80 research outputs found
Projecting Massive Scalar Fields to Null Infinity
It is known that, in an asymptotically flat spacetime, null infinity cannot
act as an initial-value surface for massive real scalar fields. Exploiting
tools proper of harmonic analysis on hyperboloids and global norm estimates for
the wave operator, we show that it is possible to circumvent such obstruction
at least in Minkowski spacetime. Hence we project norm-finite solutions of the
Klein-Gordon equation of motion in data on null infinity and, eventually, we
interpret them in terms of boundary free field theory.Comment: 26 page
Hadamard states from null infinity
Free field theories on a four dimensional, globally hyperbolic spacetime,
whose dynamics is ruled by a Green hyperbolic partial differential operator,
can be quantized following the algebraic approach. It consists of a two-step
procedure: In the first part one identifies the observables of the underlying
physical system collecting them in a *-algebra which encodes their relational
and structural properties. In the second step one must identify a quantum
state, that is a positive, normalized linear functional on the *-algebra out of
which one recovers the interpretation proper of quantum mechanical theories via
the so-called Gelfand-Naimark-Segal theorem. In between the plethora of
possible states, only few of them are considered physically acceptable and they
are all characterized by the so-called Hadamard condition, a constraint on the
singular structure of the associated two-point function. Goal of this paper is
to outline a construction scheme for these states which can be applied whenever
the underlying background possesses a null (conformal) boundary. We discuss in
particular the examples of a real, massless conformally coupled scalar field
and of linearized gravity on a globally hyperbolic and asymptotically flat
spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum
Mathematical Physics", held in Regensburg from the 29th of September to the
02nd of October 201
Ground state for a massive scalar field in BTZ spacetime with Robin boundary conditions
We consider a real, massive scalar field in BTZ spacetime, a 2+1-dimensional
black hole solution of the Einstein's field equations with a negative
cosmological constant. First, we analyze the space of classical solutions in a
mode decomposition and we characterize the collection of all admissible
boundary conditions of Robin type which can be imposed at infinity. Secondly,
we investigate whether, for a given boundary condition, there exists a ground
state by constructing explicitly its two-point function. We demonstrate that
for a subclass of the boundary conditions it is possible to construct a ground
state that locally satisfies the Hadamard property. In all other cases, we show
that bound state mode solutions exist and, therefore, such construction is not
possible.Comment: 17 pages, 3 figure
Mode solutions for a Klein-Gordon field in anti-de Sitter spacetime with dynamical boundary conditions of Wentzell type
We study a real, massive Klein-Gordon field in the Poincar\'e fundamental
domain of the -dimensional anti-de Sitter (AdS) spacetime, subject to a
particular choice of dynamical boundary conditions of generalized Wentzell
type, whereby the boundary data solves a non-homogeneous, boundary Klein-Gordon
equation, with the source term fixed by the normal derivative of the scalar
field at the boundary. This naturally defines a field in the conformal boundary
of the Poincar\'e fundamental domain of AdS. We completely solve the equations
for the bulk and boundary fields and investigate the existence of bound state
solutions, motivated by the analogous problem with Robin boundary conditions,
which are recovered as a limiting case. Finally, we argue that both Robin and
generalized Wentzell boundary conditions are distinguished in the sense that
they are invariant under the action of the isometry group of the AdS conformal
boundary, a condition which ensures in addition that the total flux of energy
across the boundary vanishes.Comment: 12 pages, 1 figure. In V3: refs. added, introduction and conclusions
expande
Dynamical Backreaction in Robertson-Walker Spacetime
The treatment of a quantized field in a curved spacetime requires the study
of backreaction of the field on the spacetime via the semiclassical Einstein
equation. We consider a free scalar field in spatially flat Robertson-Walker
space time. We require the state of the field to allow for a renormalized
semiclassical stress tensor. We calculate the sigularities of the stress tensor
restricted to equal times in agreement with the usual renormalization
