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137
Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes, Class.Quan.Grav
"... Abstract. A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes and can handle more general situations like: (i) spacetimes which are not asymptotically flat ( ..."
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Cited by 24 (3 self)
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Abstract. A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes and can handle more general situations like: (i) spacetimes which are not asymptotically flat (like the de Sitter spacetime) and (ii) spacetimes with multiple horizons having different temperatures (like the Schwarzschildde Sitter spacetime) and provide a consistent interpretation for temperature, entropy and energy. I show that it is possible to write Einstein’s equations for a spherically symmetric spacetime in the form TdS −dE = PdV near any horizon of radius a with S = (1/4)(4πa2), E  = (a/2) and the temperature T determined from the surface gravity at the horizon. The pressure P is provided by the source of the Einstein’s equations and dV is the change in the volume when the horizon is displaced infinitesimally. The same results can be obtained by evaluating the quantum mechanical partition function without using Einstein’s equations or WKB approximation for the action. Both the classical and quantum analysis provide a simple and consistent interpretation of entropy and energy for de Sitter spacetime as well as for (1 + 2) dimensional gravity. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. The approach also shows that the de Sitter horizon — like the Schwarzschild horizon — is effectively one dimensional as far as the flow of information is concerned, while the Schwarzschildde Sitter, ReissnerNordstrom horizons are not. The implications for spacetimes with multiple horizons are discussed.
HigherDimensional Algebra and PlanckScale Physics
 IN PHYSICS MEETS PHILOSOPHY AT THE PLANCK LENGTH
, 1999
"... This is a nontechnical introduction to recent work on quantum gravity using ideas from higherdimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `backgroundfree quantum theory with local degrees of freedom propagating causally'. We describe ..."
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Cited by 24 (4 self)
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This is a nontechnical introduction to recent work on quantum gravity using ideas from higherdimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `backgroundfree quantum theory with local degrees of freedom propagating causally'. We describe the insights provided by work on topological quantum field theories such as quantum gravity in 3dimensional spacetime. These are backgroundfree quantum theories lacking local degrees of freedom, so they only display some of the features we seek. However, they suggest a deep link between the concepts of `space' and `state', and similarly those of `spacetime' and `process', which we argue is to be expected in any backgroundfree quantum theory. We sketch how higherdimensional algebra provides the mathematical tools to make this link precise. Finally, we comment on attempts to formulate a theory of quantum gravity in 4dimensional spacetime using `spin networks' and `spin foams'.
Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
, 2009
"... Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant models in 3 dimensions include Einstein gravity in Chern–Simons form, as w ..."
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Cited by 21 (7 self)
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Einstein gravity in both 3 and 4 dimensions, as well as some interesting generalizations, can be written as gauge theories in which the connection is a Cartan connection for geometry modeled on a symmetric space. The relevant models in 3 dimensions include Einstein gravity in Chern–Simons form, as well as a new formulation of topologically massive gravity, with arbitrary cosmological constant, as a single constrained Chern–Simons action. In 4 dimensions the main model of interest is MacDowell–Mansouri gravity, generalized to include the Immirzi parameter in a natural way. I formulate these theories in Cartan geometric language, emphasizing also the role played by the symmetric space structure of the model. I also explain how, from the perspective of these Cartangeometric formulations, both the topological mass in 3d and the Immirzi parameter in 4d are the result of nonsimplicity of the Lorentz Lie algebra so(3, 1) and its relatives. Finally, I suggest how the language of Cartan geometry provides a guiding principle for elegantly reformulating any ‘gauge theory of geometry’.
In defence of naiveté: The conceptual status of lagrangian quantum field theory
 SYNTHESE 151
, 2001
"... I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive ’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conc ..."
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Cited by 20 (6 self)
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I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (that is, the ‘naive ’ quantum field theory used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian quantum field theory has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too illdefined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational work.
Group actions on Lorentz spaces, mathematical aspects: a survey, The Einstein equations and the large scale behavior of gravitational fields
"... From a purely mathematical viewpoint, one can say that most recent works in Lorentz geometry, concern group actions on Lorentz manifolds. For instance, the three major themes: space form problem of Lorentz homogeneous spacetimes, the completeness problem, and the classification problem of large isom ..."
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Cited by 18 (11 self)
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From a purely mathematical viewpoint, one can say that most recent works in Lorentz geometry, concern group actions on Lorentz manifolds. For instance, the three major themes: space form problem of Lorentz homogeneous spacetimes, the completeness problem, and the classification problem of large isometry groups of Lorentz manifolds, all deal with group actions. However, in the first two cases, actions are “zen ” (e.g. proper), and in the last, the action is violent (i.e. with strong dynamics). We will survey recent progress in these themes, but we will focus attention essentially on the last one, that is, on Lorentz dynamics. This work is partially supported by the ACI ”Structures géométriques
(2+1)Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
, 2007
"... We perform a nonperturbative sum over geometries in a (2+1)dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an additional notion of order on the discrete, causal geometrie ..."
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Cited by 16 (6 self)
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We perform a nonperturbative sum over geometries in a (2+1)dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an additional notion of order on the discrete, causal geometries. This simplifies the combinatorial problem of counting geometries just enough to enable us to calculate the transfer matrix between boundary states labelled by the area of the spatial universe, as well as the corresponding quantum Hamiltonian of the continuum theory. This is the first time in dimension larger than two that a Hamiltonian has been derived from such a model by mainly analytical means, and opens the way for a better understanding of scaling and renormalization issues.
New variables for classical and quantum gravity in all dimensions
 IV. Matter coupling”, Class. Quantum Grav
, 2013
"... Abstract We employ the techniques introduced in the companion papers ..."
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Cited by 14 (6 self)
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Abstract We employ the techniques introduced in the companion papers
Combinatorial quantisation of Euclidean gravity in three dimensions
, 2000
"... In the ChernSimons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat Gconnections, where G is a typically noncompact Lie group which depends on the signature of spacetime and the cosmological constant. For Euclidean signature and vanishing c ..."
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Cited by 13 (11 self)
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In the ChernSimons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat Gconnections, where G is a typically noncompact Lie group which depends on the signature of spacetime and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the threedimensional Euclidean group. For this case the Poisson structure of the moduli space is given explicitly in terms of a classical rmatrix. It is shown that the quantum Rmatrix of the quantum double D(SU(2)) provides a quantisation of that Poisson structure. MSC 17B37, 81R50, 81S10, 83C45 1
Lessons from (2+1)dimensional quantum gravity
, 2007
"... Proposals that quantum gravity gives rise to noncommutative spacetime geometry and deformations of Poincaré symmetry are examined in the context of (2+1)dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck’s constant and the ..."
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Cited by 13 (6 self)
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Proposals that quantum gravity gives rise to noncommutative spacetime geometry and deformations of Poincaré symmetry are examined in the context of (2+1)dimensional quantum gravity. The results are expressed in five lessons, which summarise how the gravitational constant, Planck’s constant and the cosmological constant enter the noncommutative and noncocommutative structures arising in (2+1)dimensional quantum gravity. It is emphasised that the much studied bicrossproduct κPoincaré algebra does not arise directly in (2+1)dimensional quantum gravity