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, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black hole

100 pages, no figures; an update of the 2003 review in Living Reviews in Relativity gr-qc/0307032 ; it includes new sections on the Validity of Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric Fluctuations of an Evaporating Black Hole

References in corpus (18)

• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox
• Hawking Radiation from Acoustic Black Holes, Short Distance and Back-Reaction Effects
• Bounds on length scales of classical spacetime foam models
• Analogue of cosmological particle creation in an ion trap
• Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation
• One-loop Corrections to Scalar and Tensor Perturbations during Inflation in Stochastic Gravity
• Scalar Field Equations from Quantum Gravity during Inflation
• Loop and spin foam quantum gravity: a brief guide for beginners
• (Non)perturbative gravity, nonlocality, and nice slices
• Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
• Cosmological perturbations from stochastic gravity
• Beyond the semi-classical description of black hole evaporation
• A lattice bosonic model as a quantum theory of gravity
• Cosmological Density Fluctuations in Stochastic Gravity -- Formalism and Linear Analysis --
• Quantum toy model for black-hole back-reaction
• New View on Quantum Gravity and the Origin of the Universe
• Effects of quantized fields on the spacetime geometries of static spherically symmetric black holes

Cited by in corpus (104)

• Gravitational Decoherence
• Linear dynamics of quantum-classical hybrids
• Problems with the Newton-Schrödinger Equations
• Loops in inflationary correlation functions
• Probing a Gravitational Cat State
• One-loop gravitational wave spectrum in de Sitter spacetime
• Quantum gravitational decoherence of light and matter
• Riemann correlator in de Sitter including loop corrections from conformal fields
• Conservative entropic forces
• Optomechanical test of the Schrödinger-Newton equation
• Stress tensor fluctuations in de Sitter spacetime
• Testing the foundations of quantum physics in space Interferometric and non-interferometric tests with Large Particles
• Towards a formal description of the collapse approach to the inflationary origin of the seeds of cosmic structure
• On the initial conditions and solutions of the semiclassical Einstein equations in a cosmological scenario
• Nonperturbative semiclassical stability of de Sitter spacetime for small metric deviations
• On the Manifestly Covariant Juttner Distribution and Equipartition Theorem
• Role of evaporation in gravitational collapse
• Spacetime foam: a review
• Nonequilibrium Steady State in Open Quantum Systems: Influence Action, Stochastic Equation and Power Balance
• Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
• Backreaction in Cosmology
• Can the fluctuations of the quantum vacuum solve the cosmological constant problem?
• Quantum Noise of Gravitons and Stochastic Force on Geodesic Separation
• Stress-energy Tensor Correlators of a Quantum Field in Euclidean $R^N$ and $Ad{S}^N$ spaces via the generalized zeta-function method
• Optomechanical tests of a Schrödinger-Newton equation for gravitational quantum mechanics
• Noise kernels of stochastic gravity in conformally-flat spacetimes
• Can the quantum vacuum fluctuations really solve the cosmological constant problem?
• Vacuum fluctuation, micro-cyclic "universes" and the cosmological constant problem
• Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
• Gravitational decoherence: a general non relativistic model
• On the Decoherence of Primordial Gravitons
• The weak field limit of quantum matter back-reacting on classical spacetime
• Expectation of primordial gravity waves generated during inflation
• Gravitational Decoherence, Alternative Quantum Theories and Semiclassical Gravity
• Fluctuation-Dissipation and Correlation-Propagation Relations from the Nonequilibrium Dynamics of Detector-Quantum Field Systems
• Reformulation of the Cosmological Constant Problem
• Primordial gravitational waves amplification from causal fluids
• Quantum fluctuations of the friction force induced by the dynamical Casimir emission
• Stochastic oscillations of general relativistic disks
• Measurable signatures of quantum mechanics in a classical spacetime
• Stochastic Emergent Quantum Gravity
• Relativistic viscous effects on the primordial gravitational waves spectrum
