arXiv subjects

John L. Friedman

Publications and source records attributed to John L. Friedman.

43 records · Page 3Linked to original sources

arXiv1997

Reduced phase space formalism for spherically symmetric geometry with a massive dust shell

We perform a Hamiltonian reduction of spherically symmetric Einstein gravity with a thin dust shell of positive rest mass. Three spatial topologies are considered: Euclidean (R^3), Kruskal (S^2 x R), and the spatial topology of a diametrically identified Kruskal (RP^3 - {a point at infinity}). For the Kruskal and RP^3 topologies the reduced phase space is four-dimensional, with one canonical pair associated with the shell and the other with the geometry; the latter pair disappears if one prescribes the value of the Schwarzschild mass at an asymptopia or at a throat. For the Euclidean topology the reduced phase space is necessarily two-dimensional, with only the canonical pair associated with the shell surviving. A time-reparametrization on a two-dimensional phase space is introduced and used to bring the shell Hamiltonians to a simpler (and known) form associated with the proper time of the shell. An alternative reparametrization yields a square-root Hamiltonian that generalizes the Hamiltonian of a test shell in Minkowski space with respect to Minkowski time. Quantization is briefly discussed. The discrete mass spectrum that characterizes natural minisuperspace quantizations of vacuum wormholes and RP^3-geons appears to persist as the geometrical part of the mass spectrum when the additional matter degree of freedom is added.

gr-qc↗

arXiv1997

Nonaxisymmetric Neutral Modes in Rotating Relativistic Stars

We study nonaxisymmetric perturbations of rotating relativistic stars. modeled as perfect-fluid equilibria. Instability to a mode with angular dependence $\exp(imϕ)$ sets in when the frequency of the mode vanishes. The locations of these zero-frequency modes along sequences of rotating stars are computed in the framework of general relativity. We consider models of uniformly rotating stars with polytropic equations of state, finding that the relativistic models are unstable to nonaxisymmetric modes at significantly smaller values of rotation than in the Newtonian limit. Most strikingly, the m=2 bar mode can become unstable even for soft polytropes of index $N \leq 1.3$, while in Newtonian theory it becomes unstable only for stiff polytropes of index $N \leq 0.808$. If rapidly rotating neutron stars are formed by the accretion-induced collapse of white dwarfs, instability associated with these nonaxisymmetric, gravitational-wave driven modes may set an upper limit on neutron-star rotation. Consideration is restricted to perturbations that correspond to polar perturbations of a spherical star. A study of axial perturbations is in progress.

gr-qc↗

arXiv1996

Upper Limit Set by Causality on the Rotation and Mass of Uniformly Rotating Relativistic Stars

Causality alone suffices to set a lower bound on the period of rotation of relativistic stars as a function of their maximum observed mass. That is, by assuming a one-parameter equation of state (EOS) that satisfies v_sound < c and that allows stars with masses as large as the largest observed neutron-star mass, M_sph^max, we find P[ms] > 0.282 + 0.196 ( M_sph^max/M_odot-1.442). The limit does not assume that the EOS agrees with a known low-density form for ordinary matter, but if one adds that assumption, the minimum period is raised by a few percent. Thus the current minimum period of uniformly rotating stars, set by causality, is 0.28ms (0.29ms for stars with normal crust). The minimizing EOS yields models with a maximally soft exterior supported by a maximally stiff core. An analogous upper limit set by causality on the maximum mass of rotating neutron stars requires a low-density match and the limit depends on the matching density, epsilon_m. We recompute it, obtaining a slightly revised value, M_rot^max \sim 6.1( 2 * 10^14 g/cm^3 epsilon_m )^1/2 M_odot.

