Pure R^2 gravity propagates three degrees of freedom nonlinearly but zero linearly around Minkowski and other traceless-Ricci R=0 spacetimes due to ten second-class constraints becoming first-class upon linearization.
3+1 Formalism and Bases of Numerical Relativity
9 Pith papers cite this work. Polarity classification is still indexing.
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abstract
These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.
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representative citing papers
Black holes with synchronized or resonant scalar hair exhibit dynamical splitting in which the horizon is ejected from the bosonic cloud center in the very hairy regime.
Constraint-satisfying scalar-field initial data for boson star binaries is constructed via the XCFC formalism, improving on superposition by ensuring the constraints are met.
A covariant zoom-in perturbation theory framework resolves geodesic breakdown via hierarchical matter horizons, producing an effective energy-momentum tensor whose backreaction explains flat galaxy rotation curves without dark matter.
New realizations of warp drive spacetimes are constructed as solutions of Einstein's equations via geodesic assumptions and relativistic Lagrangian perturbations, revealing coordinate instabilities and a direct link to cosmological models.
A one-body conformal-factor correction stabilizes boson star-black hole initial data, enabling gravitational-wave analysis that shows higher multipoles can discriminate mixed mergers from pure black-hole binaries.
Lecture notes that build the BMS group from prerequisites to applications in soft theorems, memory effects, and new material on asymptotic conformal Killing horizons.
A review that unifies analytical expressions for scalar-induced gravitational waves and emphasizes calculations for non-radiation-dominated cosmologies.
Boson stars are particle-like solutions in general relativity that model dark matter, black hole mimickers, and binary systems.
citing papers explorer
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Spectrum of pure $R^2$ gravity: full Hamiltonian analysis
Pure R^2 gravity propagates three degrees of freedom nonlinearly but zero linearly around Minkowski and other traceless-Ricci R=0 spacetimes due to ten second-class constraints becoming first-class upon linearization.
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Splitting the Gravitational Atom: Instabilities of Black Holes with Synchronized or Resonant Hair
Black holes with synchronized or resonant scalar hair exhibit dynamical splitting in which the horizon is ejected from the bosonic cloud center in the very hairy regime.
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Constraint-satisfying binary boson star initial data via XCFC
Constraint-satisfying scalar-field initial data for boson star binaries is constructed via the XCFC formalism, improving on superposition by ensuring the constraints are met.
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Cosmological zoom-in perturbation theory as a consistent beyond point-particle approximation framework
A covariant zoom-in perturbation theory framework resolves geodesic breakdown via hierarchical matter horizons, producing an effective energy-momentum tensor whose backreaction explains flat galaxy rotation curves without dark matter.
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Novel Realizations of Warp Drive Spacetimes as Solutions of General Relativity
New realizations of warp drive spacetimes are constructed as solutions of Einstein's equations via geodesic assumptions and relativistic Lagrangian perturbations, revealing coordinate instabilities and a direct link to cosmological models.
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Boson star-black hole binaries: initial data and head-on collisions
A one-body conformal-factor correction stabilizes boson star-black hole initial data, enabling gravitational-wave analysis that shows higher multipoles can discriminate mixed mergers from pure black-hole binaries.
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Lectures on the Bondi--Metzner--Sachs group and related topics in infrared physics
Lecture notes that build the BMS group from prerequisites to applications in soft theorems, memory effects, and new material on asymptotic conformal Killing horizons.
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Scalar induced gravitational waves review
A review that unifies analytical expressions for scalar-induced gravitational waves and emphasizes calculations for non-radiation-dominated cosmologies.
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Dynamical Boson Stars
Boson stars are particle-like solutions in general relativity that model dark matter, black hole mimickers, and binary systems.