29912513
Quantum gravitational corrections to the functional Schrödinger equation.
We derive corrections to the Schr\"odinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the gravitational constant. The correction terms fall into two classes: One describes the breakdown of the classical background picture while the other corresponds to quantum gravitational corrections for the matter fields themselves. The latter are independent of the factor ordering which is chosen for the gravitational kinetic term. If the total state evolves adiabatically, the only correction term that survives contains the square of the matter Hamiltonian. In the general case there are also smaller terms which describe a gravitationally induced violation of unitarity. The corrections are numerically extremely tiny except near the big bang and the final stages of a black hole. They are also of principle significance for quantum field theories near the Planck scale.
16490636
The final fate of spherical inhomogeneous dust collapse
We examine, in a general manner, the role played by the initial density and velocity distributions in the gravitational collapse of a spherically symmetric inhomogeneous dust cloud. Such a collapse is described by the Tolman - Bondi metric which has two free functions: the `mass function' and the `energy function', which are determined by the initial density and velocity profiles of the cloud. The collapse can end in either a black hole or a naked singularity, depending on the initial parameters characterizing these profiles. In the marginally bound case, we find that the collapse ends in a naked singularity if the leading non-vanishing derivative of the density at the centre is either the first one or the second one. If the first two derivatives are zero, and the third derivative non-zero, the singularity could either be naked or covered, depending on a quantity determined by the third derivative and the central density. If the first three derivatives are zero, the collapse ends in a black hole. In particular, the classic result of Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole, is recovered as a special case. Analogous results are found when the cloud is not marginally bound, and also for the case of a cloud starting from rest. A condition on the initial density profile is given for the singularity to be globally naked. We also show how the strength of the naked singularity depends on the density and velocity distribution. Our analysis generalizes and simplifies the earlier works of Christodoulou and Newman by dropping the assumption of evenness of density functions. It turns out that relaxing this assumption allows for a smooth transition from the naked singularity phase to the black hole phase, and also allows for the occurrence of strong curvature naked singularities.
1570088
Radiation flux and spectrum in the Vaidya collapse model
Abstract We consider the quantization of a massless scalar field, using the geometric optics approximation, in the background spacetime of a collapsing spherical self-similar Vaidya star, which forms a black hole or a naked singularity. We show that the outgoing radiation flux of the quantized scalar field diverges on the Cauchy horizon. The spectrum of the produced scalar partcles is non-thermal when the background develops a naked singularity. These results are analogous to those obtained for the scalar quantization on a self-similar dust cloud.
24124943
Toward a quantization of null dust collapse
Spherically symmetric, null dust clouds, like their timelike counterparts, may collapse classically into black holes or naked singularities depending on their initial conditions. We consider the Hamiltonian dynamics of the collapse of an arbitrary distribution of null dust, expressed in terms of the physical radius R, the null coordinates, V for a collapsing cloud or U for an expanding cloud, the mass function m of the null matter, and their conjugate momenta. This description is obtained from the Arnowitt-Deser-Misner description by a Kucha\ifmmode \check{r}\else \v{r}\fi{}-type canonical transformation. The constraints are linear in the canonical momenta and Dirac's constraint quantization program is implemented. Explicit solutions to the constraints are obtained for both expanding and contracting null dust clouds with arbitrary mass functions.
119086760
Comparing quantum black holes and naked singularities
There are models of gravitational collapse in classical general relativity which admit the formation of naked singularities as well as black holes. These include fluid models as well as models with scalar fields as matter. Even if fluid models were to be regarded as unphysical in their matter content, the remaining class of models (based on scalar fields) generically admit the formation of visible regions of finite but arbitrarily high curvature. Hence it is of interest to ask, from the point of view of astrophysics, as to what a stellar collapse leading to a naked singularity (or to a visible region of very high curvature) will look like, to a far away observer. The emission of energy during such a process may be divided into three phases - (i) the classical phase, during which matter and gravity can both be treated according to the laws of classical physics, (ii) the semiclassical phase, when gravity is treated classically but matter behaves as a quantum field, and (iii) the quantum gravitational phase. In this review, we first give a summary of the status of naked singularities in classical relativity, and then report some recent results comparing the semiclassical phase of black holes with the semiclassical phase of spherical collapse leading to a naked singularity. In particular, we ask how the quantum particle creation during the collapse leading to a naked singularity compares with the Hawking radiation from a star collapsing to form a black hole. It turns out that there is a fundamental difference between the two cases. A spherical naked star emits only about one Planck energy during its semiclassical phase, and the further evolution can only be determined by the laws of quantum gravity. This contrasts with the semiclassical evaporation of a black hole.
