Towards the Raychaudhuri Equation Beyond General Relativity

Abstract

In General Relativity, gravity is universally attractive, a feature embodied by the Raychaudhuri equation which requires that the expansion of a congruence of geodesics is always non-increasing, as long as matter obeys the strong or weak energy conditions. This behavior of geodesics is an important ingredient in general proofs of singularity theorems, which show that many spacetimes are singular in the sense of being geodesically incomplete and suggest that General Relativity is itself incomplete. It is possible that alternative theories of gravity, which reduce to General Relativity in some limit, can resolve these singularities, so it is of interest to consider how the behavior of geodesics is modified in these frameworks. We compute the leading corrections to the Raychaudhuri equation for the expansion due to models in string theory, braneworld gravity, $f(R)$ theories, and Loop Quantum Cosmology, for cosmological and black hole backgrounds, and show that while in most cases geodesic convergence is reinforced, in a few cases terms representing repulsion arise, weakening geodesic convergence and thereby the conclusions of the singularity theorems.

arXiv comment21 pages. v2: Added references. v3: Matches published version, references and clarifications added

References in corpus (32)

• A Large Mass Hierarchy from a Small Extra Dimension
• f(R) Theories Of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Heterotic and Type I String Dynamics from Eleven Dimensions
• The Einstein Equations on the 3-Brane World
• Non-conventional cosmology from a brane-universe
• Brane cosmological evolution in a bulk with cosmological constant
• Ghost Inflation
• G-inflation: inflation driven by the Galileon field
• Energy in Generic Higher Curvature Gravity Theories
• Brane-world cosmology
• Brane World Cosmology
• Lanczos-Lovelock models of gravity
• Are loop quantum cosmos never singular?
• The Lovelock Black Holes
• Brane-world solutions, standard cosmology, and dark radiation
• Observational Constraints on Dark Radiation in Brane Cosmology
• Singularity Resolution in Loop Quantum Cosmology: A Brief Overview
• Kaluza-Klein anisotropy in the CMB
• Quantum Raychaudhuri equation
• On the non-attractive character of gravity in f(R) theories
• Motion of Inertial Observers Through Negative Energy
• Strong energy condition and the repulsive character of f(R) gravity
• String Corrections to the Holographic RG Flow of Supersymmetric SU(N) x SU(N+M) Gauge Theory
• Geodesic completeness and homogeneity condition for cosmic inflation
• Dynamics of false vacuum bubbles with nonminimal coupling
• Defocusing of Null Rays in Infinite Derivative Gravity
• Dynamics of false vacuum bubbles in Brans-Dicke theory
• Stringy corrections to a time-dependent background solution of string and M-Theory
• Quantum no-singularity theorem from geometric flows
• Thermodynamics in Loop Quantum Cosmology
• Consistent Cosmic Bubble Embeddings

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• The classical and quantum implications of the Raychaudhuri Equation in f(T)-gravity
• The Raychaudhuri Equation in inhomogeneous FLRW space-time : A $f(R)$-gravity model
• Constraints and Horizons for de Sitter with Extra Dimensions
• Geometry of small causal diamonds
• The Raychaudhuri equation for a quantized timelike geodesic congruence
• Raychaudhuri equation in scalar-tensor theory
• Graviton noise on tidal forces and geodesic congruences
• Quantum gravitational signatures in next-generation gravitational wave detectors
• General class of "quantum deformed" regular black holes
• Black Hole Entropy production and Transport coefficients in Lovelock Gravity
• Form Invariance of Raychaudhuri equation in the presence of Inflaton-type fields
• Deriving the Gibbons-Maldacena-Nunez no-go theorem from the Raychaudhuri equation
• How Much NEC Breaking Can the Universe Endure?
• Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes
• Covariant single-field formulation of effective cosmological bounces
• Gauss-Bonnet Gravity and Spacetime Singularities