5 research outputs found
Interior of a Schwarzschild black hole revisited
The Schwarzschild solution has played a fundamental conceptual role in
general relativity, and beyond, for instance, regarding event horizons,
spacetime singularities and aspects of quantum field theory in curved
spacetimes. However, one still encounters the existence of misconceptions and a
certain ambiguity inherent in the Schwarzschild solution in the literature. By
taking into account the point of view of an observer in the interior of the
event horizon, one verifies that new conceptual difficulties arise. In this
work, besides providing a very brief pedagogical review, we further analyze the
interior Schwarzschild black hole solution. Firstly, by deducing the interior
metric by considering time-dependent metric coefficients, the interior region
is analyzed without the prejudices inherited from the exterior geometry. We
also pay close attention to several respective cosmological interpretations,
and briefly address some of the difficulties associated to spacetime
singularities. Secondly, we deduce the conserved quantities of null and
timelike geodesics, and discuss several particular cases in some detail.
Thirdly, we examine the Eddington-Finkelstein and Kruskal coordinates directly
from the interior solution. In concluding, it is important to emphasize that
the interior structure of realistic black holes has not been satisfactorily
determined, and is still open to considerable debate.Comment: 15 pages, 7 figures, Revtex4. V2: Version to appear in Foundations of
Physic
Quantization of the interior Schwarzschild black hole
We study a Hamiltonian quantum formalism of a spherically symmetric
space-time which can be identified with the interior of a Schwarzschild black
hole. The phase space of this model is spanned by two dynamical variables and
their conjugate momenta. It is shown that the classical Lagrangian of the model
gives rise the interior metric of a Schwarzschild black hole. We also show that
the the mass of such a system is a Dirac observable and then by quantization of
the model by Wheeler-DeWitt approach and constructing suitable wave packets we
get the mass spectrum of the black hole.Comment: 12 pages, 1 figure, revised versio