Dilatonic Brans-Dicke Anisotropic Collapsing Fluid Sphere And de Broglie Quantum Wave Motion
Hossein Ghaffarnejad
备注：
4 pages in letter format, 1 figure, Accepted as ORAL presentation in `5th International Conference on Mathematical Modeling in Physical Sciences, May 23-26, 2016, Athens, Greece, and will be appeared in J. of Physics (Conference series)`
发表信息：
Journal of Physics: conference Series 738 (2016)012031
Two dimensional (2D) analogue of vacuum sector of the Brans Dicke (BD) gravity [1] is studied to obtain dynamics of anisotropic spherically symmetric perfect fluid. Our obtained static solutions behave as dark matter with state equation $γ=\frac{p(ρ)}{\varrho}=-0.25$ but in non-static regimes behave as regular perfect fluid with barotropic index $γ>0.$ Positivity property of total mass of the fluid causes that the BD parameter to be $ω>\frac{2}{3}$ and/or $ω<-1$.
Locations of the event and apparent horizons of the collapsing fluid are obtained in its static regime. In case $ω>0$ the apparent horizon is covered by event horizon where the cosmic censorship hypothesis is still valid. According to the model [1], we obtain de Broglie pilot wave of our metric solution which describes particles ensemble which become distinguishable via different values of $ω.$ Incident current density of particles ensemble on the horizons is evaluated which describe the `Hawking radiation`. The de Brogle -Bohm quantum potential effect is calculated also on the event (apparent) horizon which is independent (dependent) to values of $ω.$
The 5d dilatonic gravity action with surface counterterms, motivated by the AdS/CFT correspondence and with contributions of brane quantum CFTs is considered with an AdS-like bulk. The role of quantum brane CFT consists in inducing complicated brane dilatonic gravity. For exponential bulk potentials, a number of AdS-like bulk spaces is found in an analytical form. The corresponding flat or curved (de Sitter or hyperbolic) dilatonic two-branes are created.
We supplement the discussion on localization of gravity on dilatonic domain walls in ``Solitons in Brane Worlds'' (Nucl. Phys. B576, 106, hep-th/9911218) by giving unified and coherent discussion which combines the result of this paper and the expanded results in the author's subsequent papers in an attempt to avoid misleading readers. We also discuss the possible string theory embeddings of the Randall-Sundrum type brane world scenarios through non-dilatonic and dilatonic domain walls, which straightforwardly follows from the author's previous works but was not elaborated explicitly.
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Static spherically symmetric solutions of 4d Brans-Dicke theory include a set of naked singularity solutions. Dilatonic effects near the naked singularities result in either a shielding or an antishielding effect from intruding massive test particles. One result is that for a portion of the solution parameter space, no communication between the singularity and a distant observer is possible via massive particle exchanges. Kaluza-Klein gravity is considered as a special case.
It is pointed out that the coupling of macroscopic test masses to the gravi-dilaton background of string theory is non geodesic, in general, and cannot be parametrized by a Brans-Dicke model of scalar-tensor gravity. The response of gravitational antennas to dilatonic waves should be analyzed through a generalized equation of geodesic deviation, taking into account the possible direct coupling of the background to the (composition-dependent) dilatonic charge of the antenna.
Time-dependent domain wall solutions with infinitesimal thickness are obtained in the theory of a scalar field coupled to gravity with the dilaton, i.e. the Jordan-Brans-Dicke gravity. The value of the dilaton is determined in terms of the Brans-Dicke parameter $ω$. In particular, the solutions exist for any $ω>0$ and as $ω\to\infty$ we obtain new solutions in general relativity. They have horizons whose sizes depend on $ω$.
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Regarding the wide applications of dilaton gravity in the presence of electrodynamics, we introduce a suitable Lagrangian for the coupling of dilaton with gauge field. There are various Lagrangians which show the coupling between scalar fields and electrodynamics with correct special situations. In this paper, taking into account conformal transformation of Brans-Dicke theory with an electrodynamics Lagrangian, we show that how scalar field should couple with electrodynamics in dilaton gravity. In other words, in order to introduce a correct Lagrangian of dilaton gravity, one should check at l…
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Effects of a 4d dilaton field on a falling test mass are examined from the Einstein frame perspective of scalar-tensor theory. Results are obtained for the centripetal acceleration of particles in circular orbits, and the radial acceleration for particles with pure radial motion. These results are applied to the specific case of nonrelativistic motion in the weak field approximation of Brans-Dicke theory, employing the exact Xanthopoulos-Zannias solutions. For a given parameter range, the results obtained from Brans-Dicke theory are qualitatively dramatically different from those of general re…
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Motivated by thermodynamic analogy of black holes and Van der Waals liquid/gas system, in this paper, we study $P-V$ criticality of both dilatonic Born-Infeld black holes and their conformal solutions, Brans-Dicke-Born-Infeld solutions. Due to the conformal constraint, we have to neglect the old Lagrangian of dilatonic Born-Infeld theory and its black hole solutions, and introduce a new one. We obtain spherically symmetric nonlinearly charged black hole solutions in both Einstein and Jordan frames and then, we calculate the related conserved and thermodynamic quantities. After that, we extend …
In the version \cite{Fiziev14} of this paper we presented for the first time the basic equations and relations for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG). This model is {\em locally} equivalent to the f(R) theory of gravity and gives an alternative description of the effects of dark matter and dark energy using the Branse-Dicke dilaton $Φ$. To outline the basic properties of the MDG model of SSSS and to compare them with general relativistic results, in the present paper we use the relativistic equation of state (EOS) of neutron m…
In this paper we discuss classical and quantum aspects of cosmological models in Brans-Dicke theory. First, we review cosmological bounce solution in Brans-Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then we quantize this classical model in a canonical way, establishing the corresponding Wheeler-DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case $ω<-3/2$, the energy is bounded from below and singularity-free solutions are found. However, in the cas…
We study the preheating scenario in Generalized Einstein Theories, considering a class of such theories which are conformally equivalent to those of an extra field with a modified potential in the Einstein frame. Resonant creation of bosons from oscillating inflaton has been studied before in the context of general relativity taking also into account the effect of metric perturbations in linearized gravity. As a natural generalization we include the dilatonic/Brans-Dicke field without any potential of its own and in particular we study the linear theory of perturbations including the metric pe…
In this paper we seek for relevant information on the asymptotic cosmological dynamics of the Brans--Dicke theory of gravity for several self-interaction potentials. By means of the simplest tools of the dynamical systems theory, it is shown that the general relativity de Sitter solution is an attractor of the Jordan frame (dilatonic) Brans--Dicke theory only for the exponential potential $U(\vphi)\propto\exp\vphi$, which corresponds to the quadratic potential $V(ϕ)\proptoϕ^2$ in terms of the original Brans--Dicke field $ϕ=\exp\vphi$, or for potentials which asymptote to $\exp\vphi$. At the st…
