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Approximate Isometries as an Eigenvalue Problem and Angular Momentum
Title
Approximate Isometries as an Eigenvalue Problem and Angular Momentum.
Creator
Wilder, Shawn M., Beetle, Christopher, Graduate College
Date Issued
2013-04-12
PURL
http://purl.flvc.org/fcla/dt/3361373
Subject Headings
Black holes (Astronomy), Eigenvalues
Format
Document (PDF)
Exploring the stability of an eigenvalue problem approximation technique used to define the angular momentum of almost spherical black holes
Title
Exploring the stability of an eigenvalue problem approximation technique used to define the angular momentum of almost spherical black holes.
Creator
Wilder, Shawn M., Beetle, Christopher, Graduate College
Date Issued
2011-04-08
PURL
http://purl.flvc.org/fcla/dt/3164804
Subject Headings
Eigenvalues, Black holes (Astronomy), Deformations (Mechanics)
Format
Document (PDF)
QUANTIZATIONS OF THE SCHWARZSCHILD INTERIOR FROM DIFFEOMORPHISM COVARIANCE AND OTHER CRITERIA
Title
QUANTIZATIONS OF THE SCHWARZSCHILD INTERIOR FROM DIFFEOMORPHISM COVARIANCE AND OTHER CRITERIA.
Creator
Dias, Rafael Guolo, Engle, Jonathan S., Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description
We propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the...
Show moreWe propose an approach to the quantization of the interior of a Schwarzschild black hole, represented by a Kantowski-Sachs (KS) framework, by requiring its covariance under a notion of residual diffeomorphisms. We solve for the family of Hamiltonian constraint operators satisfying the associated covariance condition, in addition to parity covariance, preservation of the Bohr Hilbert space of Loop Quantum KS and a correct (naïve) classical limit. We further explore imposing minimality of the number of terms, and compare the solution with other Hamiltonian constraints proposed for Loop Quantum KS in the literature, with special attention to a most recent case. In addition, we discuss a lapse commonly chosen to decouple the evolution of the two degrees of freedom of the model, yielding exact solubility of the model, and we show that such choice can indeed be quantized as an operator densely defined on the Bohr Hilbert space, but must include an infinite number of shift operators. Also, we show the reasons why we call the classical limit “naïve”, and point this out as a reason for one limitation of some present prescriptions.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014546
Subject Headings
Black holes (Astronomy), Quantum theory, Diffeomorphisms, Gravity
Format
Document (PDF)
ELLIPTICA: A NEW PSEUDOSPECTRAL CODE FOR THE CONSTRUCTION OF INITIAL DATA
Title
ELLIPTICA: A NEW PSEUDOSPECTRAL CODE FOR THE CONSTRUCTION OF INITIAL DATA.
Creator
Rashti, Alireza, Tichy, Wolfgang, Florida Atlantic University, Department of Physics, Charles E. Schmidt College of Science
Abstract/Description
Unveiling the secrets of gravity necessitates numerical relativity simulations of gravitational systems, as observations made by gravitational wave detectors expect an interpretation. In the other hand, these numerical simulations require physical and constraint-satisfying initial data. Therefore, the accuracy of simulations go hand in hand with the accuracy of initial data. As such, constructing accurate initial data is an indispensable task and it is the very subject of this dissertation....
Show moreUnveiling the secrets of gravity necessitates numerical relativity simulations of gravitational systems, as observations made by gravitational wave detectors expect an interpretation. In the other hand, these numerical simulations require physical and constraint-satisfying initial data. Therefore, the accuracy of simulations go hand in hand with the accuracy of initial data. As such, constructing accurate initial data is an indispensable task and it is the very subject of this dissertation. Here, we present the newly developed pseudospectral code Elliptica, an infrastructure for construction of initial data for various binary and single gravitational systems of all kinds. The elliptic equations under consideration are solved on a single spatial hypersurface of the spacetime manifold. Using coordinate maps, the hypersurface is covered by patches whose boundaries can adapt to the surface of the compact objects. To solve elliptic equations with arbitrary boundary condition, Elliptica deploys a Schur complement domain decomposition method with a direct solver. In this version, we use cubed sphere coordinate maps and the fields are expanded using Chebyshev polynomials of the first kind. Here, we explain the building blocks of Elliptica and the initial data construction algorithm for black hole-neutron star binary systems. We perform convergence tests and evolve the data to validate our results. Within our framework, the neutron star can reach spin values close to breakup with arbitrary direction, while the black hole can have arbitrary spin with dimensionless spin magnitude ~ 0.8.
