Abstract:
In this thesis, some aspects of spacetime coordinates are presented. After discussing
some non-singular coordinates for the Schwartzschild, the Reissner-Nordstr ̈m and the
o
Kerr black hole spacetimes, non-singular Kruskal-like coordinates for different cases of
general circularly symmetric black holes in (2 + 1) dimensions are constructed. The ap-
proach is further extended to construct non-singular coordinates for the rotating BTZ
black hole. As Kruskal-like coordinates do not remove the coordinate singularity for
the extreme BTZ spacetime geometry, the possibility of obtaining Carter-like coordi-
nates is discussed. It is found that these coordinates also do not remove the coordinate
singularity for this geometry.
The Double-null form has great importance in general relativity (GR), especially in
solar-terrestrial relationships, investigation of black hole spacetimes, formulating the
Newman-Penrose formalism and Numerical Relativity etc. In Chapter 3, three di-
mensional spacetimes are classified according to the possibility of converting them to
double-null form. It is found that a class of (2 + 1)−dimensional spacetimes in which
coefficient g02 or g12 is non-zero, cannot be transformed to the double-null form.
In black hole thermodynamics, it has been shown earlier for different spacetimes that
the Einstein field equations at the horizon can be expressed as the first law of black
hole thermodynamics. In Chapter 4, a simpler approach, using the concept of folia-
tion is developed to obtain such results. Using this simpler approach, thermodynamic
identities are established for the Schwarzschild, the Reissner-Nordstr ̈m, the Kerr, and
o
the Kerr-Newmann black holes. An important aspect of this approach is that one has
to essentially deal with an (n − 1)−dimensional induced metric for an n−dimensional
spacetime, which significantly simplifies the calculations to obtain such results.