astro-ph↗

arXiv1995

Topological Censorship

All three-manifolds are known to occur as Cauchy surfaces of asymptotically flat vacuum spacetimes and of spacetimes with positive-energy sources. We prove here the conjecture that general relativity does not allow an observer to probe the topology of spacetime: any topological structure collapses too quickly to allow light to traverse it. More precisely, in a globally hyperbolic, asymptotically flat spacetime satisfying the null energy condition, every causal curve from $\scri^-$ to ${\scri}^+$ is homotopic to a topologically trivial curve from $\scri^-$ to ${\scri}^+$. (If the Poincaré conjecture is false, the theorem does not prevent one from probing fake 3-spheres).

gr-qc↗

arXiv1995

Quantum field theory in Lorentzian universes-from-nothing

We examine quantum field theory in spacetimes that are time nonorientable but have no other causal pathology. These are Lorentzian universes-from-nothing, spacetimes with a single spacelike boundary that nevertheless have a smooth Lorentzian metric. Classically, such spacetimes are locally indistinguishable from their globally hyperbolic covering spaces. However, the construction of a quantum field theory (QFT) is more problematic. One can define a family of local algebras on an atlas of globally hyperbolic subspacetimes. But one cannot extend a generic positive linear function from a single algebra to the collection of all local algebras without violating positivity, while satisfying the physically appropriate overlap conditions. This difficulty can be overcome by restricting the size of neighborhoods so that the union of any pair is time- orientable. The structure of local algebras and states is then locally indistinguishable from that of QFT on a globally hyperbolic spacetime. But this size restriction on neighborhoods makes the structure unsatisfactory as a global field theory. The theory allows less information than QFT in a globally hyperbolic spacetime, because correlations between field operators at a pair of points are defined only if a curve joining the points lies in a single neigh- borhood. Moreover, to extend a local state to a collection of states, we use an antipodally symmetric state on the covering space, a state that would not yield a sensible state on the spacetime if all correlations could be measured.

gr-qc↗

arXiv1994

Existence and uniqueness theorems for massless fields on a class of spacetimes with closed timelike curves

We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC's), in which all future-directed CTC's traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a class of static geometries of this type, and for smooth initial data with all derivatives in $L_2$ on ${\cI}^{-}$, we prove existence of smooth solutions which are regular at null and spatial infinity (have finite energy and finite $L_2$-norm) and have the given initial data on $\cI^-$. A restricted uniqueness theorem is obtained, applying to solutions that fall off in time at any fixed spatial position. For a complementary class of spacetimes in which CTC's are confined to a compact region, we show that when solutions exist they are unique in regions exterior to the CTC's. (We believe that more stringent uniqueness theorems hold, and that the present limitations are our own.) An extension of these results to Maxwell fields and massless spinor fields is sketched. Finally, we discuss a conjecture that the Cauchy problem for free fields is well defined in the presence of CTC's whenever the problem is well-posed in the geometric-optics limit. We provide some evidence in support of this conjecture, and we present counterexamples that show that neither existence nor uniqueness is guaranteed under weaker conditions. In particular, both existence and uniqueness can fail in smooth, asymptotically flat spacetimes with a compact nonchronal region.

gr-qc↗

arXiv1994

Comparing Models of Rapidly Rotating Relativistic Stars Constructed by Two Numerical Methods

We present the first direct comparison of codes based on two different numerical methods for constructing rapidly rotating relativistic stars. A code based on the Komatsu-Eriguchi-Hachisu (KEH) method (Komatsu et al. 1989), written by Stergioulas, is compared to the Butterworth-Ipser code (BI), as modified by Friedman, Ipser and Parker. We compare models obtained by each method and evaluate the accuracy and efficiency of the two codes. The agreement is surprisingly good. A relatively large discrepancy recently reported (Eriguchi et al. 1994) is found to arise from the use of two different versions of the equation of state. We find, for a given equation of state, that equilibrium models with maximum values of mass, baryon mass, and angular momentum are (generically) all distinct and either all unstable to collapse or are all stable. Our implementation of the KEH method will be available as a public domain program for interested users.

astro-ph↗