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At least 307 records · Page 17Linked to original sources
arXiv2013

On the Schrödinger equation for the free gravitational field

The Hamiltonian of the metric General Relativity derived in our earlier study (Gravitation, {\bf 17}, 314 - 323 (2011)) is analyzed by the methods of Matrix Quantum Mechanics. This Hamiltonian is a quadratic function of the momenta $π^{mn}$ conjugate to the spatial components $g_{mn}$ of the metric tensor $g_{αβ}$. The Hamiltonian is reduced to the new form which is more convenient to derive the Schrödinger equation for the free gravitational field. In turn, this Schrödinger equation is used to study possible motions of the free gravitational field(s). In particular, it is shown that harmonic oscillations of the free gravitational field, or harmonic gravitational waves, cannot be observed as an actual motion of this field. We also investigate the internal structure of the solitary gravitational wave.

math-ph↗
arXiv2013

Pathways to relativistic curved momentum spaces: de Sitter case study

Several arguments suggest that the Planck scale could be the characteristic scale of curvature of momentum space. As other recent studies we assume that the metric of momentum space determines the condition of on-shellness while the momentum-space affine connection governs the form of the law of composition of momenta. We show that the possible choices of laws of composition of momenta are more numerous than the possible choices of affine connection on a momentum space. This motivates us to propose a new prescription for associating an affine connection to momentum composition, which we compare to the one most used in the recent literature. We find that the two prescriptions lead to the same picture of the so-called $κ$-momentum space, with de Sitter metric and $κ$-Poincaré connection. We also examine in greater detail than ever before the DSR-relativistic properties of $κ$-momentum space, particularly in relation to its noncommutative law of composition of momenta. We then show that in the case of "proper de Sitter momentum space", with the de Sitter metric and its Levi-Civita connection, the two prescriptions are inequivalent. Our novel prescription leads to a picture of proper de Sitter momentum space which is DSR-relativistic and is characterized by a commutative law of composition of momenta, a possibility for which no explicit curved-momentum-space picture had been previously found. We argue that our construction provides a natural test case for the study of momentum spaces with commutative, and yet deformed, laws of composition of momenta. Moreover, it can serve as laboratory for the exploration of the properties of DSR-relativistic theories which are not connected to group-manifold momentum spaces and Hopf algebras.

gr-qc↗
arXiv2013

Global existence of solutions to the Einstein-massive scalar field equations with a cosmological constant for a perfect fluid on the flat Robertson-Walker space-time

In many cases a massive nonlinear scalar field can lead to accelerated expansion in cosmological models. This paper contains mathematical results on this subject for flat Robertson-Walker space-time. Global existence to the coupled Einstein-massive scalar field system which rules the dynamics of a kind of pure matter in the presence of a massive scalar field and cosmological constant is proved, under the assumption that the scalar field ? is a non-decreasing function, in Robertson-Walker1 space-time; asymptotic behaviour are investigated in the case of a cosmological constant bounded from below by a strictly negative constant depending only on the massive scalar field.

math-ph↗
arXiv2013

The collapse of supertasks

A supertask consists in the performance of an infinite number of actions in a finite time. I show that any attempt to carry out a supertask will produce a divergence of the curvature of spacetime, resulting in the formation of a black hole. I maintain that supertasks, contrarily to a popular view among philosophers, are physically impossible. Supertasks, literally, collapse under their own weight.

physics.hist-ph↗
arXiv2018

Spin networks on adiabatic quantum computer

The article is addressing a possibility of implementation of spin network states on adiabatic quantum computer. The discussion is focused on application of currently available technologies and analyzes a concrete example of D-Wave machine. A class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor is introduced. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states, which may inspire development of new generations of adiabatic quantum computers. A possibility of simulating Loop Quantum Gravity is discussed and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed.

gr-qc↗
arXiv2018

Quantum interactions, Predictability and Emergence Of Gravity

In this paper, we will show that gravity can emerge from an effective field theory, obtained by tracing out the fermionic system from an interacting quantum field theory, when we impose the condition that the field equations must be Cauchy predictable. The source of the gravitational field can be identified with the quantum interactions that existed in the interacting QFT. This relation is very similar to the ER= EPR conjecture and strongly relies on the fact that emergence of a classical theory will be dependent on the underlying quantum processes and interactions. We consider two concrete example for reaching the result - one where initially there was no gravity and other where gravity was present. The latter case will result in first order corrections to Einstein's equations and immediately reproduces well-known results like effective event horizons and gravitational birefringence.

hep-th↗
arXiv2018

Bianchi type-I dark energy cosmology with power-law relation in Brans-Dicke theory of gravitation

