In this paper we evaluate the modified celestial amplitude for gravitons and gluons, as defined in arXiv:1801.10171[hep-th]. We find that the modified (tree) amplitude is finite for gravitons in Einstein gravity. The modified amplitude behaves like correlation function of operators inserted at various points of null-infinity in the Minkowski space-time. Therefore, unlike the standard celestial amplitudes, these are three dimensional objects. We also show that this amplitude admits conformal soft factorization recently studied in the literature.
Asymptotic symmetry plays an important role in determining physical observables of a theory. Recently, in the context of four dimensional asymptotically flat pure gravity and $\mathcal{N}=1$ supergravity, it has been proposed that OPEs of appropriate celestial amplitudes can be used to find their asymptotic symmetries. In this paper we find the asymptotic symmetry algebras of four dimensional Einstein-Yang-Mills and Einstein-Maxwell theories using this alternative approach, namely using the OPEs of their respective celestial amplitudes. The algebra obtained here are in agreement with the known…
The operator product expansion (OPE) on the celestial sphere of conformal primary gluons and gravitons is studied. Asymptotic symmetries imply recursion relations between products of operators whose conformal weights differ by half-integers. It is shown, for tree-level Einstein-Yang-Mills theory, that these recursion relations are so constraining that they completely fix the leading celestial OPE coefficients in terms of the Euler beta function. The poles in the beta functions are associated with conformally soft currents.
In this paper we study the BMS symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The celestial OPE is obtained by Mellin transforming the scattering amplitude in the (holomorphic) collinear limit. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and …
We study the effect of loop corrections to conformal correlators on the celestial sphere at null infinity. We first analyze finite one-loop celestial amplitudes in pure Yang-Mills theory and Einstein gravity. We then turn to our main focus: infrared divergent loop amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory. We compute the celestial one-loop amplitude in dimensional regularization and show that it can be recast as an operator acting on the celestial tree-level amplitude. This extends to any loop order and the re-summation of all planar loops enables us to write down an express…
Gluon amplitudes at most-subleading order in the $1/N$ expansion share a remarkable simplicity with graviton amplitudes: collinear divergences are completely absent in both and, as a consequence, their full IR behavior arises from soft gluon/graviton exchange among the external states. In this paper we study the effect of all-loop IR divergences of celestial most-subleading color gluon amplitudes and their similarities with the celestial gravity case. In particular, a simple celestial exponentiation formula for the dipole part can be written. We also analize how this exponentiation is modified…
Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mi…
We have studied a modified Yang-Mills-Higgs system coupled to Einstein gravity. The modification of the Einstein-Hilbert action involves a direct coupling of the Higgs field to the scalar curvature. In this modified system we are able to write a Bogomol'nyi type condition in curved space and demonstrate that the positive static energy functional is bounded from below. We then investigate non-Abelian sperically symmetric static solutions in a similar fashion to the `t Hooft-Polyakov monopole. After reviewing previously studied monopole solutions of this type, we extend the formalism to included…
In this work, we investigate the consequences of the spontaneous breaking of Lorentz symmetry, triggered by the bumblebee vector field, on the usual Einstein-Hilbert theory. Specifically, we consider the Einstein-Hilbert action modified by the bumblebee dynamic field, and evaluate the graviton propagator using an extended basis of Barnes-Rivers tensor projectors, involving the Lorentz-violating vector. Once the propagator is carried out, we proceed with discussing the consistency of the model, writing the dispersion relations, and analyzing causality and unitarity. We verify that this model po…
Metric Source Completions and Integrability in Celestial Gravity
Zhongtai Securities Institute for Financial Studies, Shandong University（山东大学中泰金融研究院）；Department of Physics, Southern Methodist University（南方卫理公会大学物理系）；School of Statistics, Dongbei University of Finance and Economics（东北财经大学统计学院）
In this paper we extract from a large-$r$ expansion of the vacuum Einstein's equations a dynamical system governing the time evolution of an infinity of higher-spin charges. Upon integration, we evaluate the canonical action of these charges on the gravity phase space. The truncation of this action to quadratic order and the associated charge conservation laws yield an infinite tower of soft theorems. We show that the canonical action of the higher spin charges on gravitons in a conformal primary basis, as well as conformally soft gravitons reproduces the higher spin celestial symmetries deriv…