• On the scaling rules for the anomaly-induced effective action of metric and electromagnetic field
• Past-directed scalar field gradients and scalar-tensor thermodynamics
• A healthier semi-classical dynamics
• Novel Effect Induced by Spacetime Curvature in Quantum Hydrodynamics
• Macroscopic quantum phenomena from the large N perspective
• Distinguishable consequence of classical gravity on quantum matter
• Scalar field dark matter in hybrid approach
• Newtonian Semiclassical Gravity in the Ghirardi-Rimini-Weber Theory with Matter Density Ontology
• Gravity, Quantum Fields and Quantum Information: Problems with classical channel and stochastic theories
• Eternal inflation and the quantum birth of cosmic structure
• On the weight of entanglement
• Influence of quantum matter fluctuations on geodesic deviation
• Noise Kernel for Self-similar Tolman Bondi Metric: Fluctuations on Cauchy Horizon
• Stress energy correlator in de Sitter space-time : its conformal masking or growth in connected Friedmann universes
• Kinetic theory and classical limit for real scalar quantum field in curved space-time
• Analogue gravity simulation of superpositions of spacetimes
• Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity
• A Maximum Force Perspective on Black Hole Thermodynamics, Quantum Pressure, and Near-Extremality
• Unruh deWitt probe of late time revival of quantum correlations in Friedmann spacetimes
• Introduction to gravitational redshift of quantum photons propagating in curved spacetime
• Classicalization of Quantum Variables and Quantum-Classical Hybrids
• Cosmological bounds on TeV-scale physics and beyond
• Fully renormalized stress tensor correlator in flat space
• Analogue stochastic gravity phenomena in two-component Bose-Einstein condensates: Sound cone fluctuations
• Comment on: "How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe"
• Multiplicative Noise in Euclidean Schwarzschild Manifold
• Tabletop Experiments for Quantum Gravity Are Also Tests of the Interpretation of Quantum Mechanics
• Casimir Energy Corrections by Light-Cone Fluctuations
• HBAR entropy of Infalling Atoms into a GUP-corrected Schwarzschild Black Hole and equivalence principle
• Non-Cancellation of Quantum Geometry Fluctuations
• Nonlocal effective actions in semiclassical gravity: thermal effects in stationary geometries
• Stochastic quantization of a self-interacting nonminimal scalar field in semiclassical gravity
• How Much NEC Breaking Can the Universe Endure?
• Semiclassical gravity beyond coherent states
• Wave optics of quantum gravity for massive particles
• Orbits in a stochastic Schwarzschild geometry
• Are Quantum-Classical Hybrids compatible with Ontological Cellular Automata?
• Quantum-induced Stochastic Optomechanical Dynamics
• Functional formulation of quantum theory of a scalar field in a metric with Lorentzian and Euclidean signatures
• Non-equilibrium thermodynamics of gravitational objective-collapse models
• Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity
• Metric fluctuations in higher-dimensional black holes
• Curvature fluctuations on asymptotically de Sitter spacetimes via the semiclassical Einstein's equations
• Unequal time Commutators in Friedmann universes: Deterministic evolution of massless fields
• Frequency Spectra Analysis of Space and Time Averaged Quantum Stress Tensor Fluctuations
• Correlations of the stress-energy tensor in AdS spaces via the generalized zeta-function method
• Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models
• Can Stochastic Clocks in FLRW Minisuperspace Prevent Dynamical Singularities?
• Can Newtonian Gravity Produce Quantum Entanglement?
• Semiclassical Backreaction: A Qualitative Assessment
• Emergence of phantom cold dark matter from spacetime diffusion
• Gravitational wave emission from the CMB and other thermal fields
• Newtonian self-gravity in trapped quantum systems and experimental tests
• Fluctuations in the stress energy tensor of spinor fields evolving in general FRW spacetimes
• Relational Time as a Stochastic Variable in ADM Gravity
• Geodesics in Quantum Gravity
• Waveform stability of black hole ringdown with stochastic horizon structure
• Energy Balance of a Boson Gas at Zero Temperature in Curved Spacetime
• Testing classical-quantum gravity with geodesic deviation
• Dephasing and inhibition of spin interference from semi-classical self-gravitation
• Quantum Physics in Space
• A healthier stochastic semiclassical gravity: world without Schrödinger cats