After reviewing the procedures that allow us to obtain new Lie algebras or superalgebras from giv... more After reviewing the procedures that allow us to obtain new Lie algebras or superalgebras from given ones (contractions, deformations and extensions), we briefly describe a recently introduced one, the expansion method. Then we consider certain D = 11 enlarged supersymmetry algebras, and show how these may be used to give a gauge structure to D = 11 supergravity. The relation of these algebras to an expansion of the osp(1|32) algebra is then exhibited.
It is argued that the observed thermodynamic arrow of time must arise from the boundary condition... more It is argued that the observed thermodynamic arrow of time must arise from the boundary conditions of the Universe. We analyze the consequences of the no-boundary proposal, the only reasonably complete set of boundary conditions that has been put forward. We study perturbations of a Friedmann model containing a massive scalar field, but our results should be independent of the details of the matter content. We find that gravitational wave perturbations have an amplitude that remains in the linear regime at all times and is roughly time symmetric about the time of maximum expansion. Thus gravitational wave perturbations do not give rise to an arrow of time. However, density perturbations behave very differently. They are small at one end of the Universe's history, but grow larger and become nonlinear as the Universe gets larger. Contrary to an earlier claim, the density perturbations do not get small again at the other end of the Universe's history. They therefore give rise to a thermodynamic arrow of time that points in a constant direction while the Universe expands and contracts again. The arrow of time does not reverse at the point of maximum expansion. One has to appeal to the weak anthropic principle to explain why we observe the thermodynamic arrow to agree with the cosmological arrow, the direction of time in which the Universe is expanding. PACS number(s): 98.80.Hw, 98.80.Bp Some authors have tried to account for the arrow of time on the basis of dynamic laws. The discovery that CP invariance is violated in the decay of the K meson [2] inspired a number of such attempts, but it is now generally recognized that CP violation can explain why the Universe contains baryons rather than antibaryons, but it cannot explain the arrow of time. Other authors [3] have questioned whether quantum gravity might not violate CPT, but no mechanism has been suggested. One would 0556-2821/93/47(12)/5342(15)/$06. 00 47 5342 1993 The American Physical Society 47 ORIGIN OF TIME ASYMMETRY 5343 not be satisfied with an ad hoc CPT violation that was put in by hand.
One would expect spacetime to have a foamlike structure on the Planck scale with a very high topo... more One would expect spacetime to have a foamlike structure on the Planck scale with a very high topology. If spacetime is simply connected (which is assumed in this paper), the nontrivial homology occurs in dimension two, and spacetime can be regarded as being essentially the topological sum of S x S and K3 bubbles. Comparison with the instantons for pair creation of black holes shows that the S x S bubbles can be interpreted as closed loops of virtual black holes. It is shown that scattering in such topological Buctuations leads to loss of quantum coherence, or in other words, to a superscattering matrix P that does not factorize into an S matrix and its adjoint. This loss of quantum coherence is very small at low energies for everything except scalar fields, leading to the prediction that we may never observe the Higgs particle. Another possible observational consequence may be that the 8 angle of QCD is zero without having to invoke the problematical existence of a light axion. The picture of virtual black holes given here also suggests that macroscopic black holes will evaporate down to the Planck size and then disappear in the sea of virtual black holes. PACS number(s): 04.60.m, 04.70.Dy
The formation and evaporation of two-dimensional black holes are discussed. It is shown that if t... more The formation and evaporation of two-dimensional black holes are discussed. It is shown that if the radiation in minimal scalars has positive energy, there must be a global event horizon or a naked singularity. The former would imply loss of quantum coherence while the latter would lead to an even worse breakdown of predictability. CPT invariance would suggest that there ought to be past horizons as well.
We clarify the relation between gravitational entropy and the area of horizons. We erst show that... more We clarify the relation between gravitational entropy and the area of horizons. We erst show that the entropy of an extreme Reissner-Nordstrom black hole is zero, despite the fact that its horizon has nonzero area. Next, we consider the pair creation of extremal and nonextremal black holes. It is shown that the action which governs the rate of this pair creation is directly related to the area of the acceleration horizon and (in the nonextremal case) the area of the black hole event horizon. This provides a simple explanation of the result that the rate of pair creation of nonextreme black holes is enhanced by precisely the black hole entropy. Finally, we discuss black hole annihilation, and argue that Planck scale remnants are not suKcient to preserve unitarity in quantum gravity.
