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(8)
Black Hole Thermodynamics
Equation of Motion
General Relativity
Loop Quantum Gravity
symplectic structure
Thermodynamics
Angular Momentum
First Order
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Surface terms, asymptotics and thermodynamics of the Holst action
Surface terms, asymptotics and thermodynamics of the Holst action,10.1088/02649381/27/20/205015,Classical and Quantum Gravity,Alejandro Corichi,Edwar
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Surface terms, asymptotics and thermodynamics of the Holst action
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Citations: 3
)
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Alejandro Corichi
,
Edward WilsonEwing
We consider a firstorder formalism for
general relativity
derived from the Holst action. This action is obtained from the standard PalatiniHilbert form by adding a topologicallike term and can be taken as the starting point for
loop quantum gravity
and spin foam models. The equations of motion derived from the Holst action are, nevertheless, the same as in the Palatini formulation. Here we study the form of the surface terms of the action for general boundaries as well as the symplectic current in the covariant formulation of the theory. Furthermore, we analyze the behavior of the surface terms in asymptotically flat spacetimes. We show that the contribution to the
symplectic structure
from the Holst term vanishes and one obtains the same asymptotic expressions as in the Palatini action. It then follows that the asymptotic Poincaré symmetries and conserved quantities such as energy, linear momentum and relativistic
angular momentum
found here are equivalent to those obtained from the standard Arnowitt, Deser and Misner formalism. Finally, we consider the Euclidean approach to
black hole thermodynamics
and show that the onshell Holst action, when evaluated on some static solutions containing horizons, yields the standard thermodynamical relations.
Journal:
Classical and Quantum Gravity  CLASS QUANTUM GRAVITY
, vol. 27, no. 20, 2010
DOI:
10.1088/02649381/27/20/205015
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Citation Context
(1)
...D =d +ω of the internal vector nI = ηI a na associated with the surface normal na of ∂M. For an exhaustive analysis of surface terms within the Holst setting, we strongly recommend [
13
]...
Wolfgang M. Wieland
.
Complex Ashtekar Variables and Reality Conditions for Holst’s Action
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Citations
(3)
Black hole entropy from the SU(2)invariant formulation of type I isolated horizons
(
Citations: 5
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Complex Ashtekar variables and reality conditions for Holst's action
(
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Published in 2010.
Complex Ashtekar Variables and Reality Conditions for Holst’s Action
Wolfgang M. Wieland
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Annales Henri Poincare  ANN HENRI POINCARE
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