Dynamical gravastar simulated horizon from the Tolman-Oppenheimer-Volkoff equation initial value problem with relativistic matter
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| Format: | Preprint |
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2023
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| _version_ | 1866909692021702656 |
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| author | Adler, Stephen L. Doherty, Brent |
| author_facet | Adler, Stephen L. Doherty, Brent |
| contents | We continue the study of "dynamical gravastars", constructed by solving the Tolman-Oppenheimer-Volkoff (TOV) equations with relativistic matter, undergoing a phase transition at high pressure to a state with negative energy density. We define the "simulated horizon" as the horizon-like structure that appears, and which is a well-defined concept within the class of static, spherically symmetric metrics. Since the "simulated horizon" occurs at a radius above where the pressure-induced phase transition is postulated to occur, it is solely a property of the TOV equation with relativistic matter, for appropriate small radius initial conditions. We survey the formation of a simulated horizon from this point of view. Rescaling the problem to fixed initial radius, we plot the "phase diagram" in the initial pressure--initial mass plane, showing the range of parameters where a simulated horizon dynamically forms. Reformulating the TOV equations in rescaling-invariant form yields improved numerical results for the "phase diagram", and gives a simplified model for further study consisting of a 2-dimensional autonomous system of first order differential equations. Our analysis gives a simple, natural answer to the question of how the radii where the phase transitions postulated in previous models of exotic compact objects are dynamically determined. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_13380 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamical gravastar simulated horizon from the Tolman-Oppenheimer-Volkoff equation initial value problem with relativistic matter Adler, Stephen L. Doherty, Brent General Relativity and Quantum Cosmology We continue the study of "dynamical gravastars", constructed by solving the Tolman-Oppenheimer-Volkoff (TOV) equations with relativistic matter, undergoing a phase transition at high pressure to a state with negative energy density. We define the "simulated horizon" as the horizon-like structure that appears, and which is a well-defined concept within the class of static, spherically symmetric metrics. Since the "simulated horizon" occurs at a radius above where the pressure-induced phase transition is postulated to occur, it is solely a property of the TOV equation with relativistic matter, for appropriate small radius initial conditions. We survey the formation of a simulated horizon from this point of view. Rescaling the problem to fixed initial radius, we plot the "phase diagram" in the initial pressure--initial mass plane, showing the range of parameters where a simulated horizon dynamically forms. Reformulating the TOV equations in rescaling-invariant form yields improved numerical results for the "phase diagram", and gives a simplified model for further study consisting of a 2-dimensional autonomous system of first order differential equations. Our analysis gives a simple, natural answer to the question of how the radii where the phase transitions postulated in previous models of exotic compact objects are dynamically determined. |
| title | Dynamical gravastar simulated horizon from the Tolman-Oppenheimer-Volkoff equation initial value problem with relativistic matter |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2309.13380 |