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Date Issued
2022
PURL
http://purl.flvc.org/fau/fd/FA00014006
Subject Headings
Gravitational waves, Elliptic functions, Neutron stars, Black holes (Astronomy)
Format
Document (PDF)
Binary neutron star mergeres: simulations with arbitrarily spinning stars
Title
Binary neutron star mergeres: simulations with arbitrarily spinning stars.
Creator
Tsatsin, Petr, Marronetti, Pedro, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. This dissertation presents a new method to produce initial data sets for binary neutron stars with arbitrary spins and orbital eccentricities. The method only provides approximate solutions to the constraints. However, it was shown that the corresponding constraint violations subside after a few orbits,...
Show moreThe starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. This dissertation presents a new method to produce initial data sets for binary neutron stars with arbitrary spins and orbital eccentricities. The method only provides approximate solutions to the constraints. However, it was shown that the corresponding constraint violations subside after a few orbits, becoming comparable to those found in evolutions of standard conformally flat, helically symmetric binary initial data. This dissertation presents the first spinning neutron star binary simulations in circular orbits with a orbital eccentricity less then 0.01. The initial data sets corresponding to binaries with spins aligned, zero and anti-aligned with the orbital angular momentum were evolved in time. These simulations show the orbital “hang-up” effect previously seen in binary black holes. Additionally, they show orbital eccentricities that can be up to one order of magnitude smaller than those found in helically symmetric initial sets evolutions.
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Date Issued
2013
PURL
http://purl.flvc.org/fau/fd/FA0004067
Subject Headings
Astrophysics, Black holes (Astronomy), General relativity (Physics), Gravitational waves, Neutron stars, Particles (Nuclear physics)
Format
Document (PDF)
Binary black hole mergers
Title
Binary black hole mergers: alternatives to standard puncture initial data and the impact on gravitational waveforms.
Creator
Reifenberger, George C., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
We study the evolution of binary black hole initial data schemes as alternatives to the standard puncture construction. These alternatives are based on post-Newtonian expansions that contain realistic gravitational waves. The first scheme is based on a second order post-Newtonian expansion in Arnowitt, Deser, and Misner transverse-traceless (ADMTT) gauge that has been re-summed to approach standard puncture data at the black holes. The other schemes are based on asymptotic matching of the 4...
Show moreWe study the evolution of binary black hole initial data schemes as alternatives to the standard puncture construction. These alternatives are based on post-Newtonian expansions that contain realistic gravitational waves. The first scheme is based on a second order post-Newtonian expansion in Arnowitt, Deser, and Misner transverse-traceless (ADMTT) gauge that has been re-summed to approach standard puncture data at the black holes. The other schemes are based on asymptotic matching of the 4-metrics of two tidally perturbed Schwarzschild solutions to post-Newtonian expansions at different orders. The alternatives are encouraging and lead to quasi-circular orbits and show gravitational radiation from the onset, as well as a reduction of spurious radiation. Deficiencies compared to punctures include more eccentricity during inspiral and larger constraint violations, since the alternative data sets only approximate solutions of Einstein's equations.
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Date Issued
2013
PURL
http://purl.flvc.org/fcla/dt/3362577
Subject Headings
Black holes (Astronomy), General relativity (Physics), Gravitational waves, Inertia (Mechanics), Mass (Physics), Particles (Nuclear physics)
Format
Document (PDF)
Towards reading line profiles of Bardeen-Petterson accretion disks
Title
Towards reading line profiles of Bardeen-Petterson accretion disks.
Creator
Vandernoot, Eric P., Florida Atlantic University, Miller, Warner A.
Abstract/Description
Images of highly idealized Bardeen-Petterson accretion disks around Kerr black holes and their generated energy spectra line profiles are created via computer simulations in this work. The line profiles are examined in the relation to the original disk parameters to demonstrate that Bardeen-Petterson disks can be the source of the spectra we observe, even of actual systems. The challenges in computer programming the simulations and methods to overcome the challenges are discussed in the paper...
Show moreImages of highly idealized Bardeen-Petterson accretion disks around Kerr black holes and their generated energy spectra line profiles are created via computer simulations in this work. The line profiles are examined in the relation to the original disk parameters to demonstrate that Bardeen-Petterson disks can be the source of the spectra we observe, even of actual systems. The challenges in computer programming the simulations and methods to overcome the challenges are discussed in the paper. Also discussed are the future work, improvements and intentions for the simulations. Finally, the discussion turns to the usage of indicators in these line profiles to predict parameters of the original disk systems.
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/13287
Subject Headings
Black holes (Astronomy), Accretion (Astrophysics), General relativity (Physics), Gravitation, Petterson, Jacobus Antonius,--1946-
Format
Document (PDF)