arXiv subjects

Ivan Arraut

Publications and source records attributed to Ivan Arraut.

45 records · Page 3Linked to original sources

arXiv2015

The Vainshtein conditions: The Vainshtein mechanism in terms of Stückelberg functions

Here I develop the simplest method in order to evaluate whether or not the Vainshtein mechanism can operate for a given set of parameters in a given solution. The method is based on the formulation of the mechanism in terms of the Stückelberg functions given in Int.J.Mod.Phys. D24 (2015) 1550022 and arXiv:1305.0475 [gr-qc]. In such a case, the Vainshtein scale appears as an extremal condition of the dynamical metric. If we fix the graviton mass, we can define the effective Vainshtein scale. Then for parameters where the Vainshtein scale vanishes or becomes smaller than the gravitational radius, the mechanism should be absent. At the other extreme, if the Vainshtein scale is finite or infinite, then the mechanism can operate. For consistency, if we define the Vainshtein scale as an invariant, then we should expect the effective graviton mass to become very large when the Vainshtein mechanism operates. On the other hand, if the mass scale tends to zero, then the extra-degrees of freedom are free to propagate. For clarity, here I analyze the effective mass behavior for the different type of modes.

gr-qc↗

arXiv2015

On the apparent loss of predictability inside the de-Rham-Gabadadze-Tolley non-linear formulation of massive gravity: The Hawking radiation effect

I explain in a simple and compact form the origin of the apparent loss of predictability inside the dRGT non-linear formulation of massive gravity. This apparent pathology was first reported by Kodama and the author when the stability of the Schwarzschild de-Sitter (S-dS) black-hole in dRGT was analyzed. If we study the motion of a massive test particle around the S-dS solution, we find that the total energy is not conserved in the usual sense. The conserved quantity associated with time appears as a combination of the total energy and a velocity-dependent term. If the equations of motion are written in terms of this conserved quantity, then the three-dimensional motion in dRGT will not differ with respect to the same situation of Einstein gravity (GR). The differences with respect to GR will appear whenever we have a dynamical situation. I explore the Hawking radiation as an example where we can find differences between GR and dRGT.

gr-qc↗

arXiv2014

The Komar mass function in the de-Rham-Gabadadze-Tolley non-linear theory of massive gravity

I derive the Komar mass/function for the Schwarszchild de-Sitter (S-dS) black-hole inside the dRGT non-linear theory of massive gravity by taking the usual notion of time-like Killing vector in unitary gauge. The dRGT Komar function depends on the dynamics of the Stückelberg fields through the gauge transformation function. It goes to the standard value obtained in General Relativity (GR) if the spatial derivative of the gauge function vanishes. In such a case, the (gauge) function corresponds to the usual notion of time as in GR.

gr-qc↗

arXiv2014

On the Black Holes in alternative theories of gravity: The case of non-linear massive gravity

I derive general conditions in order to explain the origin of the Vainshtein radius inside dRGT. The set of equations, which I have called "Vainshtein" conditions are extremal conditions of the dynamical metric ($g_{μν}$) containing all the degrees of freedom of the theory. The Vainshtein conditions are able to explain the coincidence between the Vainshtein radius in dRGT and the scale $r_0=\left(\frac{3}{2}r_s r_Λ^2\right)^{1/3}$, obtained naturally from the Schwarzschild de-Sitter (S-dS) space inside General Relativity (GR). In GR, this scale was interpreted as the maximum distance in order to get bound orbits. The same scale corresponds to the static observer position if we want to define the black hole temperature in an asymptotically de-Sitter space. In dRGT, the scale marks a limit after which the extra degrees of freedom of the theory become relevant.

gr-qc↗

arXiv2014

Stability of the Schwarzschild-de Sitter black hole in the dRGT massive gravity theory

The Schwarzschild-de Sitter solution in the Einstein theory with a positive cosmological constant $Λ=m^2/α$ becomes an exact solution to the dRGT non-linear massive gravity theory with the mass parameter $m$ when the theory parameters $α$ and $β$ satisfy the relation $β=α^2$. We study the perturbative behaviour of this black hole solution in the non-linear dRGT theory with $β=α^2$. We find that the linear perturbation equations become identical to those for the vacuum Einstein theory when they are expressed in terms of the gauge-invariant variables. This implies that this black hole is stable in the dRGT theory as far as the spacetime structure is concerned in contrast to the case of the bi-Schwarzschild solution in the bi-metric theory. However, we have also found a pathological feature that the general solution to the perturbation equations contain a single arbitrary function of spacetime coordinates. This implies a degeneracy of dynamics in the Stückelberg field sector at the linear perturbation level in this background. Physical significance of this degenercy depends on how the Stückelberg fields couple observable fields.

