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Gravity

Student Researchers

Students play an important part in our research group, and we work with both undergraduate and graduate students. Our research is interdisciplinary, combining theoretical physics, numerical analysis, and computer science. We have projects in each of these areas, and some that encompass all of them.

Possible Projects

We have research projects in several areas, including:

  1. Dynamics in Post-Newtonian Gravity
  2. Chaos in the General Relativity
  3. Tests of General Relativity
  4. Apparent Horizons
  5. Relativistic Fluid Dynamics
  6. Gravitational Waves
  7. Wavelets and Adaptive Mesh Refinement
  8. Optimization and Computer Algorithms

Getting Started

The best way to get started is to contact either David Neilsen or Eric Hirschmann to set up an appointment to discuss research possibilities. The learning curve in this type of research is usually long, so guidance from a research advisor can help plan the best path for individual students. We often have students concentrate first on one area or another, depending on their background and interests. Then over time, projects expand into other areas.

We have collected some information for students beginning research in relativity below.

A Note to Remember

The BYU campus is at the foot of the beautiful Wasatch mountains, so we'll begin with a mountain climbing analogy. Learning something new is like climbing a mountain. We begin the journey with a lot of excitement and energy. After cresting the foothills, we exhilarate in the view back to where we started, but turning forward to the mountain again, we notice that the peak now seems even further away. We now see new obstacles that were hidden from the base. Our energy and excitement may flag, and the goal seems to recede. The way may be long and difficult, but the challenges are known. With preparation and guidance, we can continue the journey with confidence. This process can repeat many times, until we finally are ready to ascend the summit. So, be prepared to learn new things, be patient with yourself when the process takes time, and remember to enjoy the journey.

Computational Physics

One good starting point for research is with computational physics. Students learn numerical algorithms and basic programming to solve simple dynamical problems. The problems are can be drawn from beginning physics classes, such as Newtonian gravity and electromagnetism. Extensions to include relativistic effects make connection to general relativity and astrophysics. While working on these problems, the principles of relativity can be learned over time.

We have collected some simple examples of computational physics that are available on Github. As many problems in numerical relativity require solving differential equations, these examples focus on these problems. The examples are coded in Julia, a modern programming language similar to Python. The codes can be run in Jupyter notebooks, which provide a nice interface to scientific computation and plotting. This is a new project, so the documentation and examples are not yet complete. They will be expanded and improved over time, perhaps by interested students like you.

This code can be downloaded from the Numex.jl Repository on Github with documentation on Github Pages. As an example, the notebook PostNewtonianBinaryOrbits.ipynb explores binary orbits in both Newtonian gravity and the post-Newtonian approximation to general relativity.

binaryPN0.gif
Eccentric orbit with Newtonian Gravity
binaryPN0.gif
Eccentric orbit with Newtonian Gravity
binaryPN2.gif
Relativistic Effects, calculated here with second-Order Post-Newtonian corrections, cause the same orbit to precess.
binaryPN2.gif
Relativistic Effects, calculated here with second-Order Post-Newtonian corrections, cause the same orbit to precess.

Numerical Relativity

Numerical Relativity is the branch of general relativity that focuses on methods for solving the Einstein equations on computers. This includes finding formalisms for writing the equations that are adapted for numerical work, developing numerical algorithms for solving the equations, and finding efficient computational methods to the equations.

A great introduction to numerical relativity is

  • Numerical Relativity: Starting From Scratch, by Thomas Baumgarte and Stuart Shapiro

A good book to learn about numerical solutions of differential equations is

  • Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-dependent Problems, by Randall J. LeVeque

More advanced books in numerical relativity include:

  • Numerical Relativity: Solving Einstein's Equations on the Computer, by Thomas Baumgarte and Stuart Shapiro
  • Relativistic Hydrodynamics, by Luciano Rezzolla and Olindo Zanotti
  • Introduction to 3+1 Numerical Relativity, by Miguel Alcubierre

General Relativity

There are several good textbooks for learning general relativity. At most universities in the US, general relativity is taught as a senior or graduate student-level, so most books are at this level. Some books that are easiest for undergraduates are

  • A First Course in General Relativity, by Bernard Schutz
  • Introducing Einstein's Relativity: A Deeper Understanding, by Ray d'Inverno and James Vickers
  • Gravity: An Introduction to Einstein's General Relativity, by James Hartle