In this study, the effects of the generalized uncertainty principle on the theory of gravity are analyzed. Inspired by Verlinde's entropic gravity approach and using the modified Unruh temperature, the generalized Einstein field equations with cosmological constant are obtained and corresponding conservation law is investigated. The resulting conservation law of energy-momentum tensor dictates that the generalized Einstein field equations are valid in a very limited range of accelerations. Moreover, the modified Newton's law of gravity and the modified Poisson equation are derived. In a certai…
A modified gravitational action is considered which involves the quantity $F_{μν}=\partial_μΓ_ν-\partial_νΓ_μ$, where $Γ_μ=Γ^α_{μα}$. Since $Γ_μ$ transforms like a U(1) gauge field under coordinate transformations terms such as $F^{μν}F_{μν}$ are invariant under coordinate transformations. If such a term is added to the usual gravitational action the resulting field equations, obtained from a Palatini variation, are the Einstein-Proca equations. The vector field can be coupled to point charges or to a complex scalar density of weight $ie$, where $e$ is the charge of the field. If this scalar d…
In a homogenous and isotropic cosmology, we introduce general exact solutions for some modified gravity models. In particular, we introduce exact solutions for power-law $f(R)$ gravity and Brans-Dicke theory in Einstein and Jordan conformal frames. In the Brans-Dicke case, the solutions are presented for both single and double exponential potentials in Einstein frame which correspond to power-law potentials in Jordan frame. Our analysis for extracting general exact solutions can also be generalized to those scalar-tensor theories in which the scalar field has an exponential coupling to Ricci s…
We propose a modification of Einstein-Cartan gravity equations. The modified cosmology departs from the standard model of cosmology for small Hubble parameter. A characteristic Hubble scale h0, which is intrinsically related to cosmological constant, marks the boundary between the validity domains of the standard model of cosmology and modified cosmology. For large Hubble parameter, the standard model of cosmology is restored. In the opposite limit of small Hubble parameter, which is the case for present epoch, Lorentz-violating effects would manifest themselves. One of the implications is tha…
After the study of non-inertial frames in special relativity with emphasis on the problem of clock synchronization (i.e. of how to define 3-space), an overview is given of Einstein canonical gravity in the York canonical basis and of its Hamiltonian Post-Minkowskian (PM) linearization in 3-orthogonal gauges. It is shown that the York time (the trace of the extrinsic curvature of 3-spaces) is the inertial gauge variable describing the general relativistic remnant of the clock synchronization gauge freedom. The dark matter implied by the rotation curves of galaxies can be explained with a choice…
The neutrino behavior in the Einstein$\text{-}$Hilbert$\text{-}$Bumblebee gravity around global monopole field
College Pharmacy, Guizhou University of Traditional Chinese Medicine（贵州中医药大学药学院）；School of Science, Guiyang University（贵阳学院理学院）；College of Physics, Guizhou University（贵州大学物理学院）
If one assumes a particular form of non-minimal coupling, called the conformal coupling, of a perfect fluid with gravity in the fluid-gravity Lagrangian then one gets modified Einstein field equation. In the modified Einstein equation, the effect of the non-minimal coupling does not vanish if one works with spacetimes for which the Ricci scalar vanishes. In the present work we use the Schwarzschild metric in the modified Einstein equation, in presence of non-minimal coupling with a fluid, and find out the energy-density and pressure of the fluid. In the present case the perfect fluid is part o…
We investigate the modification to Einstein's vacuum field equations which is imposed by string theory when the dilaton field is ignored. Including the cosmological constant in all calculations, we prove that such a theory of gravity admits no static isotropic solution. We then show that any isotropic solution of the equations in question must necessarily be static, therefore proving that no isotropic solution exists for this stringy modification to gravity.
The modified O'Raifeartaigh model from the context of the generalized seesaw mechanism of neutrino mass is investigated. In our evaluation of effective potentials of the theory, both the component field and the superspace formalisms to approach the problem are presented. In the component field formalism, we take into account the Bose-Einstein condensates in the scalar sector by the method of many-boson theory, i.e. we consider both the condensates and the Hartree-Fock-Bogoliubov-type self-energies of quantum fluctuations. The diagonalization of the mass matrix of the fermion sector gives the s…
Considering the general quantum corrections to the area law of black hole entropy and adopting the viewpoint that gravity interprets as an entropic force, we derive the modified forms of MOND theory of gravitation and Einstein field equations. As two special cases we study the logarithmic and power-law corrections to entropy and find the explicit form of the obtained modified equations.