Near-extreme black holes can lose their charge and decay by the emission of massive Bogomol'ni-Pr... more Near-extreme black holes can lose their charge and decay by the emission of massive Bogomol'ni-Prasad-Sommerfield charged particles. We calculate the greybody factors for low-energy charged and neutral scalar emission from four-and five-dimensional near extremal Reissner-Nordström black holes. We use the corresponding emission rates to obtain ratios of the rates of loss of excess energy by charged and neutral emission, which are moduli independent, depending only on the integral charges and the horizon potentials. We consider scattering experiments, finding that evolution towards a state in which the integral charges are equal is favored, but neutral emission will dominate the decay back to extremality except when one charge is much greater than the others. The implications of our results for the agreement between black hole and D-brane emission rates and for the information loss puzzle are then discussed. ͓S0556-2821͑97͒02612-X͔ PACS number͑s͒: 04.70.Dy, 04.65.ϩe Thus it seems that charged emission will occur most readily for the greatest charge and will tend to equalize the charges. However, when the charges are nearly equal, charged emission of any kind will be heavily suppressed. On the other *Electronic address: swh1@damtp.cam.ac.uk † Electronic address: mmt14@damtp.cam.ac.uk PHYSICAL REVIEW D
It has been suggested that an advanced civilization might have the technology to warp spacetime s... more It has been suggested that an advanced civilization might have the technology to warp spacetime so that closed timelike curves would appear, allowing travel into the past. This paper examines this possibility in the case that the causality violations appear in a finite region of spacetime without curvature singularities. There will be a Cauchy horizon that is compactly generated and that in general contains one or more closed null geodesics which will be incomplete. One can define geometrical quantities that measure the Lorentz boost and area increase on going round these closed null geodesics. If the causality violation developed from a noncompact initial surface, the averaged weak energy condition must be violated on the Cauchy horizon. This shows that one cannot create closed timelike curves with finite lengths of cosmic string. Even if violations of the weak energy condition are allowed by quantum theory, the expectation value of the energy-momentum tensor would get very large if timelike curves become almost closed. It seems the back reaction would prevent closed timelike curves from appearing. These results strongly support the chronology protection conjecture: The laws ofphysics do not allow the appear ance ofclosed timelike curves.
Various calculations of the S matrix have shown that it seems to be nonunitary for interacting fi... more Various calculations of the S matrix have shown that it seems to be nonunitary for interacting fields when there are closed timelike curves. It is argued that this is because there is loss of quantum coherence caused by the fact that part of the quantum state circulates on the closed timelike curves and is not measured at infinity. A prescription is given for calculating the superscattering matrix $ on spacetimes whose parameters can be analytically continued to obtain a Euclidean metric. It is illustrated by a discussion of a spacetime in which two disks in 8at space are identified. If the disks have an imaginary time separation, this corresponds to a heat bath. An external field interacting with the heat bath will lose quantum coherence. One can then analytically continue to an almost real separation of the disks. This will give closed timelike curves. but one will still get loss of quantum coherence. A comparison is made with the work of authors who find a nonunitary S matrix. It is shown that this is because the $ does not factor into an S matrix and its adjoint when the spacetime does not have the property of asymptotic completeness.
We consider two quantum cosmological models with a massive scalar field: an ordinary Friedmann un... more We consider two quantum cosmological models with a massive scalar field: an ordinary Friedmann universe and a universe containing primordial black holes. For both models we discuss the complex solutions to the Euclidean Einstein equations. Using the probability measure obtained from the Hartle-Hawking no-boundary proposal we find that the only unsuppressed black holes start at the Planck size but can grow with the horizon scale during the roll down of the scalar field to the minimum.
