[ { "id": "authors:jbp91-8yt29", "collection": "authors", "collection_id": "jbp91-8yt29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200805-084928954", "type": "article", "title": "A Newtonian problem as an insightful tool for the behavior of gravitational-wave sources", "author": [ { "family_name": "Apostolatos", "given_name": "Theocharis A.", "clpid": "Apostolatos-T-A" }, { "family_name": "Pappas", "given_name": "George", "clpid": "Pappas-G" }, { "family_name": "Chatziioannou", "given_name": "Katerina", "orcid": "0000-0002-5833-413X", "clpid": "Chatziioannou-K" } ], "abstract": "We present the intriguing mathematical and physical similarities arising from the study of the Kerr metric and the Euler's problem of two fixed gravitational centers. We show how one could extend these similarities to physical problems that emerge from the above integrable problems, when both are slightly perturbed.", "doi": "10.1088/1742-6596/453/1/012001", "issn": "1742-6596", "publisher": "IOP", "publication": "Journal of Physics: Conference Series", "publication_date": "2013-08-16", "volume": "453", "pages": "Art. No. 012001" }, { "id": "authors:23htd-4p547", "collection": "authors", "collection_id": "23htd-4p547", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:APOprd94", "type": "article", "title": "Spin-induced orbital precession and its modulation of the gravitational waveforms from merging binaries", "author": [ { "family_name": "Apostolatos", "given_name": "Theocharis A.", "clpid": "Apostolatos-T-A" }, { "family_name": "Cutler", "given_name": "Curt", "clpid": "Cutler-C-J" }, { "family_name": "Sussman", "given_name": "Gerald J.", "clpid": "Sussman-G-J" }, { "family_name": "Thorne", "given_name": "Kip S.", "clpid": "Thorne-K-S" } ], "abstract": "Merging compact binaries are currently regarded as the most promising source of gravitational waves for the planned Earth-based LIGO/VIRGO laser-interferometer detector system, and will be an important source also for similar, lower-frequency detectors that might be flown in space (e.g., the proposed LISA mission). During the orbital inspiral, if one or both bodies are rapidly rotating, the general relativistic spin-orbit and spin-spin coupling (i.e., the \"dragging of inertial frames\" by the bodies' spins) cause the binary's orbital plane to precess. In this paper we analyze the resulting modulation of the inspiral gravitational waveform, using post2-Newtonian equations to describe the precession of the orbital plane, but only the leading-order (Newtonian, quadrupole-moment approximation) equations to describe the orbit, the radiation reaction, the inspiral, and the wave generation. We derive all the formulas one needs to readily compute the spin-modulated gravitational waveform (within the post-Newtonian approximation and the approximation that the precession frequency is much smaller than the orbital frequency). We also develop intuition into what the modulated signals \"look like,\" by a variety of means. We provide approximate, analytical solutions for the precessional motion and the modulated waveforms for two important special cases: the case where the bodies have nearly equal masses and the case where one of the bodies has negligible spin. For these cases, for almost all choices of binary parameters, the motion is a simple precession of the orbital angular momentum around the nearly fixed direction of the total angular momentum, with a few tens of precession periods as the waves sweep through the LIGO/VIRGO observational band. However, when the spin and orbital angular momenta are approximately anti-aligned, there is a transitional-precession epoch during which their near cancellation causes the binary to \"lose its gyroscopic bearings\" and tumble in space, with a corresponding peculiar sweep of the waveform modulation. We also explore numerically the precessional behaviors that occur for general masses and spins; these typically appear quite similar to our special-case, simple-precession, and transitional-precession solutions. An Appendix develops several diagrammatic aids for understanding intuitively the relation between the precessing orbit and the modulated waveform.", "doi": "10.1103/PhysRevD.49.6274", "issn": "2470-0010", "publisher": "Physical Review D", "publication": "Physical Review D", "publication_date": "1994-06-15", "series_number": "12", "volume": "49", "issue": "12", "pages": "6274-6308" }, { "id": "authors:9zfax-1rn56", "collection": "authors", "collection_id": "9zfax-1rn56", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:APOprd93", "type": "article", "title": "Gravitational radiation from a particle in circular orbit around a black hole. III. Stability of circular orbits under radiation reaction", "author": [ { "family_name": "Apostolatos", "given_name": "Theocharis", "clpid": "Apostolatos-T-A" }, { "family_name": "Kennefick", "given_name": "Daniel", "clpid": "Kennefick-D-J" }, { "family_name": "Ori", "given_name": "Amos", "clpid": "Ori-A" }, { "family_name": "Poisson", "given_name": "Eric", "clpid": "Poisson-E" } ], "abstract": "We