1,022 research outputs found
Spherical collapse of supermassive stars: neutrino emission and gamma-ray bursts
We present the results of numerical simulations of the spherically symmetric
gravitational collapse of supermassive stars (SMS). The collapse is studied
using a general relativistic hydrodynamics code. The coupled system of Einstein
and fluid equations is solved employing observer time coordinates, by foliating
the spacetime by means of outgoing null hypersurfaces. The code contains an
equation of state which includes effects due to radiation, electrons and
baryons, and detailed microphysics to account for electron-positron pairs. In
addition energy losses by thermal neutrino emission are included. We are able
to follow the collapse of SMS from the onset of instability up to the point of
black hole formation. Several SMS with masses in the range are simulated. In all models an apparent horizon
forms initially, enclosing the innermost 25% of the stellar mass. From the
computed neutrino luminosities, estimates of the energy deposition by
-annihilation are obtained. Only a small fraction of this energy
is deposited near the surface of the star, where, as proposed recently by
Fuller & Shi (1998), it could cause the ultrarelativistic flow believed to be
responsible for -ray bursts. Our simulations show that for collapsing
SMS with masses larger than the energy deposition is
at least two orders of magnitude too small to explain the energetics of
observed long-duration bursts at cosmological redshifts. In addition, in the
absence of rotational effects the energy is deposited in a region containing
most of the stellar mass. Therefore relativistic ejection of matter is
impossible.Comment: 13 pages, 11 figures, submitted to A&
Computing Periods of Hypersurfaces
We give an algorithm to compute the periods of smooth projective
hypersurfaces of any dimension. This is an improvement over existing algorithms
which could only compute the periods of plane curves. Our algorithm reduces the
evaluation of period integrals to an initial value problem for ordinary
differential equations of Picard-Fuchs type. In this way, the periods can be
computed to extreme-precision in order to study their arithmetic properties.
The initial conditions are obtained by an exact determination of the cohomology
pairing on Fermat hypersurfaces with respect to a natural basis.Comment: 33 pages; Final version. Fixed typos, minor expository changes.
Changed code repository lin
Introduction to Arithmetic Mirror Symmetry
We describe how to find period integrals and Picard-Fuchs differential
equations for certain one-parameter families of Calabi-Yau manifolds. These
families can be seen as varieties over a finite field, in which case we show in
an explicit example that the number of points of a generic element can be given
in terms of p-adic period integrals. We also discuss several approaches to
finding zeta functions of mirror manifolds and their factorizations. These
notes are based on lectures given at the Fields Institute during the thematic
program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics
Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems
How many operations do we need on the average to compute an approximate root
of a random Gaussian polynomial system? Beyond Smale's 17th problem that asked
whether a polynomial bound is possible, we prove a quasi-optimal bound
. This improves upon the previously known
bound.
The new algorithm relies on numerical continuation along \emph{rigid
continuation paths}. The central idea is to consider rigid motions of the
equations rather than line segments in the linear space of all polynomial
systems. This leads to a better average condition number and allows for bigger
steps. We show that on the average, we can compute one approximate root of a
random Gaussian polynomial system of~ equations of degree at most in
homogeneous variables with continuation steps. This is a
decisive improvement over previous bounds that prove no better than
continuation steps on the average
The status of numerical relativity
Numerical relativity has come a long way in the last three decades and is now
reaching a state of maturity. We are gaining a deeper understanding of the
fundamental theoretical issues related to the field, from the well posedness of
the Cauchy problem, to better gauge conditions, improved boundary treatment,
and more realistic initial data. There has also been important work both in
numerical methods and software engineering. All these developments have come
together to allow the construction of several advanced fully three-dimensional
codes capable of dealing with both matter and black holes. In this manuscript I
make a brief review the current status of the field.Comment: Report on plenary talk at the 17th International Conference on
General Relativity and Gravitation (GR17), held at Dublin, Ireland, july
2004. Latex, 20 pages, 5 figure