118510273
THE CONNECTION BETWEEN "EMERGENCE OF TIME FROM QUANTUM GRAVITY" AND "DYNAMICAL COLLAPSE OF THE WAVE FUNCTION IN QUANTUM MECHANICS"
There are various reasons to believe that quantum theory could be an emergent phenomenon. Trace dynamics is an underlying classical dynamics of noncommuting matrices, from which quantum theory and classical mechanics have been shown to emerge, in the thermodynamic approximation. However, the time that is used to describe evolution in quantum theory is an external classical time, and is in turn expected to be an emergent feature — a relic of an underlying theory of quantum gravity. In this essay we borrow ideas from trace dynamics to show that classical time is a thermodynamic approximation to an operator time in quantum gravitational physics. This prediction will be put to test by ongoing laboratory experiments attempting to construct superposed states of macroscopic objects.
35249306
Quantum violation of stochastic noncontextual hidden-variable theories.
We formulate stochastic noncontextual hidden-variable theories. In such theories the hidden state λ specifies not definite values, but expectation values A − (λ), ... of observables A, ... and noncontextuality means that A − (λ) is independent of which other commuting observables commuting with A are measured together with A. We show via Bell inequalities that such theories conflict with quantum theory and propose a two-photon experimental test. We also show that for a single particle of spin (2 n −1)/2, quantum violation of classical noncontextuality grows exponentially with n.
22845460
Birkhoff's theorem for electromagnetic fields in a new scalar-tensor theory.
A result having formal similarity to Birkhoff's theorem in general relativity is proved in the presence of electromagnetic fields in a new scalar-tensor theory of gravitation proposed by Schmidt et al. for the special case when the scalar field is massless and independent of time.
13536192
Strangeness abundance as a signal for quark-gluon plasma.
We suggest that the variation of the ratio {ital n}{sub {ital K}{sup +}}/{ital n}{sub K{sup {minus}}} and {ital n}{sub {phi}}/{ital n}{sub {omega}} with baryon density (or rapidity) and/or with temperature should be studied in ultrarelativistic heavy-ion collisions and a change in the variation of these production ratios can be utilized to separate the quark-gluon-plasma contributions from the hadronic background.
36246455
The quasiopen string.
The quasiopen string in D dimensions is defined by the Nambu-Goto action and the boundary conditions (x'+x)(σ α ,τ)=V α (x'-x) (σ α ,τ), where σ=σ 1 and σ 2 denote the ends of the string, x'≡∂x/∂σ, and the V α (α=1,2) are real symmetric orthogonal matrices. (The usual open string corresponds to V 1 =V 2 =−1.) We impose Poincare invariance in d dimensions, d α ) jk =−δ jk for j,k ∈ Poincare sector and (V α ) jk =0 if only one of j,k belongs to the Poincare sector. Further quantization gives D=26 and a mass spectrum with a ground-state mass squared M G 2 =−(1−J i ||theta i ||(1-||theTa I ||)/4)/α', where ||theta i ||≤(½), exp(2iπtheta i ) are the eigenvalues of V 2 V 1 , and α' is the slope parameter in the string action. A choice of theta i giving a tachyon-free spectrum is thus possible if d≤10.
32129688
Systematics of preequilibrium contributions in (n,p) reactions at 14 MeV.
The existing up to data global data on angle integrated energy spectra (AIES) and energy integrated angular distributions (EIAD) of protons from ([ital n],[ital p]) reactions at 14 MeV nominal neutron energy have been analyzed to develop systematics in relative preequilibrium contributions (RPC). The experimental estimates of RPC were obtained either from asymmetric components of the extrapolated EIAD or from the analysis of AIES, by comparison with equilibrium contributions obtained from the Hauser-Feshbach model. The experimentally obtained RPC have been compared with those expected from recent Feschbach-Kerman-Koonin theory as extended by Kalbach [ital et] [ital al]. as well as with theoretical predictions by Brown and Muirhead. The mass number systematics of RPC manifest shell and even-odd effects. The fraction of the precompound nucleus decays obtained from RPC, using the Blann-Griffin model, is constant and small for [ital A][ge]72, and increases to about 1 for small [ital A]'s. The analysis with the Kalbach model yields the dependence of the level density parameters [ital a][sub 1] and [ital a][sub 2] on [ital A]; also values of [ital a][sub 1] and [ital a][sub 2] manifest prominent structures near closed shell nuclei. The values of [ital a][sub 1] for compound nucleus are systematically highermore » than [ital a][sub 2], for the residual nuclei by an amount much larger than expected by usual [ital A] dependence, indicating excitation energy dependence of the single particle level density [ital g]. The excitation energy dependence of [ital g] when explored in the light of Rosenzweig's positive power law, with parameters [ital n] and [ital k], reveals that for most cases 1.2[le][ital n][le]1.5, with no systematic dependence of [ital n] on [ital A], compared to reported theoretical values of [ital n][congruent]1.6 by Rosenzweig, and 0.8[le][ital k][le]3.8 with a trend of slow increase of [ital k] with [ital A].« less