Lightlike simultaneity, comoving observers and distances in general relativity

We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light aberration. We obtain that comoving observers observe the same light ray with the same frequency and direction, and so gravitational redshift effect is a particular case of Doppler effect. We also define a distance between an observer and the events that it observes, that coincides with the known affine distance. We show that affine distance is a particular case of radar distance in the Minkowski space-time and generalizes the proper radial distance in the Schwarzschild space-time. Finally, we show that affine distance gives us a new concept of distance in Robertson-Walker space-times, according to Hubble law.Comment: 17 pages, 5 figures. Since "lightlike distance" is in fact the known "affine distance", the notation has been change

Kidney and Cardiovascular Effects of Canagliflozin According to Age and Sex: A Post Hoc Analysis of the CREDENCE Randomized Clinical Trial

Rationale & Objective: It is unclear whether the effect of canagliflozin on adverse kidney and cardiovascular events in those with diabetic kid-ney disease varies by age and sex. We assessed the effects of canagliflozin among age group categories and between sexes in the Canagli-flozin and Renal Endpoints in Diabetes with Established Nephropathy Clinical Evaluation (CREDENCE) study.Study Design: Secondary analysis of a random-ized controlled trial. Setting & Participants: Participants in the CREDENCE trial. Intervention: Participants were randomly assigned to receive canagliflozin 100 mg/d or placebo.Outcomes: Primary composite outcome of kid-ney failure, doubling of serum creatinine con-centration, or death due to kidney or cardiovascular disease. Prespecified secondary and safety outcomes were also analyzed. Out-comes were evaluated by age at baseline (<60, 60-69, and >_70 years) and sex in the intention-to-treat population using Cox regression models.Results: The mean age of the cohort was 63.0 & PLUSMN; 9.2 years, and 34% were female. Older age and female sex were independently associ-ated with a lower risk of the composite of adverse kidney outcomes. There was no evidence that the effect of canagliflozin on the primary outcome (acomposite of kidney failure, a doubling of serum creatinine concentration, or death from kidney or cardiovascular causes) differed between age groups (HRs, 0.67 [95% CI, 0.52-0.87], 0.63 [0.4 8-0.82], and 0.89 [0.61-1.29] for ages <60, 60-69, and >_70 years, respectively; P = 0.3 for interaction) or sexes (HRs, 0.71 [95% CI, 0.5 4-0.95] and 0.69 [0.56-0.8 4] in women and men, respectively; P = 0.8 for interaction). No differences in safety outcomes by age group or sex were observed.Limitations: This was a post hoc analysis with multiple comparisons.Conclusions: Canagliflozin consistently reduced the relative risk of kidney events in people with diabetic kidney disease in both sexes and across age subgroups. As a result of greater background risk, the absolute reduction in adverse kidney outcomes was greater in younger participants.Funding: This post hoc analysis of the CREDENCE trial was not funded. The CREDENCE study was sponsored by Janssen Research and Development and was conducted collaboratively by the sponsor, an academic-led steering committee, and an academic research organization, George Clinical.Trial Registration: The original CREDENCE trial was registered at ClinicalTrials.gov with study number NCT02065791