# Abbott, Deser ## Stability of gravity with a cosmological constant \[Links: [DOI](https://doi.org/10.1016/0550-3213(82)90049-9)\] \[Abstract: The stability properties of Einstein theory with a cosmological constant $\Lambda$ are investigated. For $\Lambda>0$, stability is established for small fluctuations, about the de Sitter background, occurring inside the event horizon and semiclassical stability is analyzed. For $\Lambda<0$, stability is demonstrated for all asymptotically anti-de Sitter metrics. The analysis is based on the general construction of conserved flux-integral expressions associated with the symmetries of a chosen background. The effects of an event horizon, which lead to Hawking radiation, are expressed for general field hamiltonians. Stability for $\Lambda<0$ is proved, using supergravity techniques, in terms of the graded anti-de Sitter algebra with spinorial charges also expressed as flux integrals.\] # Curtright, Thorn ## Conformally Invariant Quantization of the Liouville Theory \[Links: [DOI](https://doi.org/10.1103/PhysRevLett.48.1309)\] \[Abstract: The [[0562 Liouville theory|Liouville theory]] is quantized with use of Fock-space methods, an infinite set of charges $L_n$, $n=0, \pm 1, …$, is constructed which represents the conformal algebra in two dimensions, and consequences of this algebra are discussed. It is then argued, with use of variational methods in Fock space, that the spectrum of the Liouville Hamiltonian is continuous, and that there exist energy eigenstates obeying the constraints $L_n|E\rangle=0$, $n>0$.\] # Gross, Perry, Yaffe ## Instability of flat space at finite temperature \[Links: [Inspire](https://inspirehep.net/literature/178263), [PRD](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.25.330)\] \[Abstract: The instabilities of quantum gravity are investigated using the path-integral formulation of Einstein's theory. A brief review is given of the classical [[0339 Stability of GR solutions|gravitational instabilities]], as well as the stability of flat space. The Euclidean path-integral representation of the partition function is employed to discuss the instability of flat space at finite temperature. Semiclassical, or saddle-point, approximations are utilized. We show how the Jeans instability arises as a tachyon in the graviton propagator when small perturbations about hot flat space are considered. The effect due to the Schwarzschild [[0478 Instanton|instanton]] is studied. The small fluctuations about this instanton are analyzed and a [[0489 Negative mode of Euclidean Schwarzschild solution|negative mode]] is discovered. This produces, in the semiclassical approximation, an imaginary part of the free energy. This is interpreted as being due to the metastability of hot flat space to nucleate black holes. These then evolve by evaporation or by accretion of thermal gravitons, leading to the instability of hot flat space. The nucleation rate of black holes is calculated as a function of temperature.\] ## Eigenvalue problem - $-\square \phi^{a b}-2 R^{a c b d} \phi_{c d}=\lambda \phi^{a b}$ - a negative eigenvalue means unstable Gaussian fluctuations about the instanton ## Changes to the mass and horizon area - $A=16 \pi G^2 M^2+0.94 \epsilon G$ which corresponds to a "fake" mass of $M+0.0094 \epsilon(G M)^{-1}$ (because $m=\left(A / 16 \pi G^2\right)^{1 / 2}$) - the actual ADM mass remains unchanged! - the mode decays too fast to affect the [[0487 ADM mass|ADM]] surface term (see e.g. [[2022#Marolf, Santos (Feb, b)]]) - the action decreases due to a volume term: - $I=4 \pi G M^2-0.00094 /(G M)^2 \epsilon^2$ (5.28) # Witten ## Instability of KK vacuum \[Links: [Inspire](https://inspirehep.net/literature/10780)\] \[Abstract: It is argued that the ground state of the Kaluza-Klein unified theory is unstable against a process of semiclassical barrier penetration. This is related to the fact that the positive energy conjecture does not hold for the Kaluza-Klein theory; an explicit counter-example is given. The reasoning presented here assumes that in general relativity one should include manifolds of non-vacuum topology. It is argued that the existence of elementary fermions (not present in the original Kaluza-Klein theory) would stabilize the Kaluza-Klein vacuum.\] ## Summary - constructs the [[0168 Bubble of nothing|bubble of nothing]] to show semi-classical instability of the [[0169 Kaluza-Klein|KK vacuum]]