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Often it is assumed that a quantum state or a phase-space distribution must be normalizable. Here it is shown that even if it is not normalizable, one may be able to extract normalized observational probabilities from it. [ABSTRACT FROM AUTHOR]

Inspired by the example of Abdelqader and Lake for the Kerr metric, we construct local scalar polynomial curvature invariants that vanish on the horizon of any stationary black hole: the squared norms of the wedge products of n linearly independent gradients of scalar polynomial curvature invariants, where n is the local cohomogeneity of the spacetime. [ABSTRACT FROM AUTHOR]

Abstract: Using a pair of linear invariant operators satisfying the Liouville–von Neumann equation, we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum. [Copyright &y& Elsevier]

Normally one thinks of the motion of the planets around the Sun as a highly classical phenomenon, so that one can neglect quantum gravity in the solar system. However, classical chaos in the planetary motion amplifies quantum uncertainties so that they become very large, giving huge quantum gravity effects. For example, evidence suggests that Uranus may eventually be ejected from the solar system, but quantum uncertainties would make the direction at which it leaves almost entirely uncertain, and the time of its exit uncertain by about one quadrillion years. For a time a quadrillion years from now, there are huge quantum uncertainties whether Uranus will be within the solar system, within the galaxy, or even within causal contact of the galaxy. [ABSTRACT FROM AUTHOR]

A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices with suitable Hermitian matrices. [ABSTRACT FROM AUTHOR]

Abstract: It is usually assumed that the quantum state is sufficient for deducing all probabilities for a system. This may be true when there is a single observer, but it is not true in a universe large enough that there are many copies of an observer. Then the probability of an observation cannot be deduced simply from the quantum state (say as the expectation value of the projection operator for the observation, as in traditional quantum theory). One needs additional rules to get the probabilities. What these rules are is not logically deducible from the quantum state, so the quantum state itself is insufficient for deducing observational probabilities. This is the measure problem of cosmology. [Copyright &y& Elsevier]

Abstract: By combining a renormalization group argument relating the charge e and mass of the proton by (in Planck units) with the Carter–Carr–Rees anthropic argument that gives an independent approximate relation between these two constants, both can be crudely estimated. These equations have the factor of 0.1π and the exponent of 20 which depend upon known discrete parameters (e.g., the number of generations of quarks and leptons, and the number of spatial dimensions), but they contain no continuous observed parameters. Their solution gives the charge of the proton correct to within about 8%, though the mass estimate is off by a factor of about 1000 (16% error on a logarithmic scale). When one adds a fudge factor of 10 previously given by Carr and Rees, the agreement for the charge is within about 2%, and the mass is off by a factor of about 3 (2.4% error on a logarithmic scale). If this 10 were replaced by 15, the charge agrees within 1.1% and the mass itself agrees within 0.7%. [Copyright &y& Elsevier]

Abstract: Unless our universe is decaying at an astronomical rate (i.e., on the present cosmological timescale of Gigayears, rather than on the quantum recurrence timescale of googolplexes), it would apparently produce an infinite number of observers per comoving volume by thermal or vacuum fluctuations (Boltzmann brains). If the number of ordinary observers per comoving volume is finite, this scenario seems to imply zero likelihood for us to be ordinary observers and minuscule likelihoods for our actual observations. Hence, our observations suggest that this scenario is incorrect and that perhaps our universe is decaying at an astronomical rate. [Copyright &y& Elsevier]

We construct new complete, compact, inhomogeneous Einstein metrics on Sm+2 sphere bundles over 2n-dimensional Einstein–Kähler spaces K2n, for all n⩾1 and all m⩾1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of Sm with S2 bundles over K2n, for m>1. Additionally, we construct new complete, non-compact Ricci-flat metrics with topologies Sm times R2 bundles over K2n that generalise the higher-dimensional Taub-BOLT metrics, and with topologies Sm×R2n+2 that generalise the higher-dimensional Taub-NUT metrics, again for m>1. [Copyright &y& Elsevier]

