Weakly Isolated horizons: first order actions and gauge symmetries
Por:
Corichi, Alejandro, Reyes, Juan D., Vukasinac, Tatjana
Publicada:
20 abr 2017
Categoría:
Physics and astronomy (miscellaneous)
Resumen:
The notion of Isolated Horizons has played an important role in
gravitational physics, being useful from the characterization of the
endpoint of black hole mergers to (quantum) black hole entropy. With an
eye towards a canonical formulation we consider general relativity in
terms of connection and vierbein variables and their corresponding first
order actions. We focus on two main issues: (i) The role of the internal
gauge freedom that exists, in the consistent formulations of the action
principle, and (ii) the role that a 3 + 1 canonical decomposition has in
the allowed internal gauge freedom. More concretely, we clarify in
detail how the requirement of having well posed variational principles
compatible with general weakly isolated horizons (WIHs) as internal
boundaries does lead to a partial gauge fixing in the first order
descriptions used previously in the literature. We consider the standard
Hilbert-Palatini action together with the Holst extension (needed for a
consistent 3 + 1 decomposition), with and without boundary terms at the
horizon. We show in detail that, for the complete configuration
space-with no gauge fixing-, while the Palatini action is differentiable
without additional surface terms at the inner WIH boundary, the more
general Holst action is not. The introduction of a surface term at the
horizon-that renders the action for asymptotically flat configurations
differentiable-does make the Holst action differentiable, but only if
one restricts the configuration space and partially reduces the internal
Lorentz gauge. For the second issue at hand, we show that upon
performing a 3 + 1 decomposition and imposing the time gauge, there is a
further gauge reduction of the Hamiltonian theory in terms of
Ashtekar-Barbero variables to a U(1)-gauge theory on the horizon. We
also extend our analysis to the more restricted boundary conditions of
(strongly) isolated horizons as inner boundary. We show that even when
the Holst action is indeed differentiable without the need of additional
surface terms or any gauge fixing for Type I spherically symmetric
(strongly) isolated horizons-and a preferred foliation-, this result
does not go through for more general isolated or weakly isolated
horizons. Our results represent the first comprehensive study of these
issues and clarify some contradictory statements found in the
literature.
Filiaciones:
Corichi, Alejandro:
Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, UNAM Campus Morelia,A Postal 61-3, Morelia 58090, Michoacan, Mexico
Penn State Univ, Ctr Fundamental Theory, Inst Gravitat & Cosmos, University Pk, PA 16802 USA
Reyes, Juan D.:
Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, UNAM Campus Morelia,A Postal 61-3, Morelia 58090, Michoacan, Mexico
Univ Autonoma Chihuahua, Fac Ingn, Nuevo Campus Univ, Chihuahua 31125, Mexico
Vukasinac, Tatjana:
Univ Michoacana, Fac Ingn Civil, Morelia 58000, Michoacan, Mexico
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