Characterizing repulsive gravity with curvature eigenvalues

We analytically determine the quasinormal mode (QNM) frequencies of a black hole with quadrupole moment in the eikonal limit using the light-ring method. The generalized black holes that are discussed in this work possess arbitrary quadrupole and higher mass moments in addition to mass and angular momentum. Static collapsed configurations with mass and quadrupole moment are treated in detail and the QNM frequencies associated with two such configurations are evaluated to linear order in the quadrupole moment. Furthermore, we touch upon the treatment of rotating systems. In particular, the generalized black hole that we consider for our extensive QNM calculations is a completely collapsed configuration whose exterior gravitational field can be described by the Hartle-Thorne spacetime [Astrophys. J. , 807-834 (1968)]. This collapsed system as well as its QNMs is characterized by mass M , quadrupole moment Q and angular momentum J, where the latter two parameters are treated to first and second orders of approximation, respectively. When the quadrupole moment is set equal to the relativistic quadrupole moment of the corresponding Kerr black hole, J 2 /(M c 2 ), the Hartle-Thorne QNMs reduce to those of the Kerr black hole to second order in angular momentum J. Using ringdown frequencies, one cannot observationally distinguish a generalized Hartle-Thorne black hole with arbitrary quadrupole moment from a Kerr black hole provided the dimensionless parameter given by |QM c 2 − J 2 |c 2 /(G 2 M 4 ) is sufficiently small compared to unity. 153

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“…For further recent studies of the δ-metric, see [37][38][39][40][41][42] and the references cited therein.…”

Section: Gravitational Shift Of Frequency In δ-Spacetimementioning

confidence: 99%

Quasinormal modes of a black hole with quadrupole moment

2019

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“…The ability to neglect all densities except matter and dark energy comes from the fact that we focus only on the late time universe. In such a picture, cosmography works well in the regime where H 0 a 0 /c ≫ 1, which represents the condition for obtaining an accelerated expansion today 6 , with a(t 0 ) = a 0 . In this picture, the expansion of the pressure in terms of ρ is a first example of a cosmographic series.…”

Section: The Path To Cosmography: Basic Requirements and Strategiesmentioning

confidence: 99%

On the theory and applications of modern cosmography

Dunsby

Luongo

2016

Int. J. Geom. Methods Mod. Phys.

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Cosmography represents an important branch of cosmology which aims to describe the universe without the need of postulating a priori any particular cosmological model. All quantities of interest are expanded as a Taylor series around here and now, providing in principle, a way of directly matching with cosmological data. In this way, cosmography can be regarded a model-independent technique, able to fix cosmic bounds, although several issues limit its use in various model reconstructions. The main purpose of this review is to focus on the key features of cosmography, emphasising both the strategy for obtaining the observable cosmographic series and pointing out any drawbacks which might plague the standard cosmographic treatment. In doing so, we relate cosmography to the most relevant cosmological quantities and to several dark energy models. We also investigate whether cosmography is able to provide information about the form of the cosmological expansion history, discussing how to reproduce the dark fluid from the cosmographic sound speed. Following this, we discuss limits on cosmographic priors and focus on how to experimentally treat cosmographic expansions. Finally, we present some of the latest developments of the cosmographic method, reviewing the use of rational approximations, based on cosmographic Padé polynomials. Future prospects leading to more accurate cosmographic results, able to better reproduce the expansion history of the universe are also discussed in detail.

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“…Indications of repulsive effects in gravity are not new, specially in the case of naked singularities [4]. Several intuitive approaches have been proposed to understand repulsive gravity, but only recently an invariant definition in terms of geometric objects was formulated [6]. Indeed, it was shown that the behavior of the curvature tensor eigenvalues can be used to find the places where repulsive gravity appears.…”

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confidence: 99%

“…Repulsive effects in a homogeneous and isotropic universe Although there are several intuitive ways to define repulsive gravity, only recently an invariant definition in terms of the curvature tensor eigenvalues was formulated which gives physically reasonable results in the case of all naked singularities investigated so far [6]. The idea is that the curvature tensor eigenvalues contain in an invariant manner all the information about the behavior of gravity.…”

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confidence: 99%

“…According to our invariant definition of repulsive gravity [6], the curvature eigenvalues reflect the behavior of the gravitational interaction and if gravity becomes repulsive in some regions, the eigenvalues must change accordingly; for instance, if repulsive gravity becomes dominant at a particular point, one would expect at that point a change in the sign of at least one eigenvalue. Moreover, if the gravitational field does not diverge at infinity, the eigenvalue must have an extremal at some point before it changes its sign.…”

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confidence: 99%

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Self-accelerated Universe Induced by Repulsive Effects as an Alternative to Dark Energy and Modified Gravities

Luongo

Quevedo

2017

Found Phys

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The existence of current-time universe's acceleration is usually modeled by means of two main strategies. The first makes use of a dark energy barotropic fluid entering by hand the energymomentum tensor of Einstein's theory. The second lies on extending the Hilbert-Einstein action giving rise to the class of extended theories of gravity. In this work, we propose a third approach, derived as an intrinsic geometrical effect of space-time, which provides repulsive regions under certain circumstances. We demonstrate that the effects of repulsive gravity naturally emerge in the field of a homogeneous and isotropic universe. To this end, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. Moreover, we show that repulsive gravity counterbalances the standard gravitational attraction influencing both late and early times of the universe evolution. This phenomenon leads to the present speed up and to the fast expansion due to the inflationary epoch. In so doing, we are able to unify both dark energy and inflation in a single scheme, showing that the universe changes its dynamics whenḦ H = −2Ḣ, at the repulsion onset time where this condition is satisfied. Further, we argue that the spatial scalar curvature can be taken as vanishing because it does not affect at all the emergence of repulsive gravity. We check the goodness of our approach through two cosmological fits involving the most recent union 2.1 supernova compilation.Introduction General relativity predicts a universe characterized by a decelerated expansion, if only dark matter and baryons are involved within the energymomentum tensor. Observations, however, predict a late-time accelerated universe, pushed up by some sort of exotic constituent whose nature is today unknown [1]. To account for this experimental fact, cosmologists employ in general two different strategies. The first one consists in extending the Hilbert-Einstein action, modifying general relativity by means of additional degrees of freedom [2]. The second one takes into account an additional fluid, dubbed dark energy, which enters Einstein's equations and represents a source for the cosmic speed up [3]. Both those treatments are based on the hypothesis that space-time geometry is fueled by components entering the energy-momentum tensor T µν . In such a way, the energy-momentum tensor becomes the source for gravitation and modifies the geometry itself. However, if we rewrite Einstein's equations in an equivalent way as T µν − 1 2 g µν T = χR µν , it is possible to reverse the interpretation of T µν . Indeed, one can address a dynamical problem by considering an energy-momentum tensor induced by geometry, and not vice-versa. The philosophy is completely different from the one used in higher-order theories of gravity, since no extensions are required, but only a physical mechanism inside the Einstein equations themselves, providing a geometrical source term.It is therefore possible to imagine that under certain circumstances the geometry could cor...

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Characterizing repulsive gravity with curvature eigenvalues

Cited by 42 publications

References 32 publications

Quasinormal modes of a black hole with quadrupole moment

Quasinormal modes of a black hole with quadrupole moment

On the theory and applications of modern cosmography

Self-accelerated Universe Induced by Repulsive Effects as an Alternative to Dark Energy and Modified Gravities

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