General relativity and conjugate ordinary differential equations

DOI10.1016/0022-0396(78)90012-8zbMath0362.34023OpenAlexW1980184680MaRDI QIDQ1239839

Frank J. Tipler

Publication date: 1978

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(78)90012-8

Mathematics Subject Classification ID

Linear ordinary differential equations and systems (34A30) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

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ON THE GLOBAL EXISTENCE OF TIME ⋮ Comparison theory in Lorentzian and Riemannian geometry ⋮ A gravitational collapse singularity theorem consistent with black hole evaporation ⋮ The effect of variable change on oscillation and disconjugacy criteria with applications to spectral theory and asymptotic theory ⋮ The distance between points of a solution of a second order linear differential equation satisfying general boundary conditions ⋮ A new derivation of singularity theorems with weakened energy hypotheses ⋮ Energy conditions in general relativity and quantum field theory ⋮ Lorentzian causality theory ⋮ Energy conditions, traversable wormholes and dust shells ⋮ Unnamed Item ⋮ Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes ⋮ Distance to a focal point and singularity theorems with weak timelike convergence condition ⋮ Conjugacy criteria for the half-linear second order differential equation ⋮ Unnamed Item ⋮ Convergent disfocality and nondisfocality criteria for second-order linear differential equations ⋮ Positive Mass from Holographic Causality ⋮ Hartman-Wintner type lemma, oscillation, and conjugacy criteria for half-linear difference equations ⋮ Existence of conjugate points for second and fourth order differential equations ⋮ Hawking's singularity theorem under a bounded integral norm of Ricci curvature ⋮ Conjugacy criteria for second order differential equations

Cites Work

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• The singularities of gravitational collapse and cosmology
• The Large Scale Structure of Space-Time
• Principal Quadratic Functionals
• On Self-Adjoint Differential Equations of Second Order
• Singularities and causality violation

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