324 research outputs found
Dynamics of a self-gravitating shell of matter
Dynamics of a self-gravitating shell of matter is derived from the Hilbert
variational principle and then described as an (infinite dimensional,
constrained) Hamiltonian system. A method used here enables us to define
singular Riemann tensor of a non-continuous connection {\em via} standard
formulae of differential geometry, with derivatives understood in the sense of
distributions. Bianchi identities for the singular curvature are proved. They
match the conservation laws for the singular energy-momentum tensor of matter.
Rosenfed-Belinfante and Noether theorems are proved to be still valid in case
of these singular objects. Assumption about continuity of the four-dimensional
spacetime metric is widely discussed.Comment: publishe
Energy-minimizing two black holes initial data
An attempt to construct the ``ground state'' vacuum initial data for the
gravitational field surrounding two black holes is presented. The ground state
is defined as the gravitational initial data minimizing the ADM mass within the
class of data for which the masses of the holes and their distance are fixed.
To parameterize different geometric arrangements of the two holes (and,
therefore, their distance) we use an appropriately chosen scale factor. A
method for analyzing the variations of the ADM mass and the masses (areas) of
the horizons in terms of gravitational degrees of freedom is proposed. The
Misner initial data are analyzed in this context: it is shown that they do not
minimize the ADM mass.Comment: Minor corrections, 2 references adde
Hesed: Redeemed Brokenness in a Multimedia Retelling of the Biblical Story of Ruth
Through the powerful interaction between the visual arts and music, an ancient story of brokenness and redemption is retold. This thesis seeks to give greater insight into this multimedia retelling of the biblical book of Ruth. Scholarly sources were reviewed to deepen understanding, and works from professional visual artists and musicians were examined for this project to come together. The end product is this thesis as well as a body of art and a five-movement piece of music. This combination of visual art and music allows the relevance of the biblical book of Ruth to be seen in the transforming journey of a grieving woman and her daughter
Hesed: Discovering Redeeming Brokenness in a Retelling of the Biblical Story of Ruth
Through the powerful interaction between the visual arts and music, an ancient story of brokenness and redemption is told. This thesis seeks to give greater insight into this multimedia retelling of the biblical book of Ruth. Scholarly sources were reviewed to deepen understanding, and works from professional visual artists and musicians were examined for this project to come together. The end product is this thesis paper as well as a body of art and a five-movement piece of music. This combination of visual art and music allows the relevance of the biblical book of Ruth to be seen in the transforming journey of a grieving woman and her daughter
Unconstrained Hamiltonian formulation of General Relativity with thermo-elastic sources
A new formulation of the Hamiltonian dynamics of the gravitational field
interacting with(non-dissipative) thermo-elastic matter is discussed. It is
based on a gauge condition which allows us to encode the six degrees of freedom
of the ``gravity + matter''-system (two gravitational and four
thermo-mechanical ones), together with their conjugate momenta, in the
Riemannian metric q_{ij} and its conjugate ADM momentum P^{ij}. These variables
are not subject to constraints. We prove that the Hamiltonian of this system is
equal to the total matter entropy. It generates uniquely the dynamics once
expressed as a function of the canonical variables. Any function U obtained in
this way must fulfil a system of three, first order, partial differential
equations of the Hamilton-Jacobi type in the variables (q_{ij},P^{ij}). These
equations are universal and do not depend upon the properties of the material:
its equation of state enters only as a boundary condition. The well posedness
of this problem is proved. Finally, we prove that for vanishing matter density,
the value of U goes to infinity almost everywhere and remains bounded only on
the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on
constraints and infinity elsewhere) can be obtained as the limit of a ``deep
potential well'' corresponding to non-vanishing matter. This unconstrained
description of Hamiltonian General Relativity can be useful in numerical
calculations as well as in the canonical approach to Quantum Gravity.Comment: 29 pages, TeX forma
Rigid spheres in Riemannian spaces
Choice of an appropriate (3+1)-foliation of spacetime or a (2+1)-foliation of
the Cauchy space, leads often to a substantial simplification of various
mathematical problems in General Relativity Theory. We propose a new method to
construct such foliations. For this purpose we define a special family of
topological two-spheres, which we call "rigid spheres". We prove that there is
a four-parameter family of rigid spheres in a generic Riemannian three-manifold
(in case of the flat Euclidean three-space these four parameters are: 3
coordinates of the center and the radius of the sphere). The rigid spheres can
be used as building blocks for various ("spherical", "bispherical" etc.)
foliations of the Cauchy space. This way a supertranslation ambiguity may be
avoided. Generalization to the full 4D case is discussed. Our results
generalize both the Huang foliations (cf. \cite{LHH}) and the foliations used
by us (cf. \cite{JKL}) in the analysis of the two-body problem.Comment: 23 page
Podstawowa bariera procesowa uzyskania statusu uchodźcy w Rzeczypospolitej Polskiej
Zdigitalizowano i udostępniono w ramach projektu pn. Rozbudowa otwartych zasobów naukowych Repozytorium Uniwersytetu w Białymstoku, dofinansowanego z programu „Społeczna odpowiedzialność nauki” Ministra Edukacji i Nauki na podstawie umowy SONB/SP/512497/202123925
Ochrona gruntów rolnych - prawda czy fikcja?
Zdigitalizowano i udostępniono w ramach projektu pn. Rozbudowa otwartych zasobów naukowych Repozytorium Uniwersytetu w Białymstoku, dofinansowanego z programu „Społeczna odpowiedzialność nauki” Ministra Edukacji i Nauki na podstawie umowy SONB/SP/512497/202111613
Energy and angular momentum of the weak gravitational waves on the Schwarzschild background -- quasilocal gauge-invariant formulation
It is shown that the axial and polar perturbations of the spherically
symmetric black hole can be described in a gauge-invariant way. The reduced
phase space describing gravitational waves outside of the horizon is described
by the gauge-invariant quantities. Both degrees of freedom fulfill generalized
scalar wave equation. For the axial degree of freedom the radial part of the
equation corresponds to the Regge-Wheeler result (Phys. Rev. 108, 1063-1069
(1957)) and for the polar one we get Zerilli result (Phys. Rev. D2, 2141-2160
(1970)), see also Chandrasekhar (The Mathematical Theory of Black
Holes,(Clarendon Press Oxford, 1983)), Moncrief (Annals of Physics 88, 323-342
(1974)) for both. An important ingredient of the analysis is the concept of
quasilocality which does duty for the separation of the angular variables in
the usual approach. Moreover, there is no need to represent perturbations by
normal modes (with time dependence ), we have fields in spacetime
and the Cauchy problem for them is well defined outside of the horizon. The
reduced symplectic structure explains the origin of the axial and polar
invariants. It allows to introduce an energy and angular momentum for the
gravitational waves which is invariant with respect to the gauge
transformations. Both generators represent quadratic approximation of the ADM
nonlinear formulae in terms of the perturbations of the Schwarzschild metric.
We also discuss the boundary-initial value problem for the linearized Einstein
equations on a Schwarzschild background outside of the horizon.Comment: 23 page
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