prescription for Hadamard states to perform an explicit renormalization. The
dynamical system for the Robertson Walker scale parameter coupled to the
scalar field is finally derived for the case of conformal and also general
coupling.Comment: Obtained equation of motion for non-conformal coupling, not just
counter terms as in previous version. Typos fixed, renormalization term
proportional to R adde
Spectroscopy of an AdS Reissner-Nordstrom black hole
In the framework of black hole spectroscopy, we extend the results obtained
for a charged black hole in an asymptotically flat spacetime to the scenario
with non vanishing negative cosmological constant. In particular, exploiting
Hamiltonian techniques, we construct the area spectrum for an AdS
Reissner-Nordstrom black hole.Comment: 21 pages, enhanced conclusions, references adde
Statistical entropy of the Schwarzschild black hole
We derive the statistical entropy of the Schwarzschild black hole by
considering the asymptotic symmetry algebra near the boundary of
the spacetime at past null infinity. Using a two-dimensional description and
the Weyl invariance of black hole thermodynamics this symmetry algebra can be
mapped into the Virasoro algebra generating asymptotic symmetries of anti-de
Sitter spacetime. Using lagrangian methods we identify the stress-energy tensor
of the boundary conformal field theory and we calculate the central charge of
the Virasoro algebra. The Bekenstein-Hawking result for the black hole entropy
is regained using Cardy's formula. Our result strongly supports a non-local
realization of the holographic principleComment: 3 pages no figure
A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
The generalized second law is proven for semiclassical quantum fields falling
across a causal horizon, minimally coupled to general relativity. The proof is
much more general than previous proofs in that it permits the quantum fields to
be rapidly changing with time, and shows that entropy increases when comparing
any slice of the horizon to any earlier slice. The proof requires the existence
of an algebra of observables restricted to the horizon, satisfying certain
axioms (Determinism, Ultralocality, Local Lorentz Invariance, and Stability).
These axioms are explicitly verified in the case of free fields of various
spins, as well as 1+1 conformal field theories. The validity of the axioms for
other interacting theories is discussed.Comment: 44 pages, 1 fig. v3: clarified Sec. 2; signs, factors/notation
corrected in Eq. 75-80, 105-107; reflects published version. v4: clearer
axioms in Sec. 2.3, fixed compensating factor of 2 errors in Eq. 54,74 etc.,
and other errors. Results unaffected. v5: fixed typos. v6: replaced faulty
1+1 CFT argument, added note on recent progres
Cosmological horizons and reconstruction of quantum field theories
As a starting point, we state some relevant geometrical properties enjoyed by
the cosmological horizon of a certain class of Friedmann-Robertson-Walker
backgrounds. Those properties are generalised to a larger class of expanding
spacetimes admitting a geodesically complete cosmological horizon \scrim
common to all co-moving observers. This structure is later exploited in order
to recast, in a cosmological background, some recent results for a linear
scalar quantum field theory in spacetimes asymptotically flat at null infinity.
Under suitable hypotheses on , encompassing both the cosmological de Sitter
background and a large class of other FRW spacetimes, the algebra of
observables for a Klein-Gordon field is mapped into a subalgebra of the algebra
of observables \cW(\scrim) constructed on the cosmological horizon. There is
exactly one pure quasifree state on \cW(\scrim) which fulfils a
suitable energy-positivity condition with respect to a generator related with
the cosmological time displacements. Furthermore induces a preferred
physically meaningful quantum state for the quantum theory in the
bulk. If admits a timelike Killing generator preserving \scrim, then the
associated self-adjoint generator in the GNS representation of has
positive spectrum (i.e. energy). Moreover turns out to be invariant
under every symmetry of the bulk metric which preserves the cosmological
horizon. In the case of an expanding de Sitter spacetime, coincides
with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this
case. Remarks on the validity of the Hadamard property for in more
general spacetimes are presented.Comment: 32 pages, 1 figure, to appear on Comm. Math. Phys., dedicated to
Professor Klaus Fredenhagen on the occasion of his 60th birthda
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