Date of Award
M.S. in Physics
University of Mississippi
Einstein’s field equations delineate the intricate dance between the geometry of spacetime and the energy-momentum. It is astonishing to realize how spacetime geometry is influenced by the presence of matter and energy and how this in turn affects the dynamics of matter in the spacetime background. Matter and energy are quantum mechanical in nature but the geometry of spacetime is a mathematical theory of a 4-dimensional pseudo-Riemannian manifold. Causal set theory is one of the approaches to reconcile quantum mechanics and gravity (an emergent property of spacetime geometry), and therefore it is an approach to quantum gravity. In this approach, the spacetime continuum is assumed to be discrete at very small scales (of Planckian order). The discrete points in a causal set can be seen as a continuum of spacetime if they can be embedded in a manifold such that the causal structure is preserved. In this regard, a manifold can be constructed by embedding a causal set preserving causal information between the neighboring points.
In this thesis, the area-like scaling of a black hole entropy is studied in the causal set approach and the possibility of the horizon-crossing links as a source of black hole entropy is examined in detail. We calculate the number of horizon-crossing links for a Schwarzschild black hole using a computer simulation and observe a linear scaling with the horizon area. Later, we impose a maximal/minimal condition to calculate the number of surface-crossing links close to a particular spacelike hypersurface for a generalized ��-dimensional flat black holes. Excellent linearity between the number of horizon-crossing links and the area of the horizon is observed upon computer simulation as well as numerical integration using MATLAB.
Dhital, Ayush, "Black Hole Entropy in the Causal Set Approach" (2023). Electronic Theses and Dissertations. 2674.