| Abstract : | We investigate how strongly the Hoop Conjecture (HC) is coupled with
Einstein’s theory of gravity and examine whether HC is satisfied even when we deviate
from classical solutions. We have carried out a detailed study to test the validity of HC
for classical black holes (BH) and corresponding horizonless compact stars (HCS) as well
as for quantum corrected Schwarzschild black hole and corresponding quantum corrected
horizonless compact stars. HC gives an inequality between mass and circumference,
in the first part, we carried out calculations for different types of radius corresponding to
different circumference, areas and volumes in 4 different spacetimes, namely Minkowski,
FRW (Friedmann–Robertson–Walker), LTB (Lemaitre-Tolman-Bondi) and Schwarzschild.
Further, in the second part, we carried out calculations for two different definitions of
masses namely ADM mass and mass enclosed (M_in) within a sphere of some circumference C. From our analysis, it is clear that when we use the mass definition as the ADM mass all 4 classical black holes satisfy the HC, however quantum corrected
Schwarzschild BH violates the HC. All HCS satisfy the HC, except charged spherical
HCS. On the other hand, when we have M_in as the definition of mass all black holes, except
Kerr Newman and quantum corrected Schwarzschild black holes satisfy the HC. All HCS also satisfy HC for this definition of mass. Our analysis shows that for M_in as the mass definition,
H <= 1 is a general characteristic satisfied by both BH and HCS or in other words, the HC
does not differentiate between a BH and HCS when we use M_{in} as the mass definition.
We would like to extend the HC, further to black holes formed from exotic matter whose
horizons have hair and check whether the HC is satisfied or violated. |
