Curvature conditions for the occurrence of a class of spacetime singularities

It has previously been shown [W. Rudnicki, Phys. Lett. A 224, 45 (1996)] that a generic gravitational collapse cannot result in a naked singularity accompanied by closed timelike curves. An important role in this result plays the so-called inextendibility condition, which is required to hold for certain incomplete null geodesics. In this paper, a theorem is proved that establishes some relations between the inextendibility condition and the rate of growth of the Ricci curvature along incomplete null geodesics. This theorem shows that the inextendibility condition may hold for a much more general class of singularities than only those of the strong curvature type. It is also argued that some earlier cosmic censorship results obtained for strong curvature singularities can be extended to singularities corresponding to the inextendibility condition.Comment: RevTeX, 6 pages, no figures. To be published in J. Math. Phy

On the strength of the Kerr singularity and cosmic censorship

It has been suggested by Israel that the Kerr singularity cannot be strong in the sense of Tipler, for it tends to cause repulsive effects. We show here that, contrary to that suggestion, nearly all null geodesics reaching this singularity do in fact terminate in Tipler's strong curvature singularity. Implications of this result are discussed in the context of an earlier cosmic censorship theorem which constraints the occurrence of Kerr-like naked singularities in generic collapse situations.Comment: RevTeX, 6 pages, no figures, to appear in Phys. Lett.

Generalized Strong Curvature Singularities and Cosmic Censorship

A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.Comment: LaTeX, 11 pages, no figures, to appear in Mod. Phys. Lett.

Salient signatures of entanglement in the surrounding environment

We develop a model in which presence of entanglement in a quantum system can be confirmed through coarse observations of the environment surrounding the system. This counter-intuitive effect becomes possible when interaction between the system and its environment is proportional to an observable being an entanglement witness. While presenting intuitive examples we show that: i) a cloud of an ideal gas, when subject to a linear potential coupled with the entanglement witness, accelerates in the direction dictated by the sign of the witness; ii) when the environment is a radiation field, the direction of dielectric polarization depends on the presence of entanglement; iii) quadratures of electromagnetic field in a cavity coupled with two qubits (or a four-level atom) are displaced in the same manner

Diffusion-weighted magnetic resonance imaging of 103 patients with rectal adenocarcinoma identifies the apparent diffusion coefficient as an imaging marker for tumor invasion and regional lymph node involvement

BACKGROUND: This retrospective study included 103 patients diagnosed with rectal adenocarcinoma at a single center in Poland who underwent preoperative diffusion-weighted magnetic resonance imaging (DWI) and aimed to determine whether the apparent diffusion coefficient (ADC) was an imaging marker for tumor invasion and regional lymph node involvement. MATERIAL/METHODS: We analyzed primary staging magnetic resonance examinations of the rectum of 103 consecutive patients with histologically proven non-mucinous adenocarcinoma who underwent surgical treatment. In 85 patients, surgery was preceded by long-course chemoradiotherapy (n=18) or short-course radiotherapy (n=67). The following DWI parameters were measured: ADC mean, minimum, maximum, and standard deviation in the region of interest (ADC SD-in-ROI). Values were compared between subgroups based on histological parameters from the report: tumor stage, lymph node stage, differentiation grade, the presence of extranodal tumor deposits, angioinvasion, and perineural invasion. Statistical analysis was performed using the Mann-Whitney U test and the unilateral t test. RESULTS: ADC mean values were lower for cases in which postoperative histopathological examination lymph node invasion (P=0.04) and tumor deposits were found (P=0.04). Minimal ADC value was higher in cases in which tumor deposits were not found (P=0.009). ADC SD-in-ROI values were lower in cases in which lymph nodes invasion was confirmed (P=0.014). There were no statistically significant differences for other parameters. CONCLUSIONS: The ADC values in pre-treatment DWI in patients with rectal adenocarcinoma were correlated with tumor invasion and regional lymph node metastases. Therefore, ADC values from the pre-treatment MRI may help plan adjuvant therapy in patients with rectal adenocarcinoma