One may perform a local field redefinition to transform between gravity minimally coupled to a free scalar field and gravity conformally coupled. However, the allowed field values differ in the two cases. For a minisuperspace consisting of a Friedman–Robertson–Walker geometry and a homogeneous scalar field, the conformal coupling allows a more general class of solutions of the Wheeler–DeWitt equation than does the minimal coupling. Nevertheless, there is a one-to-one correspondence between the bounded solutions in the two cases for k=1. This correspondence exploits an isomorphism between harmonic oscillator wavefunctions and solutions of the massive Klein–Gordon equation in the 1+1 dimensional Rindler wedge. [ABSTRACT FROM AUTHOR]

Abstract: If the initial quantum state of the universe is a multiverse superposition over many different sets of values of the effective coupling ‘constants’ of physics, and if this quantum state collapses to an eigenstate of the set of coupling ‘constants’ with a probability purely proportional to the absolute square of the amplitude (with no additional factor for something like life or consciousness), then one should not expect that the coupling ‘constants’ would be so biophilic as they are observed to be. Therefore, the observed biophilic values (apparent fine tuning) of the coupling ‘constants’ is statistical evidence against such simple forms of wavefunction collapse. [Copyright &y& Elsevier]

Abstract: Using a novel numerical spectral method, we have constructed an – solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. This method is independent of the Ricci–DeTurck-flow method used by Figueras, Lucietti, and Wiseman. We have perturbed the solution to get large static black hole solutions to the Randall–Sundrum II (RSII) braneworld model. Our solution agrees closely with that of Figueras et al. and also allows us to deduce the new results that to first order in , the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about . [Copyright &y& Elsevier]

Abstract: We give the general Kerr–de Sitter metric in arbitrary space–time dimension , with the maximal number of independent rotation parameters. We obtain the metric in Kerr–Schild form, where it is written as the sum of a de Sitter metric plus the square of a null-geodesic vector, and in generalised Boyer–Lindquist coordinates. The Kerr–Schild form is simpler for verifying that the Einstein equations are satisfied, and we have explicitly checked our results for all dimensions . We discuss the global structure of the metrics, and obtain formulae for the surface gravities and areas of the event horizons. We also obtain the Euclidean-signature solutions, and we construct complete non-singular compact Einstein spaces on associated bundles over , infinitely many for each odd . [Copyright &y& Elsevier]

We show that atoms falling into a black hole (BH) emit acceleration radiation which, under appropriate initial conditions, looks to a distant observer much like (but is different from) Hawking BH radiation. In particular, we find the entropy of the acceleration radiation via a simple laser-like analysis. We call this entropy horizon brightened acceleration radiation (HBAR) entropy to distinguish it from the BH entropy of Bekenstein and Hawking. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity. [ABSTRACT FROM AUTHOR]

In the firewall proposal, it is assumed that the firewall lies near the event horizon and should not be observable except by infalling observers, who are presumably terminated at the firewall. However, if the firewall is located near where the horizon would have been, based on the spacetime evolution up to that time, later quantum fluctuations of the Hawking emission rate can cause the "teleological" event horizon to have migrated to the inside of the firewall location, rendering the firewall naked. In principle, the firewall can be arbitrarily far outside the horizon. This casts doubt about the notion that firewalls are the "most conservative" solution to the information loss paradox. [ABSTRACT FROM AUTHOR]

We find that uniformly accelerated motion of a mirror yields excitation of a static two-level atom with simultaneous emission of a real photon. This occurs because of virtual transitions with probability governed by the Planck factor involving the photon frequency ν and the Unruh temperature. The result is different from the Unruh radiation of an accelerated atom, which is governed by the frequency of the atom, ω, rather than frequency of the emitted photon. We also find that the excitation probability oscillates as a function of the atomic position because of interference between contributions from the waves incident on and reflected from the mirror. [ABSTRACT FROM AUTHOR]