Certain off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $ f(R,T,R_{μν}T^{μν})$ type. We prove this statement by constructing exact and approximate solutions which encode certain models of covariant Ho\v rava type gravity with dynamical Lorentz symmetry breaking. Off-diagonal generalizations of de Sitter and nonolonomic $Λ$CDM universes are constructed which are generated through nonlinear gravitational polarization of fundamental physical constants and which model interactions with non-constant exotic fluids …
We theoretically propose an experimentally viable scheme to use an impurity atom in a dipolar Bose-Einstein condensate (BEC), in order to probe analogue low-energy Lorentz violation from the modified dispersion at high energies as suggested by quantum theories of gravity. We show that the density fluctuations in the dipolar BEC possess a Lorentz-violating Bogoliubov spectrum $ω_\mathbf{k}=c_0|\mathbf{k}|f(c_0|\mathbf{k}|/M_\star)$, with recovery of approximate Lorentz invariance (LI) at energy scales much below $M_\star$. When $f$ is adjusted to dip below unity somewhere, the impurity, analogo…
[Remark: Much more natural and important models are studied in arXiv:1405.2083. Furthermore, the physical picture given there is much more complete.] The quantum N-portrait -- black holes pictured as Bose-Einstein condensates -- is studied for a special class of models in arbitrary dimensions. In the presence of extra dimensions, the depletion rate is shown to be significantly enhanced in these models as compared to standard semi-classical results. Consequences for large as well as micro condensates are discussed. Speculations are made on a possible connection of higher-dimensional graviton co…
We formulate the nonminimal aether-modified gravity whose action represents itself as a sum of the usual Einstein-Hilbert action and the CPT-even Lorentz-breaking aether-like gravity term proposed by Carroll. For this theory, we show that the Gödel metric solves the modified Einstein equations under a corresponding modification of the matter, while, for the small Lorentz-breaking corrections, the matter turns out to be usual. On the other side, if the matter is suggested to be the same as in the usual general relativity, the Gödel metric is modified by additive aether terms.
We find general parameterizations for generic off-diagonal spacetime metrics and matter sources in general relativity (GR) and modified gravity theories when the field equations decouple with respect to certain types of nonholonomic frames of reference. This allows us to construct various classes of exact solutions when the coefficients of the fundamental geometric/ physical objects depend on all spacetime coordinates via corresponding classes of generating and integration functions and/or constants. Such (modified) spacetimes display Killing and non-Killing symmetries, describe nonlinear vacu…
We investigate the existence of analytic solutions for the field equations in the Einstein-æther theory for a static spherically symmetric spacetime and provide a detailed dynamical system analysis of the field equations. In particular, we investigate if the gravitational field equations in the Einstein-æther model in the static spherically symmetric spacetime possesses the Painlevè property, so that an analytic explicit integration can be performed. We find that analytic solutions can be presented in terms of Laurent expansion only when the matter source consists of a perfect fluid with linea…
We consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form $P(R) F(\Box) Q(R)$. For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein-Hilbert modified action and basics of gravity perturbations.
The Gross-Pitaevskii (GP) or nonlinear Schrödinger equation relevant to ultracold atomic gaseous Bose-Einstein condensates possess a modified Schrödinger symmetry in two spatial dimensions, in the presence of a harmonic trapping potential, an (artificial) constant magnetic field (or rotation) and an electric field of a quadratic electrostatic potential. We find that a variance and a center of a trapped gas with or without a vorticity can be regarded as massive Nambu-Goldstone (NG) modes associated with spontaneous breaking of the modified Schrödinger symmetry. We show that the Noether theorem …
The Anholonomic Frame and Connection Deformation Method for constructing off-diagonal solutions in (modified) Einstein gravity and nonassociative geometric flows and Finsler-Lagrange-Hamilton theories
A modified theory of gravity with the function $F(R) = R\exp(αR)$ instead of Ricci scalar $R$ in the Einstein$-$Hilbert action is considered and analyzed. The action of the model is converted into Einstein$-$Hilbert action at small value of the parameter $α$. From local tests we obtain a bound on the parameter $α\leq 10^{-6}$ cm$^2$. The Jordan and Einstein frames are investigated and the potential of the scalar field in Einstein's frame is found. The mass of a scalar degree of freedom as a function of curvature is obtained. The static solutions of the model are found corresponding to the Schw…
We perform the perturbation analysis of the Chern-Simons modified gravity around the AdS$_4$ spacetimes (its curvature radius $\ell$) to obtain the critical gravity. In general, we could not obtain an explicit form of perturbed Einstein equation which shows a massive graviton propagation clearly, but for the Kerr-Schild perturbation and Chern-Simons coupling $θ=kx/y$, we find the AdS wave as a single massive solution to the perturbed Einstein equation. Its mass squared is given by $M^2=[-9+(2\ell^2/k-1)^2]/4\ell^2$. At the critical point of $M^2=0(k=\ell^2/2)$, the solution takes the log-form …