Local characteristic algorithms for relativistic hydrodynamics
Numerical schemes for the general relativistic hydrodynamic equations are
discussed. The use of conservative algorithms based upon the characteristic
structure of those equations, developed during the last decade building on
ideas first applied in Newtonian hydrodynamics, provides a robust methodology
to obtain stable and accurate solutions even in the presence of
discontinuities. The knowledge of the wave structure of the above system is
essential in the construction of the so-called linearized Riemann solvers, a
class of numerical schemes specifically designed to solve nonlinear hyperbolic
systems of conservation laws. In the last part of the review some astrophysical
applications of such schemes, using the coupled system of the
(characteristic) Einstein and hydrodynamic equations, are also briefly
presented.Comment: 20 pages, 4 figures, To appear in the proceedings of the workshop
"The conformal structure of space-time", J. Frauendiener, H. Friedrich, eds,
Springer Lecture Notes in Physic
Simulating binary neutron stars: dynamics and gravitational waves
We model two mergers of orbiting binary neutron stars, the first forming a
black hole and the second a differentially rotating neutron star. We extract
gravitational waveforms in the wave zone. Comparisons to a post-Newtonian
analysis allow us to compute the orbital kinematics, including trajectories and
orbital eccentricities. We verify our code by evolving single stars and
extracting radial perturbative modes, which compare very well to results from
perturbation theory. The Einstein equations are solved in a first order
reduction of the generalized harmonic formulation, and the fluid equations are
solved using a modified convex essentially non-oscillatory method. All
calculations are done in three spatial dimensions without symmetry assumptions.
We use the \had computational infrastructure for distributed adaptive mesh
refinement.Comment: 14 pages, 16 figures. Added one figure from previous version;
corrected typo
The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
The Swampland Distance Conjecture claims that effective theories derived from
a consistent theory of quantum gravity only have a finite range of validity.
This will imply drastic consequences for string theory model building. The
refined version of this conjecture says that this range is of the order of the
naturally built in scale, namely the Planck scale. It is investigated whether
the Refined Swampland Distance Conjecture is consistent with proper field
distances arising in the well understood moduli spaces of Calabi-Yau
compactification. Investigating in particular the non-geometric phases of
Kahler moduli spaces of dimension , we always found
proper field distances that are smaller than the Planck-length.Comment: 71 pages, 11 figures, v2: refs added, typos correcte
Reconstructing GKZ via topological recursion
In this article, a novel description of the hypergeometric differential
equation found from Gel'fand-Kapranov-Zelevinsky's system (referred to GKZ
equation) for Givental's -function in the Gromov-Witten theory will be
proposed. The GKZ equation involves a parameter , and we will
reconstruct it as the WKB expansion from the classical limit via
the topological recursion. In this analysis, the spectral curve (referred to
GKZ curve) plays a central role, and it can be defined as the critical point
set of the mirror Landau-Ginzburg potential. Our novel description is derived
via the duality relations of the string theories, and various physical
interpretations suggest that the GKZ equation is identified with the quantum
curve for the brane partition function in the cohomological limit. As an
application of our novel picture for the GKZ equation, we will discuss the
Stokes matrix for the equivariant model and the
wall-crossing formula for the total Stokes matrix will be examined. And as a
byproduct of this analysis we will study Dubrovin's conjecture for this
equivariant model.Comment: 66 pages, 13 figures, 6 tables; v2: new subsections added, minor
revisions, typos corrected; v3: minor revisions, typos correcte
Formulations of the 3+1 evolution equations in curvilinear coordinates
Following Brown, in this paper we give an overview of how to modify standard
hyperbolic formulations of the 3+1 evolution equations of General Relativity in
such a way that all auxiliary quantities are true tensors, thus allowing for
these formulations to be used with curvilinear sets of coordinates such as
spherical or cylindrical coordinates. After considering the general case for
both the Nagy-Ortiz-Reula (NOR) and the Baumgarte-Shapiro-Shibata-Nakamura
(BSSN) formulations, we specialize to the case of spherical symmetry and also
discuss the issue of regularity at the origin. Finally, we show some numerical
examples of the modified BSSN formulation at work in spherical symmetry.Comment: 19 pages, 12 figure
- …