71 research outputs found
The Equivalence Theorem in the Generalized Gravity of f(R)-Type and Canonical Quantization
We first review the equivalence theorem of the f(R)-type gravity to Einstein
gravity with a scalar field by deriving it in a self-contained and pedagogical
way. Then we describe the problem of to what extent the equivalence holds. Main
problems are (i) Is the surface term given by Gibbons and Hawking which is
necessary in Einstein gravity also necessary in the f(R)-type gravity? (ii)
Does the equivalence hold also in quantum theory? (iii) Which metric is
physical, i.e., which metric should be identified with the observed one? In
this work, we clarify the problem (i) and review the problem (ii) in a
canonical formalism which is the generalization of the Ostrogradski one. We
briefly comment on the problem (iii). Some discussions are given on one of the
results of (ii) concerning the general relativity in non-commutative spacetime.Comment: 23 pages. Ecept for the change of style from {book} to {article} and
related changes, e.g., addition of abstract and the form of References, as
well as the addition of Appendix B, the work has been published as one of the
chapters in the book "Advances in Quantum Theory" (2012, ed. Ion I. Cotaescu;
InTech Open Access Publisher
Time without time: a stochastic clock model
We study a classical reparametrization-invariant system, in which ``time'' is
not a priori defined. It consists of a nonrelativistic particle moving in five
dimensions, two of which are compactified to form a torus. There, assuming a
suitable potential, the internal motion is ergodic or more strongly irregular.
We consider quasi-local observables which measure the system's ``change'' in a
coarse-grained way. Based on this, we construct a statistical timelike
parameter, particularly with the help of maximum entropy method and Fisher-Rao
information metric. The emergent reparametrization-invariant ``time'' does not
run smoothly but is simply related to the proper time on the average. For
sufficiently low energy, the external motion is then described by a unitary
quantum mechanical evolution in accordance with the Schr\"odinger equation.Comment: 18 pages; LaTeX. 4 (.ps) plus 2 (.gif) figure file
Third quantization of -type gravity
We examine the third quantization of -type gravity, based on its
effective Lagrangian in the case of a flat Friedmann-Lemaitre-Robertson-Walker
metric. Starting from the effective Lagrangian, we execute a suitable change of
variable and the second quantization, and we obtain the Wheeler-DeWitt
equation. The third quantization of this theory is considered. And the
uncertainty relation of the universe is investigated in the example of
-type gravity, where . It is shown, when the time is late
namely the scale factor of the universe is large, the spacetime does not
contradict to become classical, and, when the time is early namely the scale
factor of the universe is small, the quantum effects are dominating.Comment: 9 pages, Arbitrary constants in (4.19) are changed to arbitrary
functions of . Conclusions are not changed. References are added.
Typos are correcte
Classical and Quantum Solutions and the Problem of Time in Cosmology
We have studied various classical solutions in cosmology. Especially we
have obtained general classical solutions in pure \ cosmology. Even in the
quantum theory, we can solve the Wheeler-DeWitt equation in pure \
cosmology exactly. Comparing these classical and quantum solutions in \
cosmology, we have studied the problem of time in general relativity.Comment: 17 pages, latex, no figure, one reference is correcte
Some Aspects of Virtual Black Holes
In this paper we shall consistently third quantize modified gravity. Then we
shall analyse certain aspects of virtual black holes in this third quantized
modified gravity. We will see how a statistical mechanical origin for the
Bekenstein-Hawking entropy naturally arises in this model. Furthermore, in this
model the area and thus the entropy of a real macroscopic black hole is
quantized. Virtual black holes cause loss of quantum coherence and this gives
an intrinsic entropy to all physical systems which can be used to define a
direction of time and hence provide a solution to the problem of time.Comment: 11 pages, 0 figures, accepted for publication in JET
Born-Infeld Theory and Stringy Causality
Fluctuations around a non-trivial solution of Born-Infeld theory have a
limiting speed given not by the Einstein metric but the Boillat metric. The
Boillat metric is S-duality invariant and conformal to the open string metric.
It also governs the propagation of scalars and spinors in Born-Infeld theory.
We discuss the potential clash between causality determined by the closed
string and open string light cones and find that the latter never lie outside
the former. Both cones touch along the principal null directions of the
background Born-Infeld field. We consider black hole solutions in situations in
which the distinction between bulk and brane is not sharp such as space filling
branes and find that the location of the event horizon and the thermodynamic
properties do not depend on whether one uses the closed or open string metric.
Analogous statements hold in the more general context of non-linear
electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld
action to second order might be obtained from higher-curvature gravity in
Kaluza-Klein theory. Finally we point out some intriguing analogies with
Einstein-Schr\"odinger theory.Comment: 31 pages, 4 figures, LaTex; Some comments and references adde
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