Black holes came into existence together with the universe through the quantum process of pair cr... more Black holes came into existence together with the universe through the quantum process of pair creation in the inflationary era. We present the instantons responsible for this process and calculate the pair creation rate from the no boundary proposal for the wave function of the universe. We find that this proposal leads to physically sensible results, which fit in with other descriptions of pair creation, while the tunneling proposal makes unphysical predictions. We then describe how the pair-created black holes evolve during inflation. In the classical solution, they grow with the horizon scale during the slow roll down of the inflaton field; this is shown to correspond to the flux of field energy across the horizon according to the first law of black hole mechanics. When quantum effects are taken into account, however, it is found that most black holes evaporate before the end of inflation. Finally, we consider the pair creation of magnetically charged black holes, which cannot evaporate. In standard Einstein-Maxwell theory we find that their number in the presently observable universe is exponentially small. We speculate how this conclusion may change if dilatonic theories are applied.
A number of attempts have recently been made to extend the conjectured S duality of Yang-Mills th... more A number of attempts have recently been made to extend the conjectured S duality of Yang-Mills theory to gravity. Central to these speculations has been the belief that electrically and magnetically charged black holes, the solitons of quantum gravity, have identical quantum properties. This is not obvious, because, although duality is a symmetry of the classical equations of motion, it changes the sign of the Maxwell action. Nevertheless, we show that the chemical potential and charge projection that one has to introduce for electric but not magnetic black holes exactly compensate for the difference in action in the semiclassical approximation. In particular, we show that the pair production of electric black holes is not a runaway process, as one might think if one just went by the action of the relevant instanton. We also comment on the de6nition of the entropy in cosmological situations, and show that we need to be more careful when de6ning the entropy than we are in an asymptotically Hat case.
A consistent Euclidean semiclassical calculation is given for the superscattering operator g in t... more A consistent Euclidean semiclassical calculation is given for the superscattering operator g in the Russo, Susskind, and Thorlacius (RST) model for states with a constant flux of energy. The foperator 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.
It is argued that the short bursts of gravitational radiation which Weber reports most probably a... more It is argued that the short bursts of gravitational radiation which Weber reports most probably arise from the gravitational collapse of a body of stellar mass or the capture of one collapsed object by another. In both cases the bulk of the energy would be emitted in a burst lasting about a millisecond, during which the Riemann tensor would change sign from one to three times. The signal-to-noise problem for the detection of such bursts is discussed, and it is shown that by observing fluctuations in the phase or amplitude of the Brownian oscillations of a quadrupole antenna one can detect bursts which impart to the system an energy of a small fraction of kT. Applied to Weber's antenna, this method could improve the sensitivity for reliable detection by a factor of about 12. However, by using an antenna of the same physical dimensions but with a much tighter electromechanical coupling, one could obtain an improvement by a factor of up to 250. The tighter coupling would also enable one to determine the time of arrival of the bursts to within a millisecond. Such time resolution would make it possible to verify that the radiation was propagating with the velocity of light and to determine the direction of the source.
Any reasonable theory of quantum gravity will allow closed universes to branch off from our nearl... more Any reasonable theory of quantum gravity will allow closed universes to branch off from our nearly flat region of spacetime. I describe the possible quantum states of these closed universes.
The usual proof of the CPT theorem does not apply to theories which include the gravitational fie... more The usual proof of the CPT theorem does not apply to theories which include the gravitational field. Nevertheless, it is shown that CPT invariance still holds in these cases provided that, as has recently been proposed, the quantum state of the Universe is defined by a path integral over metrics that are compact without boundary. The observed asymmetry or arrow of time defined by the direction of time in which entropy increases is shown to be related to the cosmological arrow of time defined by the direction of time in which the Universe is expanding. It arises because in the proposed quantum state the Universe would have been smooth and homogeneous when it was small but irregular and inhomogeneous when it was large. The thermodynamic arrow would reverse during a contracting phase of the Universe or inside black holes. Possible observational tests of this prediction are discussed.
