A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.
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On the Numerical Integration of Einstein's Field Equations
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9
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abstract
Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial metric and extrinsic curvature tensors. Following Shibata and Nakamura, we modify these equations by factoring out the conformal factor and introducing three ``connection functions''. The evolution equations can then be reduced to wave equations for the conformal metric components, which are coupled to evolution equations for the connection functions. We evolve small amplitude gravitational waves and make a direct comparison of the numerical performance of the modified equations with the standard ADM equations. We find that the modified form exhibits much improved stability.
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gr-qc 9representative citing papers
The linearized 3+1 TEGR system has imaginary eigenvalues in its principal symbol but becomes strongly hyperbolic after gauge fixing isolated problematic sectors.
Numerical simulations of equal-mass boson-star mergers reveal larger waveform deviations from black-hole binaries in late inspiral and merger, plus odd multipole excitations for certain scalar-field phases, with some signals degenerate until IMR consistency tests are applied.
Numerical relativity simulations of triple black hole systems reveal redshift effects and gravitational lensing in ringdown signals from head-on mergers, with no additional black hole formation from amplified waves.
Numerical relativity simulations of equal-mass black holes with initial spins from -0.7 to 0.7 in hyperbolic encounters find maximum spin-up of 0.3 and mass increase of 15%, with spin-up decreasing linearly with initial spin at the threshold angle.
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.
Fits to numerical relativity data indicate that leading-order post-Newtonian dependence on mass ratio persists in several modes of binary black hole mergers through the merger, while low-degree polynomials capture deviations in higher modes.
Numerical simulations of black hole-boson star binaries show that scalar self-interactions can suppress tidal disruption while radiative efficiency depends on the chosen potential.
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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Nonlinear Lattice Framework for Inflation: Bridging stochastic inflation and the $\delta{N}$ formalism
A shear-free lattice method bridges stochastic inflation and δN formalism by enabling fully nonlinear calculations of curvature perturbations in single-field models with ultra-slow-roll phases.
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Hyperbolicity analysis of the linearised 3+1 formulation in the Teleparallel Equivalent of General Relativity
The linearized 3+1 TEGR system has imaginary eigenvalues in its principal symbol but becomes strongly hyperbolic after gauge fixing isolated problematic sectors.
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Lessons from binary dynamics of inspiralling equal-mass boson-star mergers
Numerical simulations of equal-mass boson-star mergers reveal larger waveform deviations from black-hole binaries in late inspiral and merger, plus odd multipole excitations for certain scalar-field phases, with some signals degenerate until IMR consistency tests are applied.
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The third wheel: ringdown and lensing of triple systems
Numerical relativity simulations of triple black hole systems reveal redshift effects and gravitational lensing in ringdown signals from head-on mergers, with no additional black hole formation from amplified waves.
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Spin-up and mass-gain in hyperbolic encounters of spinning black holes
Numerical relativity simulations of equal-mass black holes with initial spins from -0.7 to 0.7 in hyperbolic encounters find maximum spin-up of 0.3 and mass increase of 15%, with spin-up decreasing linearly with initial spin at the threshold angle.
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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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Persistence of post-Newtonian amplitude structure in binary black hole mergers
Fits to numerical relativity data indicate that leading-order post-Newtonian dependence on mass ratio persists in several modes of binary black hole mergers through the merger, while low-degree polynomials capture deviations in higher modes.
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Black Hole-Boson Star Binaries: Gravitational Wave Signals and Tidal Disruption
Numerical simulations of black hole-boson star binaries show that scalar self-interactions can suppress tidal disruption while radiative efficiency depends on the chosen potential.
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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.