In this paper, we have studied the interacting and non-interacting dark energy and dark matter in the spatially homogenous and anisotropic Bianchi type-I model in the Brans- Dicke theory of gravitation. The field equations have been solved by using (i) power-law relation and (ii) by assuming scale factor in terms of redshift. Here we have considered two cases of an interacting and non-interacting dark energy scenario and obtained general results. It has been found that for suitable choice of interaction between dark energy and dark matter we can avoid the coincidence problem which appears in the model. Some physical aspects and stability of the models are discussed in detail. The statefinder diagnostic pair i.e. {r, s} is adopted to differentiate our dark energy models.

gr-qc↗
arXiv2018

Cosmology of the interacting Cubic Galileon

We consider the cosmological dynamics of the cubic Galileon field model interacting with dark matter, where the interaction between the cosmic dark sectors is proportional to Hubble parameter and dark energy density. The background field equations are converted into an autonomous dynamical system of first order equations using suitable dimensionless variables. The fixed points are determined and their stability analyzed by means of the eigenvalue method. The analysis of the stability of the fixed points along that of the avoidance of ghosts and Laplacian instabilities implies negative coupling parameter. We find an attractor fixed point in the de Sitter phase, and construct an approximated tracker solution, which to a good approximation, mimics the background cosmic evolution obtained by solving numerically the autonomous system of equations. In addition, we perform the statefinder and Om diagnostics and show that for some appropriate values of the coupling constant and initial conditions, the trajectories in the statefinder parameter phase space evolves towards a stable state corresponding to Λ CDM model. The comparison with the observed distance modulus and Hubble parameter data sets clearly indicates that the cosmological dynamics of the interacting cubic model is compatible with the existence of an interaction between the dark sectors.

gr-qc↗
arXiv2013

Radial distance on a stationary frame in a homogeneous and isotropic universe

This paper presents a physical distance to all radial events in a homogeneous and isotropic universe as a transform from Friedman-Lemaitre-Robertson-Walker (FLRW) coordinates, the model that solves the Einstein Field equation for an ideal fluid. Any well behaved transform is also a solution. The problem is relating the coordinates of the transform to observables. In the present case the objective is to find T,R on a stationary frame that has the R be a physical observable for all distances. We do this by working backwards, assuming the form of the metric that we desire, with some undetermined coefficients. These coefficients are then related to the partial derivatives of the transform. The transformed coordinates T,R are found by the integration of partial differential equations in the FLRW variables. We show that dR has the same units as the radial differential of the FLRW metric, which makes it observable. We develop a criterion for how close the transformed T comes to an observable time. Close to the space origin at the present time, T also becomes physical, so that the stationary acceleration becomes Newtonian. We show that a galactic point on a R,T plot starts close to the space origin at the beginning, moves out to a physical distance and finite time where it can release light that will be seen at the origin at the present time. Lastly, because the observable R has a finite limit at a finite T for t = 0 where the galactic velocity approaches the light speed, we see that the universe filled with an ideal fluid as seen on clocks and rulers on the stationary frame has a finite extent like that of an expanding empty universe, beyond which are no galaxies and no space.

astro-ph↗
arXiv2022

Lie Symmetries, Painlevé analysis and global dynamics for the temporal equation of radiating stars

We study the temporal equation of radiating stars by using three powerful methods for the analysis of nonlinear differential equations. Specifically, we investigate the global dynamics for the given master ordinary differential equation to understand the evolution of solutions for various initial conditions as also to investigate the existence of asymptotic solutions. Moreover, with the application of Lie's theory, we can reduce the order of the master differential equation, while an exact similarity solution is determined. Finally, the master equation possesses the Painlevé property, which means that the analytic solution can be expressed in terms of a Laurent expansion.

gr-qc↗
arXiv2017

Half-maximal supersymmetry from exceptional field theory

We study $D \geq 4$-dimensional half-maximal flux backgrounds using exceptional field theory. We define the relevant generalised structures and also find the integrability conditions which give warped half-maximal $\mathrm{Minkowski}_D$ and $\mathrm{AdS}_D$ vacua. We then show how to obtain consistent truncations of type II / 11-dimensional SUGRA which break half the supersymmetry. Such truncations can be defined on backgrounds admitting exceptional generalised $\mathrm{SO}(d-1-N)$ structures, where $d = 11 - D$, and $N$ is the number of vector multiplets obtained in the lower-dimensional theory. Our procedure yields the most general embedding tensors satisfying the linear constraint of half-maximal gauged SUGRA. We use this to prove that all $D\geq 4$ half-maximal warped $\mathrm{AdS}_D$ and Minkowski$_D$ vacua of type II / 11-dimensional SUGRA admit a consistent truncation keeping only the gravitational supermultiplet. We also show to obtain heterotic double field theory from exceptional field theory and comment on the M-theory / heterotic duality. In five dimensions, we find a new $\mathrm{SO}(5,N)$ double field theory with a $(6+N)$-dimensional extended space. Its section condition has one solution corresponding to 10-dimensional ${\cal N}=1$ supergravity and another yielding six-dimensional ${\cal N}=\left(2,0\right)$ SUGRA.

