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Showing 1 to 20 of 37 for “"einstein equations"”.
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Constraint preserving boundary conditions for the linearized Einstein equations
… in Cartesian coordinates of the generalized Einstein-Christoffel system and analyze different kinds of boundary conditions that are designed to ensure that the constraints vanish throughout the computational domain: the Neumann, Dirichlet, and Sommerfeld cases. In addition to the situation in …
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Initial data to vacuum Einstein equations with asymptotic expansion
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1998.
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A Scattering Theory for Linearised Gravity on the Exterior of the Schwarzschild Black Hole
… construct a scattering theory for the linearised Einstein equations on a Schwarzschild background in a double null gauge. We perform this construction in two parts. In Part I, we construct a scattering theory for the spin ±2 Teukolsky equations, which govern certain the extremal, gauge-invariant …
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Asymptotic description of the formation of black holes from short-pulse data
… formation of black holes in the four-dimensional Einstein vacuum equations from Christodoulou's short-pulse ansatz. We identify natural scaling in a putative solution metric and use the technique of real blowup to propose a desingularized manifold and an associated rescaled tangent bundle (which …
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Critical Phenomena in Gravitational Collapses of Neutron Star Systems
… objects based on numerical solutions of the Einstein equations. We discovered that stellar objects with large kinetic energy described by an equation of state: EOS) commonly used in describing neutron star matter may undergo critical collapses. To the best of our knowledge, this is the first …
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Frequency space analysis in General Relativity
… addressing a distinct problem for the vacuum Einstein equations in General Relativity. The common theme is the use of frequency analysis as a tool to exploit fine structures within the partial differential equations. However, the two parts are structured so as to be read independently. The …
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Some problems of quantum cosmology and dark matter physics
… agree with those obtained from the classical Einstein equations.
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Causality and the initial value problem in Modified Gravity
… theories are natural generalisations of Einstein’s theory of General Relativity. They find applications in Astrophysics, Cosmology and String Theory. This dissertation discusses some issues regarding the mathematical consistency of these theories. In the first part of the thesis we study …
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ΠΑΡΑΓΩΓΗ ΝΕΩΝ ΑΚΡΙΒΩΝ ΛΥΣΕΩΝ ΤΩΝ ΕΞΙΣΩΣΕΩΝ ΤΟΥ EINSTEIN ΜΕ ΤΗ ΜΕΘΟΔΟ ΤΗΣ ΑΝΤΙΣΤΡΟΦΗΣ ΣΚΕΔΑΣΗΣ ΤΩΝ BELINSKY-ZAKHAROV
… THE CONSTRUCTION OF NEW EXACT SOLUTIONS OF THE EINSTEIN EQUATIONS. THIS METHOD IS APPLIED TO SPACETIMES POSSESING TWO COMMUTING (NON-NULL) KILLING VECTORS. THE BZ METHODIS PRESENTED IN A VERY USEFUL FORM IN THE CASE WHERE THE SEED METRIC IS DIAGONAL AND ALLOWS FOR THE EASY GENERATION OF EXACT …
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Celestial Chiral Algebras and Self-Dual Gravity
… geometries that solve some form of the self-dual Einstein equations. After an elaborate introduction, we begin by reviewing how holomorphic collinear singularities of gravity and gauge theory amplitudes in a certain basis are reminiscent of OPEs in a $2$-dimensional CFT. Then, we discuss how a …
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Numerical MHD Simulations in Dynamical Spacetimes
… same time, evolving the spacetime according to Einstein's equations of general relativity. In particular, magnetohydrodynamics (MHD) and relativistic gravity are of crucial importance in astrophysical phenomena such as stellar collapse to black holes, binary neutron star mergers, supernovae, and …
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Gravitational wave extraction in numerical relativity
The complexity of the Einstein Equations, which is due to their nonlinearity, makes a general analytical solution impossible. In order to extend the frontiers of our knowledge, physicists are especially interested in extreme scenarios. The strongest and thus most interesting source for the study of …
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Nonlinear Waves on Extremal Black Hole Spacetimes
… global behaviour of solutions of nonlinear wave equations where the nonlinearity satisfies the null condition on extremal Reissner-Nordstrom black hole spacetimes.Under the assumption of spherical symmetry I show that solutions which arise from sufficiently small compactly supported smooth data …
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Numerical Simulations Of Black Hole Binaries: Second Order Spectral Methods
Current spectral simulations of Einstein's equations require writing the system in first-order form, potentially introducing instabilities and inefficiencies. This work presents a new penalty method for pseudo-spectral evolutions of second order in space wave equations. The penalties are …
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Horizons, hyperbolic systems, and inner boundary conditions in numerical relativity
… both standard and hyperbolic formulations of the Einstein equations and how these are amenable to numerical treatment with modern parallel and adaptive computational techniques. In the course of this discussion, we present a three-dimensional implementation of the Bona-Massó hyperbolic system, and …
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Vector fields during cosmic inflation: stability analysis and phenomenological signatures.
… in the model and (2) by studying the linearized Einstein equations and showing that the solutions diverge close to horizon crossing. For models that are free of instabilities, relevant power spectra are computed and the resulting phenomenology is discussed.
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THE COVARIANT APPROACH TO SPACE TIMES ANDSOME EXTENDED THEORIES OF GRAVITY
… point of view it is shown that the field equations can be recast into Einstein's ones augmented by an arbitrary Codazzi tensor. This simplifies the search of solutions. A new cosmological theory theory was proposed by J. Harada in 2023 to describe the effects of the presence of dark energy …
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Gravitational Waves and Inspiraling Compact Binaries in Alternative Theories of Gravity
… PPN) framework, Direct Integration of Relaxed Einstein Equations: DIRE), and Matched Filtering.</p><p>In Part III, we calculate the explicit equations of motion for non-spinning compact objects: neutron stars or black holes) to 2.5 post-Newtonian order, or $O(v/c)^5$ beyond Newtonian gravity, …
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Finite difference methods for 1st Order in time, 2nd order in space, hyperbolic systems used in numerical relativity
… type of system appears in some formulations of Einstein equations, such as ADM, BSSN, NOR, and the generalized harmonic formulation. For IVP, the stability method proposed in [14] is extended from second and fourth order centered schemes, to 2n-order accuracy, including also the case when some …
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