16,689 research outputs found
On the validity of Strong Cosmic Censorship Conjecture in presence of Dirac fields
A well posed theory of nature is expected to determine the future of an
observer uniquely from a given set of appropriate initial data. In the context
of general relativity, this is ensured by Penrose's strong cosmic censorship
conjecture. But in recent years, several examples are found which suggest
breakdown of the deterministic nature of the theory in Reissner-Nordstrom-de
Sitter black holes under the influence of different fundamental fields.
Nevertheless, the situation has been reassuring for the case of astrophysically
meaningful Kerr-de Sitter black hole solutions which seems to respect the
conjecture. However, the previous analyses were done considering only the
effect of scalar fields. In this paper, we extend the study by considering
Dirac fields in Kerr-de Sitter background and show that there exist a parameter
space which does not respect the conjecture.Comment: 13 pages, 2 figures, Accepted in European Physical Journal
Eigenfunctions and Random Waves in the Benjamini-Schramm limit
We investigate the asymptotic behavior of eigenfunctions of the Laplacian on
Riemannian manifolds. We show that Benjamini-Schramm convergence provides a
unified language for the level and eigenvalue aspects of the theory. As a
result, we present a mathematically precise formulation of Berry's conjecture
for a compact negatively curved manifold and formulate a Berry-type conjecture
for sequences of locally symmetric spaces. We prove some weak versions of these
conjectures. Using ergodic theory, we also analyze the connections of these
conjectures to Quantum Unique Ergodicity.Comment: 40 page
Weak cosmic censorship, dyonic Kerr-Newman black holes and Dirac fields
It was investigated recently, with the aim of testing the weak cosmic
censorship conjecture, whether an extremal Kerr black hole can be converted
into a naked singularity by interaction with a massless classical Dirac test
field, and it was found that this is possible. We generalize this result to
electrically and magnetically charged rotating extremal black holes (i.e.
extremal dyonic Kerr-Newman black holes) and massive Dirac test fields,
allowing magnetically or electrically uncharged or nonrotating black holes and
the massless Dirac field as special cases. We show that the possibility of the
conversion is a direct consequence of the fact that the Einstein-Hilbert
energy-momentum tensor of the classical Dirac field does not satisfy the null
energy condition, and is therefore not in contradiction with the weak cosmic
censorship conjecture. We give a derivation of the absence of superradiance of
the Dirac field without making use of the complete separability of the Dirac
equation in dyonic Kerr-Newman background, and we determine the range of
superradiant frequencies of the scalar field. The range of frequencies of the
Dirac field that can be used to convert a black hole into a naked singularity
partially coincides with the superradiant range of the scalar field. We apply
horizon-penetrating coordinates, as our arguments involve calculating
quantities at the event horizon. We describe the separation of variables for
the Dirac equation in these coordinates, although we mostly avoid using it.Comment: 28 pages, LaTeX, sections 2, 3 and appendix A shortened, appendix C
omitted, subsection 4.1 and references added, results unchange
A Dirac Morphism for the Farrell-Jones Isomorphism Conjecture in K-Theory
We construct a Dirac morphism and prove that if this Dirac morphism is
invertible, then the isomorphism conjecture for non-connective algebraic
K-theory holds true.Comment: 10 page
Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape
The requirement for an ultraviolet completable theory to be well-behaved upon
compactification has been suggested as a guiding principle for distinguishing
the landscape from the swampland. Motivated by the weak gravity conjecture and
the multiple point principle, we investigate the vacuum structure of the
standard model compactified on and . The measured value of the Higgs
mass implies, in addition to the electroweak vacuum, the existence of a new
vacuum where the Higgs field value is around the Planck scale. We explore two-
and three-dimensional critical points of the moduli potential arising from
compactifications of the electroweak vacuum as well as this high scale vacuum,
in the presence of Majorana/Dirac neutrinos and/or axions. We point out
potential sources of instability for these lower dimensional critical points in
the standard model landscape. We also point out that a high scale
vacuum of the Standard Model, if exists, would be at odd with the conjecture
that all non-supersymmetric vacua are unstable. We argue that, if we
require a degeneracy between three- and four-dimensional vacua as suggested by
the multiple point principle, the neutrinos are predicted to be Dirac, with the
mass of the lightest neutrino O(1-10) meV, which may be tested by future CMB,
large scale structure and cm line observations.Comment: 56 pages, 22 figures, published versio
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