Insights into the Evolution of Horizons from Non-Orthogonal Temporal Coordinates

Details Insights into the Evolution of Horizons from Non-Orthogonal Temporal Coordinates Insights into the Evolution of Horizons from Non-Orthogonal Temporal Coordinates

2007-06-24

arxiv.org/abs/0706.3525v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

40 pages, 14 figures, Invited talk presented at the Herbert W. Jones Memorial Seminar, 19 April 2007, Florida A&M University

Scientific paper

The introduction of coordinates representing the points of view of various observers results in the possibility of horizons when acceleration and gravitation are included. A horizon is a surface of possible light beams in a region of space of finite distance from the observer, which means that since nothing travels faster than light, events on the far side of a horizon cannot influence those on the causal side. A black hole has such a horizon, where some radially outgoing light beams can never reach a distant (or even nearby) observer. However, since one suspects that black holes can swallow energy, and even evaporate by Hawking radiation, such horizons must take on a time dependency. A naive introduction of temporal dependency results in infinities (singularities) in energy densities, suggesting in such descriptions that an in-falling observer would encounter a hard surface at the horizon. However, if coordinates representing space-time as analogous to a "flowing river" are used to describe the dynamics of a black hole, no such singularities are encountered. Such a parameterization of time dependent horizons will be offered in this presentation. A Penrose space-time diagram (which represents the entire space-time on a finite diagram with light beams always moving at a 45 degree angle to vertical) describing the growth and evaporation of an example black hole, along with the resulting coordinate anomaly, will be constructed.

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