James Ripple (Physics, class of 24) along with Assistant Professor of Physics Anish Agashe recently published a research article titled, "The Tolman VII space-time in the presence of charge and a cosmological constant", in European Physical Journal C.
The authors had been working on this article since the summer of 2023 and it took slightly over a year for it to be fully prepared. However, the story of this article really began 85 years earlier in 1939 when Richard C. Tolman wrote a paper containing eight different solutions of Einstein field equations (EFEs). The EFEs are the equations of general theory of relativity that govern the dynamics of gravitational fields. The seventh solution in this paper came to be known as the Tolman VII solution. In the original article, Tolman discarded his seventh solution writing that it "is so complicated that the solution is not a convenient one for physical considerations". Over the years though, it was realised that the Tolman VII solution is actually physically viable and, is in fact, a decent candidate to model a neutron star (at least some features of one).
This is what motivated the authors to look further into the solution. The goal was to derive a more generalised form of the solution that includes both electric charge and the cosmological constant. Doing this led to many novel features, e.g., new bounds on the mass to radius ratio were found that allow for trapping of photons. In strong gravity systems like a neutron star, photons (and neutrinos) can be trapped inside the star forever as they move in circular orbits. This is a purely general relativistic phenomenon which can affect the lifespan of neutron stars.
The authors were also able to show that the Tolman VII solution can be surrounded by a new kind of space-time (called the Nariai solution). Doing this may allow one to construct two-mass solutions to EFEs (space-time describing two stars). The two-body problem in general relativity is an open problem which does not have a general solution. However, a few particular solutions exist. In one type of these solutions, the two bodies are held apart from each other due to the repulsive cosmological constant. Now that the authors were able to include the cosmological constant in the Tolman VII solution, their next goal is to construct a two-mass solution with it. This would be a good candidate to represent a binary neutron star system.
Ripple graduated summa cum laude with double majors (physics and mathematics) and double minors (astrophysics and computer science) in Spring 2024. He is currently working as a photogrammetrics software engineer at Reliance Test and Technology. He is also collaborating with Agashe's research group at SMCM and plans to apply for PhD positions next year.
This research was partially supported by the faculty development grant awarded to Agashe in Spring 2023.