hep-th↗

arXiv2013

Relative locality and relative Co-locality as extensions of the Generalized Uncertainty Principle

I introduce the spatial curvature effects inside the formalism of Relative Locality as a non-commutative structure of the momentum space in agreement with the very well known concepts of Quantum Groups. This gives a natural red-shift effect in agreement with an extended version of the Generalized Uncertainty Principle (GUP) and in agreement with the standard notions of curvature inside General Relativity. I then introduce the concept of Relative Co-locality as a reinterpretation of the usual notions of spacetime curvature. From this redefinition, I obtain the momentum space curvature effects as a non-commutativity in position space. This introduce a natural blue-shift effect in agreement with the extended version of GUP. Both effects, Relative locality and Co-locality are dual each other inside the formalism of quantum groups $SU_q(n)$ symmetric Heisenberg algebras and their q-Bargmann Fock representations. When Relative locality and Co-locality are introduced, the q-deformation parameter takes the form $q\approx 1+\sqrt{\frac{\vert p\vert \vert x\vert}{r_Λm_{pl}}}$ with the spatial curvature effects in Relative Locality appearing like $ΔX\approx \frac{\vert x\vert}{m_{pl}}ΔP$ and the momentum curvature effects in Relative Co-locality appearing like $ΔP\approx \frac{\vert p\vert}{r_Λ}ΔX$, where $r_Λ=\frac{1}{\sqrtΛ}$ is the scale defined by the Cosmological Constant $Λ$, $m_{pl}$ is the Planck mass and $ΔX/ΔP$ is a scale of position/momentum or time/energy associated with the event, p and x are the momentum and position of the observer relative to the event.

gr-qc↗

arXiv2013

Can a non-local model of gravity reproduce Dark Matter effects in agreement with MOND?

I analyze the possibility of reproducing MONDian Dark Matter effects by using a non-local model of gravity. The model was used before in order to recreate screening effects for the Cosmological Constant ($Λ$) value. Although the model in the weak-field approximation (in static coordinates) can reproduce the field equations in agreement with the AQUAL Lagrangian, the solutions are scale dependent and cannot reproduce the same dynamics in agreement with MOND.

gr-qc↗

arXiv2013

About the propagation of the Gravitational Waves in an asymptotically de-Sitter space: Comparing two points of view

We analyze the propagation of gravitational waves (GWs) in an asymptotically de-Sitter space by expanding the perturbation around Minkowski and introducing the effects of the Cosmological Constant ($Λ$), first as an additional source (de-Donder gauge) and after as a gauge effect ($Λ$-gauge). In both cases the inclusion of the Cosmological Constant $Λ$ impedes the detection of a gravitational wave at a distance larger than $L_{crit}=(6\sqrt{2}πf \hat{h}/\sqrt{5})r_Λ^2$, where $r_Λ=\frac{1}{\sqrtΛ}$ and f and $\hat{h}$ are the frequency and strain of the wave respectively. We demonstrate that $L_{crit}$ is just a confirmation of the Cosmic No hair Conjecture (CNC) already explained in the literature.

gr-qc↗

arXiv2012

The Planck length as a duality of the Cosmological Constant: S-dS and S-AdS thermodynamics from a single expression

In this paper we suggest that the Planck length $l_{pl}$ and the Cosmological Constant scale $r_Λ=\frac{1}{\sqrtΛ}$ could in principle be dual each other if we take seriously the so-called q-Bargmann Fock space representation as has been previously suggested by Kempf and others and if additionally we introduce $l_{pl}$ as an ultraviolet cut-off and $r_Λ=\frac{1}{\sqrtΛ}$ as an infrared one. As a consequence, it is possible to demonstrate that a Generalized Uncertainty Principle (GUP) given by $ΔX ΔP\geq \frac{\hbar}{2}+\frac{l_{pl}^2}{2\hbar}(ΔP)^2+\frac{\hbar}{2r_Λ^2}(ΔX)^2$, can reproduce appropriately the thermodynamic behavior for both, the Schwarzschild Anti de-Sitter (S-AdS) and the Schwarzschild de-Sitter (S-dS) space without making any analytic extension for the coefficient (parameter) related to the minimum uncertainty in momentum (already suggested in the literature). This is possible if the Black Hole temperature is described with respect to the "natural" Static Observer for the S-dS case located at a distance $l_0=(3/2r_s r_Λ^2)^{1/3}$.

gr-qc↗