of boundary conditions obtained from asymptotically flat spacetimes in three dimensions. When implementing part of this set, we obtain an analog of chiral WZW model based on a contraction of $sl(3,\mathbb{R}) \times sl(3,\mathbb{R})$. The remaining part of the boundary conditions imposes constraints on the conserved currents of the model, which allows to furt…
Nonsingular bouncing cosmologies are realized in limiting curvature mimetic gravity by means of a multi-valued potential $f(\Boxϕ)$ depending on the d'Alembertian of a scalar field $ϕ$. We determine the functional form of such a potential so as to exactly reproduce the cosmological background dynamics obtained in the group field theory approach to quantum gravity. The original proposal made by Chamseddine and Mukhanov [JCAP 1703, no. 03, 009 (2017)], which was shown to lead to a background dynamics reproducing the effective dynamics of loop quantum cosmology, is here recovered as a particular …
We establish the gravity/fluid correspondence in the nonminimally coupled scalar-tensor theory of gravity. Imposing Petrov-like boundary conditions over the gravitational field, we find that, for a certain class of background metrics, the boundary fluctuations obey the standard Navier-Stokes equation for an incompressible fluid without any external force term in the leading order approximation under the near horizon expansion. That is to say, the scalar field fluctuations does not contribute in the leading order approximation regardless of what kind of boundary condition we impose on it.
Using a Lax pair based on twisted affine $sl(2,R)$ Kac-Moody and Virasoro algebras, we deduce a r-matrix formulation of two dimensional reduced vacuum Einstein's equations. Whereas the fundamental Poisson brackets are non-ultralocal, they lead to pure c-number modified Yang-Baxter equations. We also describe how to obtain classical observables by imposing reasonable boundaries conditions.
We consider the background-free quantum gravity based on conformal gravity with the Riegert-Wess-Zumino action, which is formulated in terms of a conformal field theory. Employing the $R \times S^3$ background in practice, we construct the nilpotent BRST operator imposing diffeomorphism invariance. Physical fields and states are analyzed, which are given only by real primary scalars with a definite conformal weight. With attention to the presence of background charges, various significant properties, such as the state-operator correspondence and the norm structure, are clarified with some exam…
In this work, we show that, in the presence of non-minimal coupling to gravity, it is possible to generate sizeable tensor modes in single-field models without transplanckian field values. These transplanckian field values apparently needed in Einstein gravity to accommodate the experimental results may only be due to our insistence of imposing a minimal coupling of the inflaton field to gravity in a model with non-minimal couplings. We present three simple single-field models that prove that it is possible accommodate a large tensor-to-scalar ratio without requiring transplanckian field value…
We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann-Roberston-Walker universe in both Randall-Sundrum II gravity and Dvali-Gabadadze-Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity.
Recently, evidence has been collected that a class of gravitational theories with certain non-local operators is renormalizable. We consider one such model which, at the linear perturbative level, reproduces the effective non-local action for the light modes of bosonic closed string-field theory. Using the property of asymptotic freedom in the ultraviolet and fixing the classical behavior of the scale factor at late times, an algorithm is proposed to find general homogeneous cosmological solutions valid both at early and late times. Imposing a power-law classical limit, these solutions (includ…
We study the effective field theory that describes the low-energy physics of self-gravitating media. The field content consists of four derivatively coupled scalar fields that can be identified with the internal comoving coordinates of the medium. Imposing SO(3) internal spatial invariance, the theory describes supersolids. Stronger symmetry requirements lead to superfluids, solids and perfect fluids, at lowest order in derivatives. In the unitary gauge, massive gravity emerges, being thus the result of a continuous medium propagating in spacetime. Our results can be used to explore systematic…
We investigate a class of theories involving a symmetric two-tensor field in Minkowski spacetime with a potential triggering spontaneous violation of Lorentz symmetry. The resulting massless Nambu-Goldstone modes are shown to obey the linearized Einstein equations in a fixed gauge. Imposing self-consistent coupling to the energy-momentum tensor constrains the potential for the Lorentz violation. The nonlinear theory generated from the self-consistent bootstrap is an alternative theory of gravity, containing kinetic and potential terms along with a matter coupling. At energies small compared to…
In this paper we consider the issue of massive gravity from a pure field theoretical point of view, as the massive deformation of the gauge theory for a symmetric rank-2 tensor field. We look for the most general massive theory with well defined propagators, imposing the absence of unphysical poles (ghosts). We find several possibilities, depending on the choice of the gauge fixing term. {Amongst these, two solutions with good massless limit are found.} The request of the absence of ghosts, alone, does not isolate the Fierz-Pauli case: several examples of massive theories, which may include or…
We propose an action to describe high spin topologically massive gravity with a negative cosmological constant. With the frame-like fields and spin connections being combined into two gauge fields, the action includes two gauge field Chern-Simons actions with different levels, and also a linear term proportional to the difference of the gauge field strengths. Such linear term play the role of imposing the torsion free conditions for high spin fields. We discuss the gauge symmetry of this action and study the fluctuations around the AdS$_3$ vacuum. We show how to relate the the fluctuations of …
We begin the exploration of holographic duals to theories with generalised global (higher-form) symmetries. In particular, we focus on the case of magnetohydrodynamics (MHD) in strongly coupled plasmas by constructing and analysing a holographic dual to a recent, generalised global symmetry-based formulation of dissipative MHD. The simplest holographic dual to the effective theory of MHD that was proposed as a description of plasmas with any equation of state and transport coefficients contains dynamical graviton and two-form gauge field fluctuations in a magnetised black brane background. The…
We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate the functional form of the field renormalization factor by imposing a minimum resolvable distance scale under an infinitesimal Weyl transformation. The derived transformation is applied to two key problems in quantum gravity, its non-conformal scaling, and non-renormalizability.
