arXiv subjects

Alan Maciel

Publications and source records attributed to Alan Maciel.

9 recordsLinked to original sources

arXiv2026

Matching collapse and expansion across Matter Trapping surfaces in inhomogeneous $\Lambda$CDM models

In the present work we examine the MTS, for the restriction to spherical dust plus $\Lambda$, proving that it actually is a characteristic surface of the Cauchy problem (generated by its characteristic curves), which opens the possibility for infinite solutions. This translate as the MTS being a boundary between arbitrarily independent solutions, reminiscent of the Birkhoff theorem effects. This property is illustrated with combinations of 3 examples containing MTSs and $\Lambda$ ($\Lambda$CDM, Schwarzschild-de\,Sitter, Lema\^itre-Tolman-Bondi-de\,Sitter: LTBdS -- i.e. the inhomogeneous, spherically symmetric $\Lambda$CDM). The LTBdS model presents a static, stable MTS for the first time.

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arXiv2024

Comment on "Apparent horizons of the Thakurta spacetime and the description of cosmological black holes"

The findings discussed in "Apparent Horizons of the Thakurta Spacetime and the Description of Cosmological Black Holes" deviate from prior research, particularly our study in Phys. Rev. D 95, 084031 (2017). We clarify this inconsistency, which arises from employing a coordinate transformation covering a distinct region of spacetime -- specifically one considered inaccessible due to its location beyond a singularity, making it unreachable from infinity. Additionally, we provide a concrete example where the distinct horizons and spacetime regions are readily discernible.

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arXiv2024

New insights on null and timelike warped symmetric spacetime splittings

We explore in detail the 2+2 and 1+1+2 formalism in spherically symmetric spacetimes, spanning from deducing the dynamical equations to relating them to the well-known generalised Painlev\'e-Gullstrand (GPG) coordinate system. The evolution equations are the Raychaudhuri equations for null rays, including those also known as cross-focusing equations whose derivation, to the best of our knowledge, we present for the first time. We physically interpret the scalars that arise in this scenario, namely the flow 2-expansion $\Theta_{n}$, the flow acceleration $\mathcal{A}$, and the radial extrinsic curvature $\mathcal{B}$. We derive a coordinate independent formula for the redshift which shows that $\mathcal{B}$ is the sole source for the redshift in spherically symmetric spacetimes. We also establish the correspondence between the 1+1+2 scalars and the 1+3 splitting scalars, expansion and shear. We further make a comparison with the Newman-Penrose formalism, in order to clarify the context where each formalism is more useful, and finally, we extend our results to planar and hyperbolic symmetric warped spacetimes as well, in particular, the relationship between $\mathcal{B}$ and the redshift.

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arXiv2020

New perspectives on the TOV equilibrium from a dual null approach

The TOV equation appears as the relativistic counterpart of the classical condition for hydrostatic equilibrium. In the present work we aim at showing that a generalised TOV equation also characterises the equilibrium of models endowed with other symmetries besides spherical. We apply the dual null formalism to spacetimes with two dimensional spherical, planar and hyperbolic symmetries with a perfect fluid as the source. We also assume a Killing vector field orthogonal to the surfaces of symmetry, which gives us static solutions, in the timelike Killing field case, and homogeneous dynamical solutions in the case the Killing field is spacelike. In order to treat equally all the aforementioned cases, we discuss the definition of a quasi-local energy for the spacetimes with planar and hyperbolic foliations, since the Hawking-Hayward definition only applies to compact foliations. After this procedure, we are able to translate our geometrical formalism to the fluid dynamics language in a unified way, to find the generalized TOV equation, for the three cases when the solution is static, and to obtain the evolution equation, for the homogeneous spacetime cases. Remarkably, we show that the static solutions which are not spherically symmetric violate the weak energy condition (WEC). We have also shown that the counterpart of the TOV equation for the spatially homogeneous models is just the familiar equation \r{ho} + P = 0, defining a cosmological constant-type behaviour, both in the hyperbolic and spherical cases. This implies a violation of the strong energy condition in both cases, added to the above mentioned violation of the weak energy condition in the hyperbolic case. We illustrate our unified treatment obtaining analogs of Schwarzschild interior solution, for an incompressible fluid $ρ= ρ_0$ constant.

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arXiv2019

Charged cosmological black holes: a thorough study of a family of solutions

We study a class of charged cosmological black holes defined by the Shah-Vaidya solution, which is similar to the McVittie solution but for a central object of nonzero electric charge. We show that the Shah-Vaidya metric is a solution of Einstein's equations with a cuscuton and a Maxwell fields as sources, as well as a mass parameter. We then analyze the possible causal structures of the solution under some few physically reasonable assumptions, and determine the regions in the parameter space corresponding to well behaved charged cosmological black holes and those corresponding to naked singularities. The asymptotic behavior of the Hubble factor $H(t)$ is also determinant to the causal properties of the spacetime and a theorem explaining its effect is stated. Examples of causal diagrams covering all the possibles types of spacetimes allowed by our initial assumptions are drawn and discussed.

