1995 - otherworldlines

# Fursaev, Solodukhin ## On the Description of the Riemannian Geometry in the Presence of Conical Defects \[Links: [arXiv](https://arxiv.org/abs/hep-th/9501127), [PDF](https://arxiv.org/pdf/hep-th/9501127.pdf)\] \[Abstract: \] # Hawking, Horowitz ## The Gravitational Hamiltonian, Action, Entropy, and Surface Terms \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9501014), [PDF](https://arxiv.org/pdf/gr-qc/9501014.pdf)\] \[Abstract: We give a general derivation of the gravitational hamiltonian starting from the Einstein-Hilbert action, keeping track of all surface terms. The surface term that arises in the hamiltonian can be taken as the definition of the 'total energy', even for spacetimes that are not asymptotically flat. (In the asymptotically flat case, it agrees with the usual ADM energy.) We also discuss the relation between the euclidean action and the hamiltonian when there are horizons of infinite area (e.g. acceleration horizons) as well as the usual finite area black hole horizons. Acceleration horizons seem to be more analogous to extreme than nonextreme black holes, since we find evidence that their horizon area is not related to the total entropy.\] # Iyer, Wald ## A comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9503052), [PDF](https://arxiv.org/pdf/gr-qc/9503052.pdf)\] \[Abstract: The entropy of stationary black holes has recently been calculated by a number of different approaches. Here we compare the [[0019 Covariant phase space|Noether charge approach]] (defined for any diffeomorphism invariant Lagrangian theory) with various Euclidean methods, specifically, (i) the microcanonical ensemble approach of Brown and York, (ii) the closely related approach of Bañados, Teitelboim, and Zanelli which ultimately expresses black hole entropy in terms of the Hilbert action surface term, (iii) another formula of Bañados, Teitelboim and Zanelli (also used by Susskind and Uglum) which views black hole entropy as conjugate to a conical deficit angle, and (iv) the pair creation approach of Garfinkle, Giddings, and Strominger. All of these approaches have a more restrictive domain of applicability than the Noether charge approach. Specifically, approaches (i) and (ii) appear to be restricted to a class of theories satisfying certain properties listed in section 2; approach (iii) appears to require the Lagrangian density to be linear in the curvature; and approach (iv) requires the existence of suitable instanton solutions. However, we show that within their domains of applicability, all of these approaches yield results in agreement with the Noether charge approach. In the course of our analysis, we generalize the definition of Brown and York's quasilocal energy to a much more general class of diffeomorphism invariant, Lagrangian theories of gravity. In an appendix, we show that in an arbitrary diffeomorphism invariant theory of gravity, the "volume term" in the "off-shell" Hamiltonian associated with a time evolution vector field $t^a$ always can be expressed as the spatial integral of $t^a {\cal C}_a$, where ${\cal C}_a = 0$ are the constraints associated with the diffeomorphism invariance.\] ## Summary - compares the Noether charge method ([[1994#Iyer, Wald]]) for computing [[0004 Black hole entropy|black hole entropy]] with 4 Euclidean methods: 1. microcanonical ensemble - [[1992#Brown, York (a)]] - [[1992#Brown, York (b)]] 2. Hilbert action surface term - [[BanadosTeitelboimZanelli1993]] - also in a proceeding, see ref 6 3. conjugate of conical angle - [[BanadosTeitelboimZanelli1993]] - [[1994#Susskind, Uglum]] 4. pair creation approach - [[1993#Garfinkle, Giddings, Strominger]] - these are all restrictive methods - results all agree  # Jacobson ## Thermodynamics of Spacetime: The Einstein Equation of State \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9504004), [PDF](https://arxiv.org/pdf/gr-qc/9504004.pdf)\] \[Abstract: The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with $\delta Q$ and $T$ interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.