14 research outputs found
Static plane symmetric relativistic fluids and empty repelling singular boundaries
We present a detailed analysis of the general exact solution of Einstein's
equation corresponding to a static and plane symmetric distribution of matter
with density proportional to pressure. We study the geodesics in it and we show
that this simple spacetime exhibits very curious properties. In particular, it
has a free of matter repelling singular boundary and all geodesics bounce off
it.Comment: 9 pages, 1 figure, accepted for publication in Classical and Quantum
Gravit
Infinite slabs and other weird plane symmetric space-times with constant positive density
We present the exact solution of Einstein's equation corresponding to a
static and plane symmetric distribution of matter with constant positive
density located below . This solution depends essentially on two
constants: the density and a parameter . We show that this
space-time finishes down below at an inner singularity at finite depth. We
match this solution to the vacuum one and compute the external gravitational
field in terms of slab's parameters. Depending on the value of , these
slabs can be attractive, repulsive or neutral. In the first case, the
space-time also finishes up above at another singularity. In the other cases,
they turn out to be semi-infinite and asymptotically flat when .
We also find solutions consisting of joining an attractive slab and a
repulsive one, and two neutral ones. We also discuss how to assemble a
"gravitational capacitor" by inserting a slice of vacuum between two such
slabs.Comment: 8 page
On well-posedness of the Cauchy problem for the wave equation in static spherically symmetric spacetimes
We give simple conditions implying the well-posedness of the Cauchy problem
for the propagation of classical scalar fields in general (n+2)-dimensional
static and spherically symmetric spacetimes. They are related to properties of
the underlying spatial part of the wave operator, one of which being the
standard essentially self-adjointness. However, in many examples the spatial
part of the wave operator turns out to be not essentially selfadjoint, but it
does satisfy a weaker property that we call here quasi essentially
self-adjointness, which is enough to ensure the desired well-posedness. This is
why we also characterize this second property.
We state abstract results, then general results for a class of operators
encompassing many examples in the literature, and we finish with the explicit
analysis of some of them.Comment: 36 pages. Final version to appear in Classical and Quantum Gravit
An alternative well-posedness property and static spacetimes with naked singularities
In the first part of this paper, we show that the Cauchy problem for wave
propagation in some static spacetimes presenting a singular time-like boundary
is well posed, if we only demand the waves to have finite energy, although no
boundary condition is required. This feature does not come from essential
self-adjointness, which is false in these cases, but from a different
phenomenon that we call the alternative well-posedness property, whose origin
is due to the degeneracy of the metric components near the boundary.
Beyond these examples, in the second part, we characterize the type of
degeneracy which leads to this phenomenon.Comment: 34 pages, 3 figures. Accepted for publication in Class. Quantum Gra
On the energy-momentum tensor
We clarify the relation among canonical, metric and Belinfante's
energy-momentum tensors for general tensor field theories. For any tensor field
T, we define a new tensor field \til {\bm T}, in terms of which the
Belinfante tensor is readily computed. We show that the latter is the one that
arises naturally from Noether Theorem for an arbitrary spacetime and it
coincides on-shell with the metric one.Comment: 11 pages, 1 figur
Empty singularities in higher-dimensional Gravity
We study the exact solution of Einstein's field equations consisting of a
()-dimensional static and hyperplane symmetric thick slice of matter, with
constant and positive energy density and thickness , surrounded by
two different vacua. We explicitly write down the pressure and the external
gravitational fields in terms of and , the pressure is positive and
bounded, presenting a maximum at an asymmetrical position. And if
is small enough, the dominant energy condition is satisfied
all over the spacetime. We find that this solution presents many interesting
features. In particular, it has an empty singular boundary in one of the vacua.Comment: 13 page
The electromagnetic energy-momentum tensor
We clarify the relation between canonical and metric energy-momentum tensors.
In particular, we show that a natural definition arises from Noether's Theorem
which directly leads to a symmetric and gauge invariant tensor for
electromagnetic field theories on an arbitrary space-time of any dimension