Modifcations to gravitational waves due to matter shells
- Authors: Naidoo, Monogaran
- Date: 2021-10-29
- Subjects: Gravitational waves , General relativity (Physics) , Einstein field equations , Cosmology , Matter shells
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/191118 , vital:45062 , 10.21504/10962/191119
- Description: As detections of gravitational waves (GWs) mount, the need to investigate various effects on the propagation of these waves from the time of emission until detection also grows. We investigate how a thin low density dust shell surrounding a gravitational wave source affects the propagation of GWs. The Bondi-Sachs (BS) formalism for the Einstein equations is used for the problem of a gravitational wave (GW) source surrounded by a spherical dust shell. Using linearised perturbation theory, we and the geometry of the regions exterior to, interior to and within the shell. We and that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. This finding is novel. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable; but the effect would be measurable if a GW event were to occur with a source surrounded by a massive shell and with the radius of the shell and the wavelength of the GWs of the same order. We extended our investigation to astrophysical scenarios such as binary black hole (BBH) mergers, binary neutron star (BNS) mergers, and core collapse supernovae (CCSNe). In these scenarios, instead of a monochromatic GW source, as we used in our initial investigation, we consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. We show that GW echoes that are claimed to be present in the Laser Interferometer Gravitational-Wave Observatory (LIGO) data of certain events, could not have been caused by a matter shell. We do and, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity. Substantial use is made of computer algebra in these investigations. In setting the scene for our investigations, we trace the evolution of general relativity (GR) from Einstein's postulation in 1915 to vindication of his theory with the confirmation of the existence of GWs a century later. We discuss the implications of our results to current and future considerations. Calculations of GWs, both analytical and numerical, have normally assumed their propagation from source to a detector on Earth in a vacuum spacetime, and so discounted the effect of intervening matter. As we enter an era of precision GW measurements, it becomes important to quantify any effects due to propagation of GWs through a non-vacuum spacetime Observational confirmation of the modification effect that we and in astrophysical scenarios involving black holes (BHs), neutron stars (NSs) and CCSNe, would also enhance our understanding of the details of the physics of these bodies. , Thesis (PhD) -- Faculty of Science, Mathematics (Pure and Applied), 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Naidoo, Monogaran
- Date: 2021-10-29
- Subjects: Gravitational waves , General relativity (Physics) , Einstein field equations , Cosmology , Matter shells
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/191118 , vital:45062 , 10.21504/10962/191119
- Description: As detections of gravitational waves (GWs) mount, the need to investigate various effects on the propagation of these waves from the time of emission until detection also grows. We investigate how a thin low density dust shell surrounding a gravitational wave source affects the propagation of GWs. The Bondi-Sachs (BS) formalism for the Einstein equations is used for the problem of a gravitational wave (GW) source surrounded by a spherical dust shell. Using linearised perturbation theory, we and the geometry of the regions exterior to, interior to and within the shell. We and that the dust shell causes the gravitational wave to be modified both in magnitude and phase, but without any energy being transferred to or from the dust. This finding is novel. In the context of cosmology, apart from the gravitational redshift, the effects are too small to be measurable; but the effect would be measurable if a GW event were to occur with a source surrounded by a massive shell and with the radius of the shell and the wavelength of the GWs of the same order. We extended our investigation to astrophysical scenarios such as binary black hole (BBH) mergers, binary neutron star (BNS) mergers, and core collapse supernovae (CCSNe). In these scenarios, instead of a monochromatic GW source, as we used in our initial investigation, we consider burst-like GW sources. The thin density shell approach is modified to include thick shells by considering concentric thin shells and integrating. Solutions are then found for these burst-like GW sources using Fourier transforms. We show that GW echoes that are claimed to be present in the Laser Interferometer Gravitational-Wave Observatory (LIGO) data of certain events, could not have been caused by a matter shell. We do and, however, that matter shells surrounding BBH mergers, BNS mergers, and CCSNe could make modifications of order a few percent to a GW signal. These modifications are expected to be measurable in GW data with current detectors if the event is close enough and at a detectable frequency; or in future detectors with increased frequency range and amplitude sensitivity. Substantial use is made of computer algebra in these investigations. In setting the scene for our investigations, we trace the evolution of general relativity (GR) from Einstein's postulation in 1915 to vindication of his theory with the confirmation of the existence of GWs a century later. We discuss the implications of our results to current and future considerations. Calculations of GWs, both analytical and numerical, have normally assumed their propagation from source to a detector on Earth in a vacuum spacetime, and so discounted the effect of intervening matter. As we enter an era of precision GW measurements, it becomes important to quantify any effects due to propagation of GWs through a non-vacuum spacetime Observational confirmation of the modification effect that we and in astrophysical scenarios involving black holes (BHs), neutron stars (NSs) and CCSNe, would also enhance our understanding of the details of the physics of these bodies. , Thesis (PhD) -- Faculty of Science, Mathematics (Pure and Applied), 2021
