Akbar, Mohammad

Permanent URI for this collectionhttps://hdl.handle.net/10735.1/5766

Mohammad Akbar serves as a Clinical Associate Professor in the department of Mathematical Sciences. His research interests include:

  • General theory of relativity,
  • Differential geometry,
  • Quantum gravity, and
  • Ricci flow.
Dr. Akbar has received several teaching awards since joining the UT Dallas faculty. These include the NSM Dean's Award for Outstanding Teaching (2013 and 2016), the UT Dallas President's Teaching Award (2010), and the UT System Regent's Teaching Award in 2013.


Recent Submissions

Now showing 1 - 1 of 1
  • Item
    Spherical Spacelike Geometries in Static Spherically Symmetric Spacetimes: Generalized Painleve-Gullstrand Coordinates, Foliation, and Embedding
    (Elsevier B.V., 2017-04-06) Akbar, Mohammad; 56212773400 (Akbar, M); Akbar, Mohammad
    It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painleve-Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painleve-Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.

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