Unified formalism for Palatini and unimodular gravity using frame bundle canonical forms.
problem Unified formalism for Palatini and unimodular gravity.
method Employing a relationship between Griffiths variational problem and Lepage-equivalent problem, using canonical forms on the first jet of frame bundle.
result Unified formalism for Palatini and unimodular gravity formulated in a geometrical fashion.
Unified framework for gravity on manifolds with corners.
problem Unified description of gravity on manifolds with corners.
method Derivation of corner Poisson structure, reduction procedure, equivalent affine Poisson description.
result Unified framework for bulk, boundary, and corner structures of Palatini-Cartan gravity.
Unified framework for gravity on manifolds with corners derived.
problem Unified description of gravity on manifolds with corners.
method Derivation of corner Poisson structure and reduction procedure.
result Unified framework for bulk, boundary, and corner structures of Palatini-Cartan gravity.
The study finds geometric obstructions for Einstein-Hilbert-Palatini theories.
problem Geometric obstructions for Einstein-Hilbert-Palatini theories.
method Generalization of Einstein-Hilbert-Palatini functional over n-manifolds, analysis of algebraic conditions for non-null functionals.
result Geometric obstructions for Einstein manifolds in various geometries.
The study reveals non-trivial torsion in certain gravity theories with Ricci-dependent Lagrangians.
problem Exploring the appearance of non-trivial torsion in gravity theories with Ricci-dependent Lagrangians.
method Investigates theories with Lagrangians of the form L(L(R_{μν})), analyzing the equations of motion and the role of torsion.
result Theories with Ricci-dependent Lagrangians admit non-zero torsion even in simple space-time dimensions, suggesting its importance.
Finsler gravity vacuum equation reduces to Ricci vanishing under specific conditions.
problem Solving Einstein vacuum equations in Finsler gravity
method Identifying conditions for vacuum equation reduction
result Scalar Finsler gravity vacuum equation reduces to Ricci vanishing
Develops Palatini formalism in generalized geometry for string theory.
problem Formulating Palatini variation in generalized geometry.
method Palatini formalism within generalized Riemannian geometry of Courant algebroids.
result Natural emergence of generalized Levi-Civita connection and string effective actions.
Develops Palatini formalism for pseudo-Finsler metrics, recovering classical results.
problem Developing a formalism for pseudo-Finsler metrics of any signature.
method Substituting scalar curvature with Finslerian Ricci scalar in Einstein-Hilbert-Palatini functional.
result Recovery of classical results in Lorentzian signature with vanishing mean Landsberg tensor.
Geometric obstructions prevent gravity in high dimensions.
problem Obstacles to realizing gravity in various geometries.
method Analyzing the tetradic Einstein-Hilbert-Palatini action in different geometric settings.
result Gravity is only meaningful in Lorentzian geometry for dimensions n≥4. Proposes a new variational principle for Einstein gravity.
problem Formulating Einstein gravity as a gauge theory for the conformal group.
method First order formulation of conformal tractor geometry, variational principle based on abstract principal bundle.
result Provides first order field equations without requiring supplementary constraints.
Contravariant gravity on Poisson manifolds is linked to Einstein gravity.
problem Exploring the relationship between Poisson gravity and Einstein gravity.
method Investigating the compatibility of Poisson and Riemann structures to define a unique connection and derive the contravariant gravity theory.
result The contravariant gravity theory can be described as an equivalent system of Einstein gravity coupled to matter.
Introduces a new relation between BF theory and gravity.
problem Formulating gauge theories based on 2-connections.
method Categorical generalization of BF theory coupled to gravity.
result Alternative relation between BFCG and gravity.
Study General Relativity using field theories and Poisson brackets.
problem Defining a Poisson bracket structure on solution spaces of field theories.
method Applying Poisson bracket structure to first order Hamiltonian field theories, focusing on General Relativity as a gauge theory.
result Established a Poisson bracket structure for General Relativity.
Proposes new conformal parametrizations for modified Einstein gravity.
problem Initial data in modified Einstein gravity theories.
method Proposes conformal parametrizations that lead to conformally covariant systems.
result Some conformal parametrizations give rise to conformally covariant systems.
PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.
problem Characterizing and solving Finsler gravity equations.
method Analysis of Berwald spaces, (α,β)-metrics, and exact solutions to Finsler gravity equations. result Exact vacuum solutions in Finsler gravity.
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…
A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the defo…
We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization …
We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conf…
A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gr…
De Donder form for gravity is globally defined.
problem Defining a globally defined De Donder form for second order gravity.
method Using Ostrogradski's Legendre transformation and diffeomorphism invariance.
result De Donder form is globally defined by local coordinate descriptions.
We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.
problem Constructing and understanding conformal gravity actions in different dimensions.
method Streamlined construction of 6D action, proving existence of 8D action, relating to Q-curvature.
result A unique 8D conformal gravity action exists with Einstein metrics as solutions.
It is shown that the first order (Palatini) variational principle for a generic nonlinear metric-affine Lagrangian depending on the (symmetrized) Ricci square invariant leads to an almost-product Einstein structure or to an almost-complex anti-Hermitian Einstein structure on a manifold. It is proved that a real anti-He…
Analyzing static solutions in Finsler gravity, extending known results.
problem Extending the analyticity of static vacuum solutions to Finsler spacetimes.
method Examining Finsler spacetimes with properties similar to static Lorentzian spacetimes.
result Finsler spacetimes with vanishing Ricci scalar are analytic.
