Level: MSci, MSc
Title: Marginally stable circular orbits for higher dimensional black holes
Supervisor:

Dr Shabnam Beheshti
Research Area: Geometry and Analysis
Description:

The study of test bodies and light rays in circular orbits around massive objects (e.g., black holes, neutron stars, etc.) plays a key role in understanding and predicting astrophysical phenomena such as estimating transition regions between inspiralling and merging phases of binary systems, estimating inner radii of accretion disks.

 

This project will involve the investigation of a sequence of papers in which necessary and sufficient conditions for determining marginally stable circular orbits (MSCOs) are derived under symmetry assumptions. The student will first review the classical potential method and contrast it with the geometric approach given in [1]. Surprisingly, the MSCO conditions in the stationary axisymmetric case reduce to understanding an algebraic system of equations! She/he will then modify existing Mathematica code to begin addressing circular orbits of higher-dimensional black holes. Depending on progress, work done in this latter case could constitute new scientific research in theoretical high-energy astrophysics.

  1. S. Beheshti and E. Gasperin, Marginally Stable Circular Orbits in stationary axisymmetric spacetimes, Phys. Rev. D 94 024015 (2016).
Further Reading:

  • C. Misner, K. Thorne and J. Wheeler. Gravitation, WH Freeman New York, 1973.

  • T. Igata and H. Ishihara, Toroidal spiral Nambu-Goto strings around higher-dimensional black holes, Phys. Rev. D 82 044014 (2010).

  • A. Chowdhury, M. Patil, D. Malafarina and P.Joshi, Circular geodesics and accretion disks in the Janis-Newman-Winicour and gamma metric spacetimes, Phys. Rev. D 85 104031 (2012).
Key Modules:

MTH5102 Calculus III

MTH6132 Relativity
Other Information:

Knowledge of Mathematica (or willingness to learn) is required for this project.
Current Availability: Yes