hep-th↗
arXiv2013

Features of warped geometry in presence of Gauss-Bonnet coupling

We study the role of the Gauss-Bonnet corrections and two loop higher genus contribution to the gravity action on the Kaluza-Klien modes and their interactions for different bulk fields which enable one to study various phenomenological implications of string loop corrected Gauss-Bonnet modified warped geometry model in one canvas. We have explicitly derived a phenomenological bound on the Gauss-Bonnet parameter so that the required Planck to TeV scale hierarchy can be achieved through the warp factor in the light of recently discovered Higgs like boson at 125 GeV. Moreover due to the presence of small perturbative Gauss-Bonnet as well as string loop corrections we have shown that the warping solution can be obtained for both de-Sitter and anti-de-Sitter bulk which is quite distinct from Randall-Sundrum scenario. Finally we have evaluated various interactions among these bulk fields and determined the coupling parameters and the Kaluza- Klien mode masses which is crucial to understand the phenomenology of a string two loop corrected Einstein-Gauss-Bonnet warp geometry.

hep-th↗
arXiv2022

On the Stability of String Theory Vacua

Vacuum compactifications may suffer from instabilities under small perturbations or tunnel effects; both are difficult to analyze. In this paper we consider the issue from a higher-dimensional perspective. We first look at how stability works for supersymmetric vacua, where it is widely expected to hold. We first show that the nucleation of brane bubbles in type II AdS compactifications is forbidden in the probe approximation by a simple argument involving pure spinors and calibrations. We then adapt familiar positive-energy theorems directly to M-theory and type II supergravity, rather than to their effective lower-dimensional reductions, also showing how to consistently include localised sources. We finally initiate an analysis of how these arguments might be extended to non-supersymmetric vacua. In M-theory, at the lower-derivative level, we find that the most natural modifications fail to stabilize the skew-whiffed and Englert vacua.

hep-th↗
arXiv2013

Thermalization of Causal Holographic Information

We study causal wedges associated with a given sub-region in the boundary of asymptotically AdS spacetimes. Part of our motivation is to better understand the recently proposed holographic observable, causal holographic information (CHI), which is given by the area of a bulk co-dimension two surface lying on the boundary of the causal wedge. It has been suggested that CHI captures the basic amount of information contained in the reduced density matrix about the bulk geometry. To explore its properties further we examine its behaviour in time-dependent situations. As a simple model we focus on null dust collapse in an asymptotically AdS spacetime, modeled by the Vaidya-AdS geometry. We argue that while CHI is generically quasi-telelogical in time-dependent backgrounds, for suitable choice of sub-regions in conformal field theories, the temporal evolution of CHI is entirely causal. We comment on the implications of this observation and more generally on features of causal constructions and contrast our results with the behaviour of holographic entanglement entropy. Along the way we also derive the rate of early time growth and late time saturation (to the thermal value) of both CHI and entanglement entropy in these backgrounds.

hep-th↗
arXiv2013

Hawking Radiation in a Plebanski-Demianski Black Hole

In this paper, we show the flux of Hawking radiation in a Plebański-Demiański black hole from the point of view of gauge and gravitational anomalies. We will use the consistent anomaly method to guarantee that our results are valid in the de Sitter space. This is because we are including the cosmological constant into our parameters and the covariant anomaly method gives a wrong value for the Hawking temperature. We also show that these calculations are a general result. In order to verify the consistence of our results, we can reproduce earlier known results as certain limiting cases.

hep-th↗
arXiv2013

Lobachevsky holography in conformal Chern-Simons gravity

We propose Lobachevsky boundary conditions that lead to asymptotically H^2xR solutions. As an example we check their consistency in conformal Chern-Simons gravity. The canonical charges are quadratic in the fields, but nonetheless integrable, conserved and finite. The asymptotic symmetry algebra consists of one copy of the Virasoro algebra with central charge c=24k, where k is the Chern-Simons level, and an affine u(1). We find also regular non-perturbative states and show that none of them corresponds to black hole solutions. We attempt to calculate the one-loop partition function, find a remarkable separation between bulk and boundary modes, but conclude that the one-loop partition function is ill-defined due to an infinite degeneracy. We comment on the most likely resolution of this degeneracy.

hep-th↗
arXiv2013

Monopoles On $S^2_F$ From The Fuzzy Conifold

The intersection of the conifold $z_1^2+z_2^2+z_3^2 =0$ and $S^5$ is a compact 3--dimensional manifold $X^3$. We review the description of $X^3$ as a principal U(1) bundle over $S^2$ and construct the associated monopole line bundles. These monopoles can have only even integers as their charge. We also show the Kaluza--Klein reduction of $X^3$ to $S^2$ provides an easy construction of these monopoles. Using the analogue of the Jordon-Schwinger map, our techniques are readily adapted to give the fuzzy version of the fibration $X^3 \rightarrow S^2$ and the associated line bundles. This is an alternative new realization of the fuzzy sphere $S^2_F$ and monopoles on it.

hep-th↗