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arXiv2018

Revisiting the Birkhoff theorem from a dual null point of view

The Birkhoff theorem is a well-known result in general relativity and it is used in many applications. However, its most general version, due to Bona, is almost unknown and presented in a form less accessible to the relativist and cosmologist community. Moreover, many wield it mistakenly as a simple transposition of Newton's iron sphere theorem. In the present work, we propose a modern, dual null, presentation --- useful in many explorations, including black holes --- of the theorem that renders accessible most of the results of Bona's version. In addition, we discuss the fluid contents admissible for the application of the theorem, beyond a vacuum, and we demonstrate how the formalism greatly simplifies solving the dynamical equations and allows one to express the solution as a power expansion in $r$. We present a family of solutions that share the properties predicted by the Birkhoff theorem and discuss the existence of trapped and antitrapped regions. The formalism manifestly shows how the type of region --- trapped or untrapped --- determines the character of the Killing vector.

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arXiv2017

Evolving black holes from conformal transformations of static solutions

A class of nonstationary spacetimes is obtained by means of a conformal transformation of the Schwarzschild metric, where the conformal factor $a(t)$ is an arbitrary function of the time coordinate only. We investigate several situations including some where the final state is a central object with constant mass. The metric is such that there is an initial big-bang type singularity and the final state depends on the chosen conformal factor. The Misner-Sharp mass is computed and a localized central object may be identified. The trapping horizons, geodesic and causal structure of the resulting spacetimes are investigated in detail. When $a(t)$ asymptotes to a constant in a short enough time scale, the spacetime presents an event horizon and its analytical extension reveals black-hole or white-hole regions. On the other hand, when $a(t)$ is unbounded from above as in cosmological models, the spacetime presents no event horizons and may present null singularities in the future. The energy-momentum content and other properties of the respective spacetimes are also investigated.

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arXiv2016

Quasilocal approach to general universal horizons

Theories of gravity with a preferred foliation usually display arbitrarily fast signal propagation, changing the black hole definition. A new inescapable barrier, the universal horizon, has been defined and many static and spherically symmetric examples have been studied in the literature. Here, we translate the usual definition of the universal horizon in terms of an optical scalar built with the preferred flow defined by the preferred spacetime foliation. The new expression has the advantages of being of quasilocal nature and independent of specific spacetime symmetries in order to be well defined. Therefore, we propose it as a definition for general quasilocal universal horizons. Using the new formalism we show that there are no universal analog of cosmological horizons for FLRW models for any scale factor function, and we also state that quasilocal universal horizons are restricted to trapped regions of the spacetime. Using the evolution equation, we analyze the formation of universal horizons under a truncated Horava-Lifshitz theory, in spherical symmetry, showing the existence of regions in parameter space where the universal horizon formation cannot be smooth from the center, under some physically reasonable assumptions. We conclude with our view on the next steps for the understanding of black holes in nonrelativistic gravity theories.

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arXiv2015

A dual null formalism for the collapse of fluids in a cosmological background

In this work we revisit the definition of Matter Trapping Surfaces (MTS) introduced in previous investigations and show how it can be expressed in the so-called dual null formalism developed for Trapping Horizons (TH). With the aim of unifying both approaches, we construct a 2+2 threading from the 1+3 flow, and thus isolate one prefered spatial direction, that allows straightforward translation into a dual nul subbasis, and to deduce the geometric apparatus that follows. We remain as general as possible, reverting to spherical symmetry only when needed, and express the MTS conditions in terms of 2-expansion of the flow, then in purely geometric form of the dual null expansions. The Raychadhuri equations that describe both MTS and TH are written and interpreted using the previously defined gTOV (generalized Tolman-Oppenheimer-Volkov) functional introduced in previous work. Further using the Misner-Sharp mass and its previous perfect fluid definition, we relate the spatial 2-expansion to the fluid pressure, density and acceleration. The Raychaudhuri equations also allows us to define the MTS dynamic condition with first order differentials so the MTS conditions are now shown to be all first order differentials. This unified formalism allows one to realise that the MTS can only exist in normal regions, and so it can exist only between black hole horizons and cosmological horizons. Finally we obtain a relation yielding the sign, on a TH, of the non-vanishing null expansion which determines the nature of the TH from fluid content, and flow characteristics. The 2+2 unified formalism here investigated thus proves a powerful tool to reveal, in the future extensions, more of the very rich and subtle relations between MTS and TH.

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