Quasi-Stationary Solutions in Gravity Theories with Modified Dispersion Relations and Finsler-Lagrange-Hamilton Geometry

Abstract

Modified gravity theories, MGTs, with modified (nonlinear) dispersion relations, MDRs, encode via indicator functionals possible modifications and effects of quantum gravity; in string/brane, noncommutative and/or nonassociative gravity theories etc. MDRs can be with global and/or local Lorentz invariance violations, LIVs, determined by quantum fluctuations, random, kinetic, statistical and/or thermodynamical processes etc. Such MGTs with MDRs and corresponding models of locally anisotropic spacetime and curved phase spaces can be geometrized in an axiomatic form for theories constructed on (co) tangent bundles with base spacetime Lorentz manifolds. In certain canonical nonholonomic variables, the geometric/physical objects are defined equivalently as in generalized Einstein-Finsler and/or Lagrange-Hamilton spaces. In such Finsler like MGTs, the coefficients of metrics and connections depend both on local Lorentz spacetime coordinates and, additionally, on (co) fiber velocity and/or momentum type variables. The main goal of this work is to elaborate on a nonholonomic diadic "shell by shell" formulation of MGTs with MDRs, with a conventional (2+2)+(2+2) splitting of total phase space dimensions, when the (dual) modified Einstein-Hamilton equations can be decoupled in general forms. We show how this geometric formalism allows us to construct various classes of exact and parametric solutions determined by generating and integration functions and effective sources depending, in principle, on all phase space coordinates. This work provides a self-consistent geometric and analytic method for constructing in our further partner papers different types of black hole solutions for theories with MDRs and LIVs and elaborating various applications in modern cosmology and astrophysics.

arXiv commentlatex 2e, 11pt, 60 pages with a table of contents (72 pages in the journal), v3 closed to the published version

References in corpus (22)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Data Tables for Lorentz and CPT Violation
• Resembling dark energy and modified gravity with Finsler-Randers cosmology
• Clifford and Riemann-Finsler Structures in Geometric Mechanics and Gravity
• Superstrings in Higher Order Extensions of Finsler Superspaces
• Locally Anisotropic Gravity and Strings
• Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces
• Critical Remarks on Finsler Modifications of Gravity and Cosmology by Zhe Chang and Xin Li
• Off-Diagonal Deformations of Kerr Black Holes in Einstein and Modified Massive Gravity and Higher Dimensions
• Quantum-Gravity Induced Lorentz Violation and Dynamical Mass Generation
• Modified Einstein and Finsler Like Theories on Tangent Lorentz Bundles
• On General Solutions for Field Equations in Einstein and Higher Dimension Gravity
• Black Holes with MDRs and Bekenstein-Hawking and Perelman Entropies for Finsler-Lagrange-Hamilton Spaces
• Geometric Flows and Perelman's Thermodynamics for Black Ellipsoids in $R^2$ and Einstein Gravity Theories
• Off-Diagonal Ekpyrotic Scenarios and Equivalence of Modified, Massive and/or Einstein Gravity
• Dark matter stability and one-loop neutrino mass generation based on Peccei-Quinn symmetry
• Space-Time Quasicrystal Structures and Inflationary and Late Time Evolution Dynamics in Accelerating Cosmology
• Heterotic Supergravity with Internal Almost-Kähler Spaces, Instantons for $SO(32)$, or $E_8\times E_8$, Gauge Groups, and Deformed Black Holes with Soliton, Quasiperiodic and/or Pattern-forming Structures
• Off-Diagonal Deformations of Kerr Metrics and Black Ellipsoids in Heterotic Supergravity
• Black Ring and Kerr Ellipsoid - Solitonic Configurations in Modified Finsler Gravity

Cited by in corpus (9)

• Backgrounds in gravitational effective field theory
• Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields
• Searches for beyond-Riemann gravity
• Broken Scale Invariance, Gravity Mass, and Dark Energy in Modified Einstein Gravity with Two Measure Finsler Like Variables
• Decoupling and integrability of nonassociative vacuum phase space gravitational equations with star and R-flux parametric deformations
• Classical and quantum geometric information flows and entanglement of relativistic mechanical systems
• Nonassociative black ellipsoids distorted by R-fluxes and four dimensional thin locally anisotropic accretion disks
• 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
• Constantin Carathéodory axiomatic approach and Grigory Perelman thermodynamics for geometric flows and cosmological solitonic solutions