252 research outputs found
Is classical flat Kasner spacetime flat in quantum gravity?
Quantum nature of classical flat Kasner spacetime is studied using effective
spacetime description in loop quantum cosmology. We find that even though the
spacetime curvature vanishes at the classical level, non-trivial quantum
gravitational effects can arise. For the standard loop quantization of
Bianchi-I spacetime, which uniquely yields universal bounds on expansion and
shear scalars and results in a generic resolution of strong singularities, we
find that a flat Kasner metric is not a physical solution of the effective
spacetime description, except in a limit. The lack of a flat Kasner metric at
the quantum level results from a novel feature of the loop quantum Bianchi-I
spacetime: quantum geometry induces non-vanishing spacetime curvature
components, making it not Ricci flat even when no matter is present. The
non-curvature singularity of the classical flat Kasner spacetime is avoided,
and the effective spacetime transits from a flat Kasner spacetime in asymptotic
future, to a Minkowski spacetime in asymptotic past. Interestingly, for an
alternate loop quantization which does not share some of the fine features of
the standard quantization, flat Kasner spacetime with expected classical
features exists. In this case, even with non-trivial quantum geometric effects,
the spacetime curvature vanishes. These examples show that the character of
even a flat classical vacuum spacetime can alter in a fundamental way in
quantum gravity and is sensitive to the quantization procedure.Comment: 14 pages, 2 figures. Prepared for IJMPD special issue on Loop Quantum
Cosmolog
Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
We study the generic resolution of strong singularities in loop quantized
effective Bianchi-IX spacetime in two different quantizations - the connection
operator based `A' quantization and the extrinsic curvature based `K'
quantization. We show that in the effective spacetime description with
arbitrary matter content, it is necessary to include inverse triad corrections
to resolve all the strong singularities in the `A' quantization. Whereas in the
`K' quantization these results can be obtained without including inverse triad
corrections. Under these conditions, the energy density, expansion and shear
scalars for both of the quantization prescriptions are bounded. Notably, both
the quantizations can result in potentially curvature divergent events if
matter content allows divergences in the partial derivatives of the energy
density with respect to the triad variables at a finite energy density. Such
events are found to be weak curvature singularities beyond which geodesics can
be extended in the effective spacetime. Our results show that all potential
strong curvature singularities of the classical theory are forbidden in
Bianchi-IX spacetime in loop quantum cosmology and geodesic evolution never
breaks down for such events.Comment: 23 page
Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
Generic resolution of singularities and geodesic completeness in the loop
quantization of Bianchi-II spacetimes with arbitrary minimally coupled matter
is investigated. Using the effective Hamiltonian approach, we examine two
available quantizations: one based on the connection operator and second by
treating extrinsic curvature as connection via gauge fixing. It turns out that
for the connection based quantization, either the inverse triad modifications
or imposition of weak energy condition is necessary to obtain a resolution of
all strong singularities and geodesic completeness. In contrast, the extrinsic
curvature based quantization generically resolves all strong curvature
singularities and results in a geodesically complete effective spacetime
without inverse triad modifications or energy conditions. In both the
quantizations, weak curvature singularities can occur resulting from
divergences in pressure and its derivatives at finite densities. These are
harmless events beyond which geodesics can be extended. Our work generalizes
previous results on the generic resolution of strong singularities in the loop
quantization of isotropic, Bianchi-I and Kantowski-Sachs spacetimes.Comment: 24 pages. Revised version to appear in CQG. Clarifications on
quantization prescriptions and triad orientations adde
Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
Resolution of singularities in the Kantowski-Sachs model due to
non-perturbative quantum gravity effects is investigated. Using the effective
spacetime description for the improved dynamics version of loop quantum
Kantowski-Sachs spacetimes, we show that even though expansion and shear
scalars are universally bounded, there can exist events where curvature
invariants can diverge. However, such events can occur only for very exotic
equations of state when pressure or derivatives of energy density with respect
to triads become infinite at a finite energy density. In all other cases
curvature invariants are proved to remain finite for any evolution in finite
proper time. We find the novel result that all strong singularities are
resolved for arbitrary matter. Weak singularities pertaining to above potential
curvature divergence events can exist. The effective spacetime is found to be
geodesically complete for particle and null geodesics in finite time evolution.
Our results add to a growing evidence for generic resolution of strong
singularities using effective dynamics in loop quantum cosmology by
generalizing earlier results on isotropic and Bianchi-I spacetimes.Comment: Revised version. Discussion in the proof on absence of strong
singularities expanded. References added. To appear in CQ
Loop quantization of the Schwarzschild interior revisited
The loop quantization of the Schwarzschild interior region, as described by a
homogeneous anisotropic Kantowski-Sachs model, is re-examined. As several
studies of different -inequivalent- loop quantizations have shown, to date
there exists no fully satisfactory quantum theory for this model. This fact
poses challenges to the validity of some scenarios to address the black hole
information problem. Here we put forward a novel viewpoint to construct the
quantum theory that builds from some of the models available in the literature.
The final picture is a quantum theory that is both independent of any auxiliary
structure and possesses a correct low curvature limit. It represents a subtle
but non-trivial modification of the original prescription given by Ashtekar and
Bojowald. It is shown that the quantum gravitational constraint is well defined
past the singularity and that its effective dynamics possesses a bounce into an
expanding regime. The classical singularity is avoided, and a semiclassical
spacetime satisfying vacuum Einstein's equations is recovered on the "other
side" of the bounce. We argue that such metric represents the interior region
of a white-hole spacetime, but for which the corresponding "white-hole mass"
differs from the original black hole mass. Furthermore, we find that the value
of the white-hole mass is proportional to the third power of the starting black
hole mass.Comment: Revised version. Comparison with Ashtekar-Bojowald quantization
expanded. A figure showing dependence of the white hole mass on the fiducial
cell in Ashtekar-Bojowald quantization added. To appear in CQ
Reply to `Comment on "Quantum Bounce and Cosmic Recall"' [arXiv:0811.2790]
A recent Comment [arXiv:0811.2790] on the Letter 'Quantum Bounce and Cosmic
Recall' by the authors is shown to arise from an incorrect understanding of the
issues at hand and of our analysis. The conclusions of Bojowald's Comment are
shown to add little to our work, to be irrelevant at best, and are further
shown to be in contradiction with his own claims in the literature.Comment: 2 page
Matter-Antimatter Asymmetry Generated by Loop Quantum Gravity
We show that Loop Quantum Gravity provides new mechanisms through which
observed matter-antimatter asymmetry in the Universe can naturally arise at
temperatures less than GUT scale. This is enabled through the introduction of a
new length scale , much greater than Planck length (), to obtain
semi-classical weave states in the theory. This scale which depends on the
momentum of the particle modifies the dispersion relation for different
helicities of fermions and leads to lepton asymmetry.Comment: To appear in Phys. Lett. B. Minor changes in presentation. References
adde
Field Theories from the Relativistic Law of Motion
From the relativistic law of motion we attempt to deduce the field theories
corresponding to the force law being linear and quadratic in 4-velocity of the
particle. The linear law leads to the vector gauge theory which could be the
abelian Maxwell electrodynamics or the non-abelian Yang-Mills theory. On the
other hand the quadratic law demands spacetime metric as its potential which is
equivalent to demanding the Principle of Equivalence. It leads to the tensor
theory of gravitational field -- General Relativity. It is remarkable that a
purely dynamical property of the force law leads uniquely to the corresponding
field theories.Comment: LaTeX, 14 pages. Accepted in Mod. Phys. Lett.
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