\] ## Summary - shows that Einstein equation arises from thermodynamics, taking Rindler horizon as the basic setting ## Refs - [[0302 Gravity from entanglement]] - [[0045 Einstein equation from thermodynamics]] # Louko, Sorkin ## Complex actions in two-dimensional topology change \[Links: [arXiv](https://arxiv.org/abs/gr-qc/9511023), [PDF](https://arxiv.org/pdf/gr-qc/9511023.pdf)\] \[Abstract: \] ## Comments - mentioned in [[2020#Colin-Ellerin, Dong, Marolf, Rangamani, Wang]] - singularity in Lorentzian causal structure is associated with imaginary contributions to the Lorentzian action ## Summary - *investigates* topology change in (1+1) dimensions - *calculates* the contribution of the action $\int R$ due to the point with a degenerate metric - *contrasts* the results with vielbein-cum-connection formulation of Einstein gravity # Pradisi, Sagnitti, Stanev (Mar) ## Planar Duality in SU(2) WZW Models \[Links: [arXiv](https://arxiv.org/abs/hep-th/9503207), [PDF](https://arxiv.org/pdf/hep-th/9503207)\] \[Abstract: We show how to generalize the SU(2) [[0601 Weiss-Zumino-Witten models|WZW]] models to allow for [[0548 Boundary CFT|open]] and [[0620 Non-orientable CFT|unoriented]] sectors. The construction exhibits some novel patterns of Chan-Paton charge assignments and projected spectra that reflect the underlying current algebra.\] # Pradisi, Sagnotti, Stanev (Jun) ## The Open Descendants of Non-Diagonal SU(2) WZW Models \[Links: [arXiv](https://arxiv.org/abs/hep-th/9506014), [PDF](https://arxiv.org/pdf/hep-th/9506014)\] \[Abstract: We extend the construction of open descendants to the $SU(2)$ [[0601 Weiss-Zumino-Witten models|WZW]] models with non-diagonal left-right pairing, namely $E_7$ and the $D_{odd}$ series in the ADE classification of Cappelli, Itzykson and Zuber. The structure of the resulting models is determined to a large extent by the ''[[0620 Non-orientable CFT|crosscap constraint]]'', while their Chan-Paton charge sectors may be embedded in a general fashion into those of the corresponding diagonal models.\] # Schultens ## Heegaard splittings of Seifert fibered spaces with boundary \[Links: [DOI](https://www.ams.org/journals/tran/1995-347-07/S0002-9947-1995-1297537-5/)\] \[Abstract: We give the classification theorem for Heegaard splittings of fiberwise orientable Seifert fibered spaces with nonempty boundary. A thin position argument yields a reducibility result which, by induction, shows that all Heegaard splittings of such manifolds are vertical in the sense of Lustig-Moriah. Algebraic arguments allow a classification of the vertical Heegaard splittings.\] # Teschner ## On the Liouville three-point function \[Links: [arXiv](https://arxiv.org/abs/hep-th/9507109), [PDF](https://arxiv.org/pdf/hep-th/9507109.pdf)\] \[Abstract: The recently proposed expression for the general three point function of exponential fields in quantum [[0562 Liouville theory|Liouville theory]] on the sphere is considered. By exploiting locality or crossing symmetry in the case of those four-point functions, which may be expressed in terms of hypergeometric functions, a set of functional equations is found for the general three point function. It is shown that the expression proposed by the [[1995#Zamolodchikov, Zamolodchikov|Zamolodchikovs]] solves these functional equations and that under certain assumptions the solution is unique.\] # Zamolodchikov, Zamolodchikov ## Structure Constants and Conformal Bootstrap in Liouville Field Theory \[Links: [arXiv](https://arxiv.org/abs/hep-th/9506136), [PDF](https://arxiv.org/pdf/hep-th/9506136.pdf)\] \[Abstract: An analytic expression is proposed for the three-point function of the exponential fields in the [[0562 Liouville theory|Liouville field theory]] on a sphere. In the classical limit it coincides with what the classical Liouville theory predicts. Using this function as the structure constant of the operator algebra we construct the four-point function of the exponential fields and verify numerically that it satisfies the [[0036 Conformal bootstrap|conformal bootstrap]] equations, i.e., that the operator algebra thus defined is associative. We consider also the Liouville reflection amplitude which follows explicitly from the structure constants.\]