Chronal Isomorphism, Singularities and Black Holes

The concept of Chronal Isomorphism was discussed in [1]. This paper discusses more properties which include images of past and future sets, naked singular points introduced by Penrose [7] and black holes. The validity of the singularity theorem of Joshi [10] in the image space is also discussed.     

Einstein-Proca Model, Micro Black Holes, and Naked Singularities

The Einstein-Proca equations, describing a spin-1 massive vector field in general relativity, are studied in the static spherically-symmetric case. The Proca field equation is a highly nonlinear wave equation, but can be solved to good accuracy in perturbation theory, which should be very accurate for a wide range of mass scales. The resulting first order metric reduces to the Reissner-Nordström solution in the limit as the range parameter goes to zero. The additional terms in the g ₀₀ metric coefficient are positive, as in Reissner-Nordström, in agreement with previous numerical solutions, and hence involve naked singularities.     

Topology,unitary representations and charged particles

The quantum mechanics of the charged particles with rigid and local symmetries propagating on the manifoldM is studied. It is shown that the classical rigid symmetries of this model may be anomalous. These anomalies are of local and global type, and they related to topological obstructions to lifting a group action of a groupG onM to a principalU(1) bundleP overM. The charged particles with local symmetries may have additional anomalies and the representation theory of the groupC is used to study these anomalies. Finally, the quantum mechanics of the supersymmetric charged particles with symmetries is examined.     

Topology, phase transitions, and the spherical model

The topological hypothesis states that phase transitions should be related to changes in the topology of configuration space. The necessity of such changes has already been demonstrated. We characterize exactly the topology of the configuration space of the short range Berlin-Kac spherical model, for spins lying in hypercubic lattices of dimension d. We find a continuum of changes in the topology and also a finite number of discontinuities in some topological functions. We show, however, that these discontinuities do not coincide with the phase transitions which happen for d > or = 3, and conversely, that no topological discontinuity can be associated with them. This is the first short range, confining potential for which the existence of special topological changes are shown not to be sufficient to infer the occurrence of a phase transition.     

Black Holes,Information Loss and the Measurement Problem

The information loss paradox is often presented as an unavoidable consequence of well-established physics. However, in order for a genuine paradox to ensue, not-trivial assumptions about, e.g., quantum effects on spacetime, are necessary. In this work we will be explicit about these additional, speculative assumptions required. We will also sketch a map of the available routes to tackle the issue, highlighting the, often overlooked, commitments demanded of each alternative. Finally, we will display the strong link between black holes, the issue of information loss and the measurement problem.     

Eternal Inflation, Black Holes, and the Future of Civilizations

We discuss the large-scale structure of the universe in inflationary cosmologyand the implications that it may have for the long-term future of civilizations.Although each civilization is doomed to perish, it may be possible to transmitits accumulated knowledge to future civilizations. We consider several scenariosof this sort. If the cosmological constant is positive, it eventually dominates theuniverse and bubbles of inflationary phase begin to nucleate at a constant rate.Thermalized regions inside these inflating bubbles will give rise to new galaxiesand civilizations. It is possible in principle to send a message to one of them. Itmight even be possible to send a device whose purpose is to recreate anapproximation of the original civilization in the new region. However, the messageor device will almost certainly be intercepted by black holes, which nucleate ata much higher rate than inflating bubbles. Formation of new inflating regionscan also be triggered by gravitational collapse, but again the probability is low,and the number of attempts required for a positive outcome is enormous. Theprobability can be higher if the energy scale of inflation is closer to the Planckscale, but a high energy scale produces a tight bound on the amount of informationthat can be transmitted. One can try to avoid quantum tunneling altogether, butthis requires a violation of quantum inequalities which constrain the magnitudeof negative energy densities. However, the limits of validity of quantuminequalities are not clear, and future research may show that the required violationis in fact possible. Therein lies the hope for the future of civilizations.     

Black Holes and Inflation

A model for black hole collapse and evaporation in which the black hole is supposed to be an excited state of one of the Planck black holes pervading the structure of spacetime is discussed. By assuming a Coleman-Weinberg gravitational effective potential for a scalar field inside the collapse matter, it is shown that the black hole state cannot be attained neither through bubble tunneling nor by the rolling down of the field.     

黑洞与奇点

黑洞可以说是引力最极端的体现,其视界内是个连光也逃不出去的时空区域。近来黑洞在天 文观测方面取得令人惊讶的发展,这其中包括：黑洞碰撞的引力波探测以及M87 星系的超大质量 黑洞的所谓第一张黑洞照片。但是在理论的层面上,黑洞物理尚有许多未解之谜。其中,信息遗失 的悖论是最有名的。但是,有另一个问题至少和信息的丢失一样{甚至更加{令人费解的,就是黑洞 内部的奇点性质。时空奇点是广义相对论本身无法描述的,在那里究竟发生什么事？黑洞内部的奇 点和宇宙大爆炸时的奇点有何不同？奇点是否会裸露在黑洞外面？所谓“宇宙监督猜想”的假设目 前有何进展？我们在这篇半科普的文章中简单的介绍这些课题,希望本文章对物理和数学的本科生 有所帮助。     

Topology, phase instabilities, and wetting of microemulsion networks

We predict theoretically the gradual formation of fluctuating, connected microemulsion networks from disconnected globules as the spontaneous curvature is varied, in agreement with recent direct measurements of these topological transitions. The connectivity induced instability together with emulsification failure of the network relate the ultralow tensions and wetting transition to the changing microstructure.     

Spinning Strings,Black Holes and Stable Closed Timelike Geodesics

The existence and stability under linear perturbation of closed timelike curves in the spacetime associated to Schwarzschild black hole pierced by a spinning string are studied. Due to the superposition of the black hole, we find that the spinning string spacetime is deformed in such a way to allow the existence of closed timelike geodesics.     

Primordial Black Holes: Pair Creation, Lorentzian Condition, and Evaporation

The wave function of the universe is usuallytaken to be a functional of the threemetric on aspacelike section, , which is measured. It issometimes better, however, to work in the conjugaterepresentation, where the wave function depends on a quantityrelated to the second fundamental form of . Thismakes it possible to ensure that is part of aLorentzian universe by requiring that the argument of the wave function be purely imaginary. Wedemonstrate the advantages of this formalism first inthe well-known examples of the nucleation of a de Sitteror a Nariai universe. We then use it to calculate the pair creation rate for submaximal blackholes in de Sitter space, which had been thought tovanish semiclassically. We also study the quantumevolution of asymptotically de Sitter black holes. Forblack holes whose size is comparable to that of thecosmological horizon, this process differs significantlyfrom the evaporation of asymptotically flat black holes.Our model includes the one-loop effective action in the s-wave and large-N approximation.Black holes of the maximal mass are in equilibrium.Unexpectedly, we find that nearly maximal quantumSchwarzschild–de Sitter black holes antievaporate.However, there is a different perturbative mode thatleads to evaporation. We show that this mode will alwaysbe excited when a pair of maximal cosmological blackholes nucleates.