use the Teukolsky perturbation formalism to show that (i) a particle in circular motion around a nonrotating black hole remains in a circular orbit under the influence of radiation reaction, and (ii) circular orbits are stable only if the orbital radius is greater than a critical radius rc -~ 6.6792M, where M is the mass of the black hole. A circular orbit is stable if, when slightly perturbed so that it acquires a small eccentricity, the radiation reaction decreases the eccentricity; a circular orbit is unstable if the radiation reaction increases the eccentricity. Our analysis is restricted by four major assumptions: (i) the black hole is nonrotating, (ii) the eccentricity is always small, (iii) the gravitational perturbations are linear, and (iv) the adiabatic approximation (that the radiation reaction takes place over a time scale much larger than the orbital period) is valid. On the other hand, our analysis is not limited to weak-field, slow-motion situations; it is valid for particle motion in strong gravitational fields.", "doi": "10.1103/PhysRevD.47.5376", "issn": "2470-0010", "publisher": "American Physical Society", "publication": "Physical Review D", "publication_date": "1993-06-15", "series_number": "12", "volume": "47", "issue": "12", "pages": "5376-5388" }, { "id": "authors:t6xbp-gjz23", "collection": "authors", "collection_id": "t6xbp-gjz23", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CUTprl93", "type": "article", "title": "The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries", "author": [ { "family_name": "Cutler", "given_name": "Curt", "clpid": "Cutler-C-J" }, { "family_name": "Apostolatos", "given_name": "Theocharis A.", "clpid": "Apostolatos-T-A" }, { "family_name": "Bildsten", "given_name": "Lars", "clpid": "Bildsten-L" }, { "family_name": "Finn", "given_name": "Lee Samuel", "clpid": "Finn-L-S" }, { "family_name": "Flanagan", "given_name": "Eanna E.", "clpid": "Flanagan-\u00c9-\u00c9" }, { "family_name": "Kennefick", "given_name": "Daniel", "clpid": "Kennefick-D-J" }, { "family_name": "Markovic", "given_name": "Dragoljub M.", "clpid": "Markovic-D-M" }, { "family_name": "Ori", "given_name": "Amos", "clpid": "Ori-A" }, { "family_name": "Poisson", "given_name": "Eric", "clpid": "Poisson-E" }, { "family_name": "Sussman", "given_name": "Gerald Jay", "clpid": "Sussman-G-J" }, { "family_name": "Thorne", "given_name": "Kip S.", "clpid": "Thorne-K-S" } ], "abstract": "Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary's accumulated orbital phase can be measured to a fractional accuracy \u226a10^-3 and relativistic effects are large, the wave forms will be far more complex and carry more information than has been expected. Improved wave form modeling is needed as a foundation for extracting the waves' information, but is not necessary for wave detection.", "doi": "10.1103/PhysRevLett.70.2984", "issn": "0031-9007", "publisher": "American Physical Society", "publication": "Physical Review Letters", "publication_date": "1993-05-17", "series_number": "20", "volume": "70", "issue": "20", "pages": "2984-2987" }, { "id": "authors:vpm1j-t0f90", "collection": "authors", "collection_id": "vpm1j-t0f90", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:APOprd92", "type": "article", "title": "Rotation halts cylindrical, relativistic gravitational collapse", "author": [ { "family_name": "Apostolatos", "given_name": "Theocharis A.", "clpid": "Apostolatos-T-A" }, { "family_name": "Thorne", "given_name": "Kip S.", "clpid": "Thorne-K-S" } ], "abstract": "It is shown, in a simple analytic example, that an infinitesimal amount of rotation can halt the general relativistic gravitational collapse of a pressure-free cylindrical body. The example is a thin cylindrical shell (a shell with translational symmetry and rotation symmetry), made of counterrotating dust particles. Half of the particles rotate about the symmetry axis in one direction with (conserved) angular momentum per unit rest mass \u03b1, and the other half rotate in the opposite direction with the same \u03b1. It is shown, using C-energy arguments, that the shell can never collapse to a circumference smaller than C=8\u03c0\u03b1\u039b, where \u039b is the shell's nonconserved mass per unit proper length. Equivalently, if R\u2261\u2016\u2202/\u2202\u03c6\u2225\u2202/\u2202z\u2016 is the product of the lengths of the rotational and translational Killing vectors at the shell's location and \u03bb is the shell's conserved rest mass per unit Killing length z, then the shell can never collapse smaller than R=4\u03b1\u03bb. It is also shown that after its centrifugally induced bounce, the shell will oscillate radially and will radiate gravitational waves as it oscillates, the waves will carry away C energy, and this loss of C energy will force the shell to settle down to a static, equilibrium radius.", "doi": "10.1103/PhysRevD.46.2435", "issn": "2470-0010", "publisher": "Physical Review D", "publication": "Physical Review D", "publication_date": "1992-09-15", "series_number": "6", "volume": "46", "issue": "6", "pages": "2435-2444" } ]