18,122 research outputs found
The Effect of Multiple Heat Sources on Exomoon Habitable Zones
With dozens of Jovian and super-Jovian exoplanets known to orbit their host
stars in or near the stellar habitable zones, it has recently been suggested
that moons the size of Mars could offer abundant surface habitats beyond the
solar system. Several searches for such exomoons are now underway, and the
exquisite astronomical data quality of upcoming space missions and ground-based
extremely large telescopes could make the detection and characterization of
exomoons possible in the near future. Here we explore the effects of tidal
heating on the potential of Mars- to Earth-sized satellites to host liquid
surface water, and we compare the tidal heating rates predicted by tidal
equilibrium model and a viscoelastic model. In addition to tidal heating, we
consider stellar radiation, planetary illumination and thermal heat from the
planet. However, the effects of a possible moon atmosphere are neglected. We
map the circumplanetary habitable zone for different stellar distances in
specific star-planet-satellite configurations, and determine those regions
where tidal heating dominates over stellar radiation. We find that the
`thermostat effect' of the viscoelastic model is significant not just at large
distances from the star, but also in the stellar habitable zone, where stellar
radiation is prevalent. We also find that tidal heating of Mars-sized moons
with eccentricities between 0.001 and 0.01 is the dominant energy source beyond
3--5 AU from a Sun-like star and beyond 0.4--0.6 AU from an M3 dwarf star. The
latter would be easier to detect (if they exist), but their orbital stability
might be under jeopardy due to the gravitational perturbations from the star.Comment: accepted for publication in A&A, 8 pages, 4 figure
Conceptual Unification of Gravity and Quanta
We present a model unifying general relativity and quantum mechanics. The
model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid
\Gamma = E \times G where E is the total space of the frame bundle over
spacetime, and G the Lorentz group. The differential geometry, based on
derivations of \mbox{{\cal A}}, is constructed. The eigenvalue equation for the
Einstein operator plays the role of the generalized Einstein's equation. The
algebra \mbox{{\cal A}}, when suitably represented in a bundle of Hilbert
spaces, is a von Neumann algebra \mathcal{M} of random operators representing
the quantum sector of the model. The Tomita-Takesaki theorem allows us to
define the dynamics of random operators which depends on the state \phi . The
same state defines the noncommutative probability measure (in the sense of
Voiculescu's free probability theory). Moreover, the state \phi satisfies the
Kubo-Martin-Schwinger (KMS) condition, and can be interpreted as describing a
generalized equilibrium state. By suitably averaging elements of the algebra
\mbox{{\cal A}}, one recovers the standard geometry of spacetime. We show that
any act of measurement, performed at a given spacetime point, makes the model
to collapse to the standard quantum mechanics (on the group G). As an example
we compute the noncommutative version of the closed Friedman world model.
Generalized eigenvalues of the Einstein operator produce the correct components
of the energy-momentum tensor. Dynamics of random operators does not ``feel''
singularities.Comment: 28 LaTex pages. Substantially enlarged version. Improved definition
of generalized Einstein's field equation
Noncommutative Unification of General Relativity and Quantum Mechanics. A Finite Model
We construct a model unifying general relativity and quantum mechanics in a
broader structure of noncommutative geometry. The geometry in question is that
of a transformation groupoid given by the action of a finite group G on a space
E. We define the algebra of smooth complex valued functions on the groupoid,
with convolution as multiplication, in terms of which the groupoid geometry is
developed. Owing to the fact that the group G is finite the model can be
computed in full details. We show that by suitable averaging of noncommutative
geometric quantities one recovers the standard space-time geometry. The quantum
sector of the model is explored in terms of the regular representation of the
groupoid algebra, and its correspondence with the standard quantum mechanics is
established.Comment: 20 LaTex pages, General Relativity and Gravitation, in pres
Geometry and General Relativity in the Groupoid Model with a Finite Structure Group
In a series of papers we proposed a model unifying general relativity and
quantum mechanics. The idea was to deduce both general relativity and quantum
mechanics from a noncommutative algebra defined on a
transformation groupoid determined by the action of the Lorentz group
on the frame bundle over space-time . In the present work,
we construct a simplified version of the gravitational sector of this model in
which the Lorentz group is replaced by a finite group and the frame bundle
is trivial . The model is fully computable. We define the
Einstein-Hilbert action, with the help of which we derive the generalized
vacuum Einstein equations. When the equations are projected to space-time
(giving the "general relativistic limit"), the extra terms that appear due to
our generalization can be interpreted as "matter terms", as in
Kaluza-Klein-type models. To illustrate this effect we further simplify the
metric matrix to a block diagonal form, compute for it the generalized Einstein
equations and find two of their "Friedmann-like" solutions for the special case
when . One of them gives the flat Minkowski space-time (which,
however, is not static), another, a hyperbolic, linearly expanding universe.Comment: 32 page
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