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Register a new userEntropic force, running gravitational coupling and future singularities
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The effects of a running gravitational coupling and the entropic force on future singularities are considered. Although it is expected that the quantum corrections remove the future singularities or change the singularity type, treating the running gravitational coupling as a function of energy density is found to cause no change in the type of singularity but causes a delay in the time that a singularity occurs. The entropic force is found to replaces the singularity type $II$ by $bar{III}$ ($a=$const., $H=$const., $dot{H} to infty$, $p to infty$, $rho to infty$) which differs from previously known type $III$ and to remove the $w$-singularity. We also consider an effective cosmological model and show that the types $I$ and $II$ are replaced by the singularity type $III$.
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Starting from the dipole representation of small-$x$ evolution we implement the running of the coupling in a self-consistent way. This results in an evolution equation for the dipole density in Borel $(b)$ space. We show that the Borel image of the dipole density is analytic in the neighbourhood of $b=0$ and that it is equal to the BFKL solution at $b=0$. We study the Borel singularity structure of the dipole cascade emanating from a virtual photon at small $x$ and find a branch cut on the positive $b$-semiaxis starting at $b=1/ beta_0$. This indicates the presence of $1/Q^2$ power corrections to the small-$x$ structure functions. Finally we present numerical results in the context of D.I.S.
We link observational parameters such as the deceleration parameter, the jerk, the kerk (snap) and higher-order derivatives of the scale factor, called statefinders, to the conditions which allow to develop sudden future singularities of pressure with finite energy density. In this context, and within the framework of Friedmann cosmology, we also propose higher-order energy conditions which relate time derivatives of the energy density and pressure which may be useful in general relativity.
Entropic force originates in the assumption that there is a horizon for the universe. This horizon gives rise to additional terms in the equations of motion. Using dynamical system calculations, our results show that in the presence of dark energy for certain conditions, the last attractor of this theory will be dark energy epoch, but in the absence of dark energy, entropic force energy portion will have the lead role in the late time universe and is responsible for accelerated expansion of that. Interestingly, assuming both entropic force terms and dark energy to have their share of energy density of the universe, we have found that, in certain conditions entropic force dominated epoch is a stable fixed point while the dark energy epoch is a saddle point.
Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is essential in many cases such as the quasinormal ringdown following the merger of a binary system, tidally perturbed compact objects, and extreme-mass-ratio inspirals. In this review, motivated primarily by small-mass-ratio binaries but not limited to them, we provide an overview of essential methods in (i) black hole perturbation theory, (ii) orbital mechanics in Kerr spacetime, and (iii) gravitational self-force theory. Our treatment of black hole perturbation theory covers most common methods, including the Teukolsky and Regge-Wheeler-Zerilli equations, methods of metric reconstruction, and Lorenz-gauge formulations, presenting them in a new consistent and self-contained form. Our treatment of orbital mechanics covers quasi-Keplerian and action-angle descriptions of bound geodesics and accelerated orbits, osculating geodesics, near-identity averaging transformations, multiscale expansions, and orbital resonances. Our summary of self-force theorys foundations is brief, covering the main ideas and results of matched asymptotic expansions, local expansion methods, puncture schemes, and point particle descriptions. We conclude by combining the above methods in a multiscale expansion of the perturbative Einstein equations, leading to adiabatic and post-adiabatic evolution schemes. Our presentation is intended primarily as a reference for practitioners but includes a variety of new results. In particular, we present the first complete post-adiabatic waveform-generation framework for generic (nonresonant) orbits in Kerr.
Possibilities emerging out of the dynamical evolutions of collapsing systems are addressed in this thesis through analytical investigations of the highly non-linear Einstein Field Equations. Studies of exact solutions and their properties, play a non-trivial role in general relativity, even in the current context. Finding non-trivial solutions to the Einstein field equations requires some reduction of the problem, which usually is done by exploiting symmetries or other properties. Exact solutions of the Einsteins field equations describing an unhindered gravitational collapse are studied which generally predict an ultimate singular end-state. In the vicinity of such a spacetime singularity, the energy densities, spacetime curvatures, and all other physical quantities blow up. Despite exhaustive attempts over decades, the famous conjecture that the formation of a singularity during stellar collapse necessarily accompanies the formation of an event horizon, thereby covering the central singularity, still remains without a proof. Moreover, there are examples of stellar collapse models with reasonable matter contribution in which an event horizon does not form at all, giving rise to a naked singularity from which both matter and radiation can fall in and come out. These examples suggest that the so-called cosmic censorship conjecture may not be a general rule. Therefore one must embark upon analysis of realistic theoretical models of gravitational collapse and gradually generalizing previous efforts.
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