59,445 research outputs found
Quantum hoop conjecture and a natural cutoff for vacuum energy of a scalar field
We propose here a quantum hoop conjecture which states: the de Broglie
wavelength of a quantum system cannot be arbitrarily small, it must be larger
than the characterized Schwarzschild radius of the quantum system. Based on
this conjecture, we find an upper bound for the wave number (or the momentum)
of a particle, which offers a natural cutoff for the vacuum energy of a scalar
field.Comment: 3 pages, no figure
Constraints from accretion onto a Tangherlini-Reissner-Nordstrom black hole
We investigate spherically symmetric, steady state, adiabatic accretion onto
a Tangherlini-Reissner-Nordstrom black hole in arbitrary dimensions by using
-dimensional general relativity. We obtain basic equations for accretion and
determine analytically the critical points, the critical fluid velocity, and
the critical sound speed. We lay emphasis on the condition under which the
accretion is possible. This condition constrains the ratio of mass to charge in
a narrow limit, which is independent of dimension for large dimension. This
condition may challenge the validity of the cosmic censorship conjecture since
a naked singularity is eventually produced as the magnitude of charge increases
compared to the mass of black hole.Comment: 8 pages, no figure
Gravitational waves in conformal gravity
We consider the gravitational radiation in conformal gravity theory. We
perturb the metric from flat Mikowski space and obtain the wave equation after
introducing the appropriate transformation for perturbation. We derive the
effective energy-momentum tensor for the gravitational radiation, which can be
used to determine the energy carried by gravitational waves.Comment: 8 pages, no figures, some errors are correcte
New types of gravity
Recently theories based on modifications of teleparallel gravity where
torsion is the geometric object describing gravity instead of curvature have
been proposed to explain the present cosmic accelerating expansion. The field
equations are always second order, remarkably simpler than theories. In
analogy to the theory, we consider here three types of gravity,
and find that all of them can give rise to cosmic acceleration with interesting
features, respectively.Comment: 6 pages, 9 figures, some changes are mad
Large-scale structure in superfluid Chaplygin gas cosmology
We investigate the growth of large-scale structure in the superfluid
Chaplygin gas (SCG) model. Both linear and non-linear growth, such as
and the skewness , are discussed. We find the growth factor of
SCG reduces to the EdS case at early times while differs from the CDM
case in the large limit. We also find there will be much stricture growth
on large scales in the SCG scenario than in CDM and the variations of
and between SCG and CDM can not be discriminated.Comment: 10 pages, 6 figures, minor errors are correcte
Learning to Prove Theorems via Interacting with Proof Assistants
Humans prove theorems by relying on substantial high-level reasoning and
problem-specific insights. Proof assistants offer a formalism that resembles
human mathematical reasoning, representing theorems in higher-order logic and
proofs as high-level tactics. However, human experts have to construct proofs
manually by entering tactics into the proof assistant. In this paper, we study
the problem of using machine learning to automate the interaction with proof
assistants. We construct CoqGym, a large-scale dataset and learning environment
containing 71K human-written proofs from 123 projects developed with the Coq
proof assistant. We develop ASTactic, a deep learning-based model that
generates tactics as programs in the form of abstract syntax trees (ASTs).
Experiments show that ASTactic trained on CoqGym can generate effective tactics
and can be used to prove new theorems not previously provable by automated
methods. Code is available at https://github.com/princeton-vl/CoqGym.Comment: Accepted to ICML 201
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