It is believed that first-order phase transitions occurred in the very early universe when the te... more It is believed that first-order phase transitions occurred in the very early universe when the temperature dropped below the grand-unification and Weinberg-Salam energies. Bubbles of the new, broken-symmetry phase would have formed surrounded by the symmetric phase. The energy released in the phase transition would have caused the walls of the bubbles to accelerate outwards. We study what happens when the walls collide with each other. We find that the energy in the walls would not be thermalized for a considerable time. In the inflationary-universe scenario, in which the bubble nucleation rate is low, thermalization could not occur until long after the baryon and nucleosynthesis eras and would not be complete. We also investigate the formation of primordial black holes in bubble collisions. The Weinberg-Salam phase transition is not likely to produce black holes but, under certain circumstances, the grand-unified phase transition might give rise to black holes of 103 g.
It is assumed that the Universe is in the quantum state defined, by a path integral over compact ... more It is assumed that the Universe is in the quantum state defined, by a path integral over compact four-metrics. This can be regarded as a boundary condition for the wave function of the Universe on superspace, the space of all three-metrics and matter field configurations on a three-surface. We extend previous work on finite-dimensional approximations to superspace to the full infinitedimensional space. We treat the two homogeneous and isotropic degrees of freedom exactly and the others to second order. We justify this approximation by showing that the inhomogeneous or anisotropic modes start off in their ground state. We derive time-dependent Schrodinger equations for each mode. The modes remain in their ground state until their wavelength exceeds the horizon size in the period of exponential expansion. The ground-state fluctuations are then amplified by the subsequent expansion and the modes reenter the horizon in the matter-or radiation-dominated era in a highly excited state. We obtain a scale-free spectrum of density perturbations which could account for the origin of galaxies and all other structure in the Universe. The fluctuations would be compatible with observations of the microwave background if the mass of the scalar field that drives the inflation is 10' GeV or less.
It is shown that the close connection between event horizons and thermodynamics which has been fo... more It is shown that the close connection between event horizons and thermodynamics which has been found in the case of black holes can be extended to cosmological models with a repulsive cosmological constant. An observer in these models will have an event horizon whose area can be interpreted as the entropy or lack of information of the observer about the regions which he cannot see. Associated with the event horizon is a surface gravity v which enters a classical "first law of event horizons*' in a manner similar to that in which temperature occurs in the first law of thermodynamics. It is shown that this similarity is more than an analogy: An observer with a particle detector will indeed observe a background of thermal radiation coming apparently from the cosmological event horizon. If the observer absorbs some of this radiation, he will gain energy and entropy at the expense of the region beyond his ken and the event horizon will shrink. The derivation of these results involves abandoning the idea that particles should be defined in an observerindependent manner. They also suggest that one has to use something like the Everett-Wheeler interpretation of quantum mechanics because the back reaction and hence the spacetime metric itself appear to be observerdependent, if one assumes, as seems reasonable, that the detection of a particle is accompanied by a change in the gravitational field.
The path-integral method seems to be the most suitable for the quantization of gravity. One would... more The path-integral method seems to be the most suitable for the quantization of gravity. One would expect the dominant contribution to the path integral to come from metrics which are near background metrics that are solutions of classical Einstein equations. The action of these background metrics gives rise to a new phenomenon in field theory, intrinsic quantum entropy. This is shown to be related to the scaling behavior of the gravitational action and to the topology of the gravitational field. The quadratic terms in the Taylor series of the action about the background metrics give the one-loop corrections. In a supersymmetric theory the quartic and quadratic but not the so-called logarithmic divergences cancel to give a one-loop term that is finite without regularization. From the one-loop term one can obtain the effective energy-momentum tensor on the background metric. In the case of an evaporating black hole, the energy-momentum tensor will be regular on the future horizon. The usual perturbation expansion breaks down for quantum gravity because the higher (interaction) terms in the Taylor series are not bounded by the quadratic (free) ones. To overcome this I suggest that one might replace the path integrals over the terms in the Taylor series by a discrete sum of the exponentials of the actions of all complex solutions of the Einstein equations, each solution being weighted by its one-loop term. This approach seems to give a picture of the gravitational vacuum as a sea of virtual Planck-mass black holes.
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