- Full Text:
- Date Issued: 2021-10-29
Numerical evolution of plane gravitational waves
- Authors: Hakata, Jonathan
- Date: 2021-10
- Subjects: Gravitational waves , Space and time , Einstein field equations , de Sitter metric , Perturbed spacetime
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/190248 , vital:44977
- Description: Unlike electromagnetic waves, gravitational waves self interact. This interaction is non-linear and can have very interesting properties which effect the curvature of space-time. A gravitational plane wave collider, implemented in the Python package COFFEE [20] that been developed in recent years by the Otago relativity group and implements the method of lines, can be reliably used to study this self-interaction. This was shown to work well numerically as profounded by Frauendiener, Stevens and Whale in 2014 [24]. For this reason, COFFEE will be used to study these gravitational wave propagations and subsequently collisions. The Einstein field equations are formulated as a well-posed initial boundary value problem (IBVP) in the Friedrich-Nagy gauge [26] and due to the large class of boundary conditions admitted by this framework, a variety of investigations into the propagation of plane gravitational waves could be carried out. This study focuses on the propagation of plane gravitational waves in the de Sitter (dS) space-time, which is the maximally symmetric solution of the Einstein’s vacuum field equations with a positive cosmological constant λ. There is substantial cosmological evidence that our universe is asymptotically de Sitter, yet no work, analytical nor numerical, has been done on gravitational plane waves propagating on such a space-time, mainly due to the increased complexity from the non-vanishing λ. Firstly, it is found analytically that with an arbitrary cosmological constant λ and a non-vanishing energy momentum tensor, the constraints will propagate. This means that we still have a wellposed IBVP, which is nontrivial since the Friedrich-Nagy gauge has only been shown to lead to a wellposed IBVP without matter [26]. Using this system, we consider one ingoing wave propagating on said space-time in vacuum. The area of the ingoing wave profile is varied and inferences are made about the different phenomena that arise in the curvature of space-time during the evolution. It is found that there exists a critical value of the wave’s area, ac, whereby taking the area below this value the system asymptotes to its initial state, and above the system diverges, indicating the presence of a singularity. Furthermore, we define an expansion parameter H to measure how the gravitational waves influence the accelerated expansion, generalising (numerically) results of Tsamis and Woodard. , Thesis (MSc) -- Faculty of Science, Mathematics, 2021
- Full Text:
- Date Issued: 2021-10
- Authors: Hakata, Jonathan
- Date: 2021-10
- Subjects: Gravitational waves , Space and time , Einstein field equations , de Sitter metric , Perturbed spacetime
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/190248 , vital:44977
- Description: Unlike electromagnetic waves, gravitational waves self interact. This interaction is non-linear and can have very interesting properties which effect the curvature of space-time. A gravitational plane wave collider, implemented in the Python package COFFEE [20] that been developed in recent years by the Otago relativity group and implements the method of lines, can be reliably used to study this self-interaction. This was shown to work well numerically as profounded by Frauendiener, Stevens and Whale in 2014 [24]. For this reason, COFFEE will be used to study these gravitational wave propagations and subsequently collisions. The Einstein field equations are formulated as a well-posed initial boundary value problem (IBVP) in the Friedrich-Nagy gauge [26] and due to the large class of boundary conditions admitted by this framework, a variety of investigations into the propagation of plane gravitational waves could be carried out. This study focuses on the propagation of plane gravitational waves in the de Sitter (dS) space-time, which is the maximally symmetric solution of the Einstein’s vacuum field equations with a positive cosmological constant λ. There is substantial cosmological evidence that our universe is asymptotically de Sitter, yet no work, analytical nor numerical, has been done on gravitational plane waves propagating on such a space-time, mainly due to the increased complexity from the non-vanishing λ. Firstly, it is found analytically that with an arbitrary cosmological constant λ and a non-vanishing energy momentum tensor, the constraints will propagate. This means that we still have a wellposed IBVP, which is nontrivial since the Friedrich-Nagy gauge has only been shown to lead to a wellposed IBVP without matter [26]. Using this system, we consider one ingoing wave propagating on said space-time in vacuum. The area of the ingoing wave profile is varied and inferences are made about the different phenomena that arise in the curvature of space-time during the evolution. It is found that there exists a critical value of the wave’s area, ac, whereby taking the area below this value the system asymptotes to its initial state, and above the system diverges, indicating the presence of a singularity. Furthermore, we define an expansion parameter H to measure how the gravitational waves influence the accelerated expansion, generalising (numerically) results of Tsamis and Woodard. , Thesis (MSc) -- Faculty of Science, Mathematics, 2021
- Full Text:
- Date Issued: 2021-10
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