Stochastic Gravity: Theory and Applications

Abstract

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.

75 pages, no figures, submitted to Living Reviews in Relativity

References in corpus (22)

• Analogue Gravity
• Quantum Contributions to Cosmological Correlations
• Gravitational Vacuum Condensate Stars
• Information Loss in Black Holes
• Photons and electrons as emergent phenomena
• Hawking Radiation from Acoustic Black Holes, Short Distance and Back-Reaction Effects
• Selected topics in Planck-scale physics
• Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator
• Stochastic Gravity: A Primer with Applications
• Probing spacetime foam with extragalactic sources
• Induced quantum metric fluctuations and the validity of semiclassical gravity
• Information locking in black holes
• The Effects of Stress Tensor Fluctuations upon Focusing
• Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space
• Cosmological perturbations from stochastic gravity
• Beyond the semi-classical description of black hole evaporation
• On the quantum width of a black hole horizon
• Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric
• Black Hole Fluctuations and Backreaction in Stochastic Gravity
• Effects of Quantum Stress Tensor Fluctuations with Compact Extra Dimensions
• Path Integral Over Black Hole Fluctuations
• Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Conformally-Optical Metrics: Schwarzschild Black Holes

Cited by in corpus (106)

• Analogue Gravity
• Relativistic Brownian Motion
• Emergent/Quantum Gravity: Macro/Micro Structures of Spacetime
• Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator
• Radiation reaction and gravitational waves in the effective field theory approach
• Holographic Foam, Dark Energy and Infinite Statistics
• Problems with the Newton-Schrödinger Equations
• Short distance and initial state effects in inflation: stress tensor and decoherence
• One-loop Corrections to Scalar and Tensor Perturbations during Inflation in Stochastic Gravity
• Can Spacetime be a Condensate?
• Probing the f(R) formalism through gravitational wave polarizations
• One-loop gravitational wave spectrum in de Sitter spacetime
• Probability distributions of smeared quantum stress tensors
• Probability distributions for quantum stress tensors in four dimensions
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Conservative entropic forces
• Generating dynamical black hole solutions
• Testing the foundations of quantum physics in space Interferometric and non-interferometric tests with Large Particles
• On the initial conditions and solutions of the semiclassical Einstein equations in a cosmological scenario
• Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
• Cosmological perturbations from stochastic gravity
• Radiating black hole solutions in arbitrary dimensions
• Stability of de Sitter spacetime under isotropic perturbations in semiclassical gravity
• Metric fluctuations and decoherence
• General relativistic statistical mechanics
• Stochastic Inflation Revisited: Non-Slow Roll Statistics and DBI Inflation
• From spacetime foam to holographic foam cosmology
• Backreaction from non-conformal quantum fields in de Sitter spacetime
• Probability Distributions for Quantum Stress Tensors Measured in a Finite Time Interval
• Decoherence and entropy of primordial fluctuations II. The entropy budget
• Analog model for quantum gravity effects: phonons in random fluids
• Enhanced Black Hole Horizon Fluctuations
• Quantum-Gravity Decoherence Effects in Neutrino Oscillations: Expected Constraints from CNGS and J-PARC
• Methods of approaching decoherence in the flavour sector due to space-time foam
• Self-Force with a Stochastic Component from Radiation Reaction of a Scalar Charge Moving in Curved Spacetime
• Fokker-Planck type equations for a simple gas and for a semi-relativistic Brownian motion from a relativistic kinetic theory
• Spectral Line Broadening and Angular Blurring due to Spacetime Geometry Fluctuations
• Possible Constraints on the Duration of Inflationary Expansion from Quantum Stress Tensor Fluctuations
• Metric fluctuations and the Weak Equivalence Principle
• Stochastic modification of the Schrodinger-Newton equation
• Cosmological Density Fluctuations in Stochastic Gravity -- Formalism and Linear Analysis --
• Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work
• Quantum Stress Tensor Fluctuations of a Conformal Field and Inflationary Cosmology
• Exterior and interior metrics with quadrupole moment
• Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid
• Vacuum fluctuation, micro-cyclic "universes" and the cosmological constant problem
• Decoherence in Quantum Gravity: Issues and Critiques
• Gravitational decoherence: a general non relativistic model
• Thermal Radiation from a Fluctuating Event Horizon
• Black hole fluctuations and dynamics from back-reaction of Hawking radiation: Current work and further studies based on stochastic gravity
• Reformulation of the Cosmological Constant Problem
• Fluctuation-Dissipation and Correlation-Propagation Relations from the Nonequilibrium Dynamics of Detector-Quantum Field Systems
• Stochastic Emergent Quantum Gravity
• Semi-analytical approach for the Vaidya metric in double-null coordinates
• Past-directed scalar field gradients and scalar-tensor thermodynamics
• On the scaling rules for the anomaly-induced effective action of metric and electromagnetic field
• Novel Effect Induced by Spacetime Curvature in Quantum Hydrodynamics
• Real time approach to tunneling in open quantum systems: decoherence and anomalous diffusion
• Newtonian Semiclassical Gravity in the Ghirardi-Rimini-Weber Theory with Matter Density Ontology
• Scalar field dark matter in hybrid approach
• Vacuum Quantum Stress Tensor Fluctuations: A Diagonalization Approach
• Stochastic Einstein equations with fluctuating volume
• On the weight of entanglement
• Gravity, Quantum Fields and Quantum Information: Problems with classical channel and stochastic theories
• Influence of quantum matter fluctuations on geodesic deviation
• Quadratic Isocurvature Cross-Correlation, Ward Identity, and Dark Matter
• Enhanced Geometry Fluctuations in Minkowski and Black Hole Spacetimes
• Radiating black holes in Einstein-Yang-Mills theory and cosmic censorship
• Nonstationary regime for quasinormal modes of the charged Vaidya metric
• Kinetic theory and classical limit for real scalar quantum field in curved space-time
• Stress energy correlator in de Sitter space-time : its conformal masking or growth in connected Friedmann universes
• N-dimensional Vaidya metric with cosmological constant in double-null coordinates
• About Starobinsky inflation
• Cosmological bounds on TeV-scale physics and beyond
• Large Zero Point Density Fluctuations in Fluids
• Classical Einstein-Langevin Equation and Proposed Applications
• Appearing Out of Nowhere: The Emergence of Spacetime in Quantum Gravity
• Fully renormalized stress tensor correlator in flat space
• Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime
• The Semiclassical Einstein Equation on Cosmological Spacetimes
• Bianchi $VI{I}_A$ solutions of quadratic gravity
• Stochastic Gravity: Beyond Semiclassical Gravity
• Fluctuations of spacetime and holographic noise in atomic interferometry
• Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime-II
• Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity
• Probing Gravitational Cat States in Canonical Quantum Theory vs Objective Collapse Theories
• Orbits in a stochastic Schwarzschild geometry
• Bianchi I solutions of effective quadratic gravity
• Diffusion and Self-Organized Criticality in Ricci Flow Evolution of Einstein and Finsler Spaces
• Stochastic Mechanics Without Ad Hoc Quantization: Theory And Applications To Semiclassical Gravity
• Homogeneous Solutions of Quadratic Gravity
• Exploration of Possible Quantum Gravity Effects with Neutrinos I: Decoherence in Neutrino Oscillations Experiments
• Functional formulation of quantum theory of a scalar field in a metric with Lorentzian and Euclidean signatures
• Thermodynamic structure of field equations near apparent horizon for radiating black holes
• Are accelerated detectors sensitive to Planck scale changes?
• Quantum Stress Tensor Fluctuation Effects in Inflationary Cosmology
• Curvature fluctuations on asymptotically de Sitter spacetimes via the semiclassical Einstein's equations
• Noise Kernel for Reissner Nordstrom Metric: Results at Cauchy Horizon
• Quantum Noise and Fluctuations in Gravitation and Cosmology
• Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models
• Probing black hole microstructure with the kinetic turnover of phase transition
• Double null formulation of the general Vaidya metric
• Random walkers on a deformable medium
• Unified meta-theory of information, consciousness, time and the classical-quantum universe
• Spacetime as a deformable solid
• Semiclassical Newtonian Field Theories Based On Stochastic Mechanics I