Identifies null hypersurfaces with constant surface gravity.
problem Understanding null hypersurfaces in spacetimes.
method Analyzes spacetimes satisfying null convergence condition.
result Null hypersurfaces admit null sections with constant surface gravity.
Explains non-lorentzian theories and their dynamics.
problem Understanding non-lorentzian kinematics and dynamics.
method Review of kinematical spacetimes, construction of particle dynamics actions, discussion of gravity theories and field theories.
result Introduction and analysis of non-lorentzian gravity and field theories.
HR in 8D encodes unique conformal gravity with negative curvature.
problem Holographic Renormalisation in 8D Einstein Gravity.
method Relating HR to Topological Regularisation and adding the Euler term.
result The unique conformal gravity theory reproduces the polynomial and cancels divergent terms.
Special issue honors Stanley Deser, focusing on advanced physics topics.
problem None explicitly stated in the abstract.
method Collection of articles in memory of Stanley Deser.
result No specific key result mentioned in the abstract.
Projective connection explains gravity dynamics in 2D.
problem Understanding dynamics in 2D gravity with projective connection.
method Using projective connection over affine connections, defining action with curvature invariants.
result Projective connection naturally describes metric interaction in 2D gravity.
Study Codazzi tensors in space-times, linking to Cotton gravity.
problem Understanding Codazzi tensors and their role in space-times.
method Analyzing geometric properties and proving conditions for Codazzi tensors.
result Codazzi tensors restrict space-times, influencing energy-momentum tensors in Cotton gravity.
Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex SL(2,C) Chern-Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity.
We developed a perturbation model for affine gravity theories.
problem Cosmological perturbations in theories without metric.
method Segregated perturbations into symmetric and antisymmetric components, decomposing into irreducible elements.
result Fully addressed gauge freedom in affine gravity theories.
The study characterizes spacetimes with specific solitons in f(R)-gravity.
problem Characterizing spacetimes with specific solitons in f(R)-gravity. method Analyzing η-Ricci solitons, gradient η-Ricci solitons, gradient Einstein Solitons, and gradient m-quasi Einstein solitons in perfect fluid spacetimes obeying f(R)-gravity. result Established conditions for the behavior of η-Ricci solitons and derived significant theorems about dark matter. The (2k)-th Gauss-Bonnet curvature is a generalization to higher dimensions of the (2k)-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for k=1. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known a…
Shielding gravity fields using special potentials.
problem Gravitational shielding challenges.
method Third-order metric potentials for linearised gravity.
result Avoids solving singular equations in shielding.
The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.
problem Computing volumes for physical gravity models.
method Topological recursion and physical two-dimensional gravity models.
result Derivation of Virasoro constraints and cut-and-join equations for generalized Mirzakhani's recursions.
We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern-Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets …
CNN outperforms other methods in gravity inversion.
problem Estimating subsurface density from gravitational field data.
method CNN, VAEs, GANs, iterative solvers (GD, GMRES, LGMRES, ICG).
result CNN provides the most reliable reconstructions.
Study of Randers spacetimes and their Finsler gravity solutions.
problem Analyzing Finsler gravity field equations for Randers spacetimes.
method Examined Berwald-type Randers spacetimes and Finsler gravity field equations, showing equivalence to Einstein gravity.
result Found exact solutions for vacuum Finsler gravity are composed of pp-waves and 1-forms.
Theory for gravity coupled with fields on manifolds with null-boundary.
problem Formulating a theory for gravity coupled with scalar, SU(n), and spinor fields on manifolds with null-boundary.
method Symplectic reduction of boundary fields and constraints analysis.
result The set of constraints does not form a first class system for the three couplings.
New models predict mobility flows as well as complex machine learning but are simpler and interpretable.
problem Incomplete understanding and modeling of human mobility flows.
method Developed simple machine-learned, closed-form models of mobility.
result These models predict mobility flows more accurately than gravity or complex machine/deep learning models.
We show that holographic renormalization of relativistic gravity in asymptotically Lifshitz spacetimes naturally reproduces the structure of gravity with anisotropic scaling: The holographic counterterms induced near anisotropic infinity take the form of the action for gravity at a Lifshitz point, with the appropriate …
Kepler metrics linked to gravity and string theory.
problem Kepler metrics and their geometric properties.
method Sasakian and Hessian geometry approaches.
result Established connection between gravity and string theory.
Two Pin groups fit fermions in gravity.
problem Matching fermion behavior with gravity.
method Examined eight Pin groups; identified two compatible with gravity.
result Only two Pin groups fit fermions in gravity.
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical …
Study on the geometry of Cotton gravity field equations.
problem Analyzing the geometry of Cotton gravity field equations.
method Describes the local structure of spatial Riemannian factors and provides sufficient conditions for reduction to φ-static perfect fluid space-time. result Provides sufficient conditions for a C-φ-PF to reduce to a φ-SPFST. A first-order formulation of gravity is developed in which the fundamental fields consist of an SL(2,C) connection and two spinor-valued 1-forms. It is shown that the first term of an expansion of the Einstein-Hilbert action leads to an action for these fields which consists of dynamic L2 inner products of their covari…
This study analyzes a non-orientable spacetime model in 1+1D quantum gravity.
problem Analyzing a non-orientable spacetime model in 1+1D quantum gravity.
method Formulated a Jackiw-Teitelboim gravity toy model on the Möbius band, computed Stiefel-Whitney classes, and analyzed the Dirac operator.
result Half-integer momentum quantization, spectral symmetry, vanishing mod-2 index, and η_D(0) = 0 follow.