Author ORCID Identifier

https://orcid.org/0000-0002-8993-0567

Semester

Fall

Date of Graduation

2025

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Physics and Astronomy

Committee Chair

Maura McLaughlin

Committee Member

Zachariah Etienne

Committee Member

Maria Babuic Hamilton

Committee Member

Paul Cassak

Abstract

Multi-messenger astrophysics opens a new era in our understanding of the most dynamic and energetic systems in the Universe. Correlating gravitational-wave and electromagnetic signals in space and time enables stringent tests of models for core-collapse supernovae, merging supermassive black-hole binaries with accretion disks and jets, and mergers of compact object binaries such as binary neutron stars (BNS) and white dwarfs. Comparisons between models and multi-messenger observations may be used to constrain the neutron-star equation of state (EOS), formation channels for compact-object binaries, and emission mechanisms behind short gamma-ray bursts.

In modeling such astrophysical systems, great success has been achieved by treating the matter in the perfect-fluid limit, and evolving it with the equations of general relativistic hydrodynamics (GRHD), a covariant generalization of the Newtonian Euler equations. To capture the full dynamics when the spacetime itself changes rapidly, i.e. dynamical spacetimes, the GRHD equations must be coupled to an evolution of the spacetime. We describe the spacetime using Einstein’s equations, but these are a set of coupled, nonlinear partial differential equations that admit no closed-form solutions for generic sources; instead, they are solved numerically using numerical relativity. By evolving the fluid equations and Einstein’s equations together, with communication between the two schemes, one obtains a self-consistent description of relativistic fluids in dynamical spacetimes.

In this dissertation we construct such a modeling framework, and use it to model a variety of systems. We begin with the key ingredients to develop such a numerical framework, drawing parallels to solving Maxwell’s equations, and sketching out the core components needed to solve the GRHD equations. We then extend the GRHD equations to singular curvilinear coordinates using the reference-metric approach, and derive the full set of modified equations, which are suitable for numerical implementation. We solve these equations in our newly developed GRHD code, GRoovy, which evolves matter configurations self-consistently with dynamical spacetimes. We present results from a suite of rigorous tests on the GRoovy code, presenting results from two- and three-dimensional shock tests. We then show a number of results from tests in which we model non-rotating and rotating neutron stars (NSs), in both fixed and dynamical spacetimes. We also test our code’s ability to model NSs using realistic equations of state, and neutrino emission in curved spacetimes. Notably, we show that when using a reference metric, we can simulate NSs using spherical and cylindrical coordinates, leading to computational savings on the order of up to ∼104, in the case of spherical coordinates, as compared to Cartesian coordinates.

Finally, we describe further improvements to GRoovy, including Charm++-based parallelization and increased robustness when using realistic equations of state. Using this upgraded version, we model non-axisymmetric instabilities in rapidly rotating NSs that produce transient, elongated “bar” deformations and emit gravitational waves. We present preliminary constraints on the threshold for this instability and examine how that threshold depends on uncertainties in the nuclear EOS.

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