On black hole singularities in quantum gravity

We show that absence of space-like boundaries in 1+1 dimensional dilaton gravity implies a catastrophic event at the end point of black hole evaporation. The proof is completely independent of the physics at Planck scales, which suggests that the same will occur in any theory of quantum gravity which only admits trivial space-time topologies.Comment: 8 pages, 3 figures (included), UTTG-32-9

Open Inflation, the Four Form and the Cosmological Constant

Fundamental theories of quantum gravity such as supergravity include a four form field strength which contributes to the cosmological constant. The inclusion of such a field into our theory of open inflation (hep-th/9802030) allows an anthropic solution to the cosmological constant problem in which the cosmological constant gives a small but non-negligible contribution to the density of today's universe. We include a discussion of the role of the singularity in our solution and a reply to Vilenkin's recent criticism (hep-th/9803084).Comment: 11 pages, RevTex file. Replaced version contains major corrections, including a crucial new surface term, and important additions. A connection to eleven dimensional supergravity is made. The anthropic solution of the cosmological constant problem now holds with a real four form in the Lorentzian region. The previously claimed solution to the empty universe problem is shown to be incorrect, but a new solution is suggeste

Black-Hole Uncertainty Entails an Intrinsic Time Arrow. a Note on the Hawking-Penrose Controversy

Any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. Only determinism enables time reversal of entropy increase. A contradiction therefore arises between two statements of Hawking. A simulation of a system under time reversal shows how an intrinsic time arrow re-emerges, destroying the time reversal, when even slight failure of determinism occurs.Comment: 9 pages, 4 figure

A Euclidean Bianchi Model Based On S3/D8∗S^3/D_8^*

We explain how the round four-sphere can be sliced along homogeneous 3~-~manifolds of topology $S^3/D_8^*$. This defines a Euclidean Bianchi type IX model for Einstein's equations with cosmological constant. The geometric properties of this model are investigated.Comment: 15 Pages, Plain-TeX, no figure

Pair Creation of Black Hole in Anti-de Sitter Space Background

In the absence of a general no-boundary proposal for open creation, the complex constrained instanton is used as the seed for the open pair creations of black holes in the Kerr-Newman-anti-de Sitter family. The relative probability of the chargeless and nonrotating black hole pair is the exponential of the negative of the entropy, and that of the charged and (or) rotating black hole pair is the exponential of the negative of one quarter of the sum of the outer and inner black hole horizon areas

Entropy from the foam

A simple model of spacetime foam, made by N wormholes in a semiclassical approximation, is taken under examination. We show that the Bekenstein-Hawking entropy is here ``quantized'' in agreement with the heuristic calculation of Bekenstein.Comment: Revtex 3.0, 15 pages, accepted in Phys.Lett.

Semiclassical suppression of black hole production in particle collisions

It is argued that the cross section for production of large black holes, for which a semiclassical description is applicable, cannot be given by the geometric area of the black hole horizon, as claimed recently in the literature. Rather the production cross section in a few-particle collision is suppressed by at least a factor exp(-I_E) with I_E being the Gibbons-Hawking (Euclidean) action for the black hole. Thus only essentially non-classical small black holes with mass of the order of the Planck mass can possibly be produced in few-particle collisions at trans-Planckian energies.Comment: 6 page

``Faster than Light'' Photons in Gravitational Fields -- Causality, Anomalies and Horizons

A number of general issues relating to superluminal photon propagation in gravitational fields are explored. The possibility of superluminal, yet causal, photon propagation arises because of Equivalence Principle violating interactions induced by vacuum polarisation in QED in curved spacetime. Two general theorems are presented: first, a polarisation sum rule which relates the polarisation averaged velocity shift to the matter energy-momentum tensor and second, a `horizon theorem' which ensures that the geometric event horizon for black hole spacetimes remains a true horizon for real photon propagation in QED. A comparision is made with the equivalent results for electromagnetic birefringence and possible connections between superluminal photon propagation, causality and the conformal anomaly are exposed.Comment: 15 pages, Plain Te

A speculative remark on holography

Holography suggests a considerable reduction of degrees of freedom in theories with gravity. However it seems to be difficult to understand how holography could be realized in a closed re--contracting universe. In this letter we claim that a scenario which achieves that goal will eliminate all spatial degrees of freedom. This would require a different concept of quantum mechanics and would imply an intriguing increase of power for the natural laws.Comment: 14 pages, a reference adde

The Superscattering Matrix for Two Dimensional Black Holes

A consistent Euclidean semi classical calculation is given for the superscattering operator $\$$ in the RST model for states with a constant flux of energy. The $\$$ operator is CPT invariant. There is no loss of quantum coherence when the energy flux is less than a critical rate and complete loss when the energy flux is critical.Comment: 12 pages (R/94/4