arXiv subjects

Néstor Ortiz

Publications and source records attributed to Néstor Ortiz.

27 records · Page 2Linked to original sources

arXiv2015

Observational distinction between black holes and naked singularities: the role of the redshift function

We suggest that the redshift of photons traveling from past to future null infinity through a collapsing object could provide an observational signature capable of differentiating between the formation of a globally naked singularity and the formation of an event horizon. Supporting evidence for this idea is drawn from the analysis of photons with zero angular momentum through the center of a collapsing spherical dust cloud. We show that the frequency shift as a function of proper time with respect to stationary observers has distinct features depending on whether the object collapses to a black hole or a naked singularity.

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arXiv2015

Shadow of a naked singularity

We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on the sky of the asymptotic observer. We find that the resulting redshift and properties of the shadow depend crucially on whether the final outcome of the complete gravitational collapse is a black hole or a naked singularity. In the black hole case, the shadow is due to the high redshift acquired by the photons as they approach the event horizon, implying that their energy is gradually redshifted toward zero within a few crossing times associated with the event horizon radius. In contrast to this, a naked singularity not only absorbs photons originating from the source, but it also emits infinitely redshifted photons with and without angular momenta. This emission introduces an abrupt cutoff in the frequency shift of the photons detected in directions close to the radial one, and it is responsible for the shadow masking the source in the naked singularity case. Furthermore, even though the shadow forms and begins to grow immediately after the observer crosses the Cauchy horizon, it takes many more crossing times than in the black hole case for the source to be occulted from the observer's eyes. We discuss possible implications of our results for testing the weak cosmic censorship hypothesis. Even though at late times the image of the source perceived by the observer looks the same in both cases, the dynamical formation of the shadow and the redshift images has distinct features and time scales in the black hole versus the naked singularity case. For stellar collapse, these time scales seem to be too short to be resolved with existing technology. However, our results may be relevant for the collapse of seeds leading to supermassive black holes.

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arXiv2015

On the behaviour of non-radial null geodesics in self-similar Tolman-Bondi collapse

Motivated by recent work on the structure of the singularity in inhomogeneous Tolman-Bondi collapse models, we investigate the behaviour of null geodesics in the particular case where the collapse is self-similar. The presence of the homothetic Killing vector field implies that the geodesic equation can be described by an integrable Hamiltonian system, and exploiting this fact we provide a full qualitative picture for its phase flow.

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arXiv2014

The gravitational redshift of photons traversing a collapsing dust cloud and observable consequences

We analyze the frequency shift of photons propagating on an asymptotically flat spacetime describing a collapsing, spherical dust cloud. We focus on the case where the interaction of the photons with the matter can be neglected. Under fairly general assumptions on the initial data characterizing the collapse, we show that photons with zero angular momentum which travel from past to future null infinity, crossing the collapsing cloud through its center, are always redshifted with respect to stationary observers. We compute this redshift as a function of proper time of a distant stationary observer and discuss its dependency on the mass distribution of the cloud. Possible implications of this redshift effect for weak cosmic censorship and light propagation in cosmological spacetimes are also briefly discussed.

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arXiv2013

Cauchy horizon stability in a collapsing spherical dust cloud I: geometric optic approximation and spherically symmetric test fields

A spherical dust cloud which is initially at rest and which has a monotonously decaying density profile collapses and forms a shell-focussing singularity. Provided the density profile is not too flat, meaning that its second radial derivative is negative at the center, this singularity is visible to local, and sometimes even to global observers. According to the strong cosmic censorship conjecture, such naked singularities should be unstable under generic, nonspherical perturbations of the initial data or when more realistic matter models are considered. In an attempt to gain some understanding about this stability issue, in this work we initiate the analysis of a simpler but related problem. We discuss the stability of test fields propagating in the vicinity of the Cauchy horizon associated to the naked central singularity. We first study the high-frequency limit and show that the fields undergo a blueshift as they approach the Cauchy horizon. However, in contrast to what occurs at inner horizons of black holes, we show that the blueshift is uniformly bounded along incoming and outgoing null rays. Motivated by this boundedness result, we take a step beyond the geometric optic approximation and consider the Cauchy evolution of spherically symmetric test scalar fields. We prove that under reasonable conditions on the initial data a suitable rescaled field can be continuously extended to the Cauchy horizon. In particular, this result implies that the physical field is everywhere finite on the Cauchy horizon away from the central singularity.

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arXiv2013

Linear perturbations of self-gravitating spherically symmetric configurations

We present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity. The advantage of this formalism relies in the fact that it does not require a decomposition of the perturbations into spherical tensor harmonics. Furthermore, it does not assume the background to be vacuum, nor does it require its staticity. In the particular case of vacuum perturbations, we derive two master equations describing the propagation of arbitrary linear gravitational waves on a Schwarzschild black hole. When decomposed into spherical harmonics, they reduce to covariant generalizations of the well-known Regge-Wheeler and Zerilli equations. Next, we discuss the general case where the metric perturbations are coupled to matter fields and derive a new constrained wave system describing the propagation of three gauge-invariant scalars from which the complete metric perturbations can be reconstructed. We apply our formalism to the Einstein-Euler system, dividing the fluid perturbations into two parts. The first part, which decouples from the metric perturbations, obeys simple advection equations along the background flow and describes the propagation of the entropy and the vorticity. The second part describes a perturbed potential flow, and together with the metric perturbations it forms a closed wave system.

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arXiv2012

Initial data giving rise to naked singularities in spherically symmetric dust collapse

The phase space corresponding to a particular four-parameter family of initial data for the gravitational collapse of a spherically symmetric dust cloud is investigated. In a certain limit of the parameters, this family reproduces the case of homogenous mass density -constant mass distribution- and zero initial velocity, while in another limit, it generates a globally naked singularity. We show that for initial data characterizing flat density profiles, as well as large initial velocities, the probability of forming a globally naked singularity is low.

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arXiv2012

Conformal diagrams for the gravitational collapse of a spherically symmetric dust cloud

We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of radial null geodesics. As an application we generate conformal diagrams for collapsing spherical dust clouds and analyze the causal structure of the resulting spacetimes.

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arXiv2011

Conformal diagrams for the gravitational collapse of a spherical dust cloud

We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of the radial null geodesics and a local analysis of their behavior close to the singularity. As an application, we consider a collapsing spherical dust cloud, generate the corresponding conformal diagram and analyze the structure of the resulting singularity. A new bound on the initial data which guarantees that the singularity is visible from future null infinity is also obtained.

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