Néstor Ortiz

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 observers 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.

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.

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.

Highly compact neutron stars in scalar-tensor theories of gravity: Spontaneous scalarization versus gravitational collapse

Scalar-tensor theories of gravity are extensions of General Relativity (GR) including an extra, nonminimally coupled scalar degree of freedom. A wide class of these theories, albeit indistinguishable from GR in the weak field regime, predicts a radically different phenomenology for neutron stars, due to a nonperturbative, strong-field effect referred to as spontaneous scalarization. This effect is known to occur in theories where the effective linear coupling

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

\beta_0

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

between the scalar and matter fields is sufficiently negative, i.e.

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

\beta_0 \lesssim -4.35

Cauchy horizon stability in a collapsing spherical dust cloud: II. Energy bounds for test fields and odd-parity gravitational perturbations

, and has been strongly constrained by pulsar timing observations. In the test-field approximation, spontaneous scalarization manifests itself as a tachyonic-like instability. Recently, it was argued that, in theories where

Cauchy horizon stability in a collapsing spherical dust cloud: I. Geometric optics approximation and spherically symmetric test fields

\beta_0>0

Global crustal dynamics of Magnetars in relation to their bright X-ray outbursts

, a similar instability would be triggered by sufficiently compact neutron stars obeying realistic equations of state. In this work we investigate the endstate of this instability for some representative coupling functions with