The Contribution of the Cosmological Constant to the Relativistic Bending of Light Revisited

We study the effect of the cosmological constant $\Lambda$ on the bending of light by a concentrated spherically symmetric mass. Contrarily to previous claims, we show that when the Schwarzschild-de Sitter geometry is taken into account, $\Lambda$ does indeed contribute to the bending.Comment: 5 pages, 2 figure

An intuitive approach to inertial forces and the centrifugal force paradox in general relativity

As the velocity of a rocket in a circular orbit near a black hole increases, the outwardly directed rocket thrust must increase to keep the rocket in its orbit. This feature might appear paradoxical from a Newtonian viewpoint, but we show that it follows naturally from the equivalence principle together with special relativity and a few general features of black holes. We also derive a general relativistic formalism of inertial forces for reference frames with acceleration and rotation. The resulting equation relates the real experienced forces to the time derivative of the speed and the spatial curvature of the particle trajectory relative to the reference frame. We show that an observer who follows the path taken by a free (geodesic) photon will experience a force perpendicular to the direction of motion that is independent of the observers velocity. We apply our approach to resolve the submarine paradox, which regards whether a submerged submarine in a balanced state of rest will sink or float when given a horizontal velocity if we take relativistic effects into account. We extend earlier treatments of this topic to include spherical oceans and show that for the case of the Earth the submarine floats upward if we take the curvature of the ocean into account.Comment: 14 pages, 21 figure

Associations between overweight, obesity, and mental health: a retrospective study among European adults aged 50+

BackgroundThe comorbidities associated with overweight and obesity have been well researched and scientifically proven while their relationship to mental health is still not verified.MethodsThis study is aimed at investigating reciprocal associations between obesity and mental health, and is intended to further analyze possible long-term effects using data from the Survey of Health, Ageing and Retirement in Europe (SHARE). In order to do that, waves 4 and 8, conducted in 2010 and 2019/20 of this survey, were analyzed in a cross-lagged panel approach including 16,184 adult Europeans (50+) using multiple linear regression analysis focusing on the Body Mass Index (BMI), depression status and quality of life (QoL).ResultsFindings yield significant cross-lagged effects in one direction regarding BMI predicting QoL and depression state, whereas depression state and QoL do not significantly predict BMI. Findings include people living with obesity, overweight, and underweight showing significantly decreased levels of QoL as well as increased depression scores compared to people of normal weight over a lag time of 10 years, where people living with obesity indicate the strongest effect.ConclusionsHowever, results do not confirm reciprocal associations in the long term. Hence, there is a strong need to carry out further research on this issue

Relativity: Special, General, and Cosmological

Relativistic cosmology has in recent years become one of the most exciting and active branches of current research. In conference after conference the view is expressed that cosmology today is where particle physics was forty years ago, with major discoveries just waiting to happen. Also gravitational wave detectors, presently under construction or in the testing phase, promise to open up an entirely novel field of physics. It is to take into account such recent developments, as well as to improve the basic text, that this second edition has been undertaken. The most affected is the last part on cosmology, but there are smaller additions, corrections, and additional exercises throughout. The books basic purpose is to make relativity come alive conceptually. Hence the emphasis on the foundations and the logical subtleties rather than on the mathematics or the detailed experiments per se. Aided by some 300 exercises, the book promotes a deep understanding and the confidence to tackle any fundamental relativistic problem.Includes bibliographical references and index.Relativistic cosmology has in recent years become one of the most exciting and active branches of current research. In conference after conference the view is expressed that cosmology today is where particle physics was forty years ago, with major discoveries just waiting to happen. Also gravitational wave detectors, presently under construction or in the testing phase, promise to open up an entirely novel field of physics. It is to take into account such recent developments, as well as to improve the basic text, that this second edition has been undertaken. The most affected is the last part on cosmology, but there are smaller additions, corrections, and additional exercises throughout. The books basic purpose is to make relativity come alive conceptually. Hence the emphasis on the foundations and the logical subtleties rather than on the mathematics or the detailed experiments per se. Aided by some 300 exercises, the book promotes a deep understanding and the confidence to tackle any fundamental relativistic problem

Essential Relativity

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Problems in relativistic cosmology

After a brief survey of the cosmological features of the observable universe the two main techniques used in theoretical cosmology are developed. These are the Kinematic technique as first used in Kinematic Relativity, based on the concept of a Kinematic equivalence, and the Riemannian technique as first used in General relativity based on the concept of a Riemannian space-time map. Formulae for proper distance, red=shift, etc. are developed independently in each technique. Others like nebular count formulae, which are less readily amenable to the Kinematic technique, are discussed by the Riemannian technique only. The two techniques pre then correlated. It is found that any homogeneous and isotropic model-universe with given Kinematic properties can be described end discussed in terms of either technique and that a relation exists between the arbitrary elements in the two descriptions. It is shown how formulae associated with either technique can be translated into formulae associated with the other. Thus the geometric apparatus of the Riemannian technique end other useful formulae become available to the Kinematic technique. The correlation extends the scope of the Kinematic technique and at the same time throws light on certain aspects of the Riemannian technique. The red-shift formulae developed earlier are now used to analyse the new Humason-Mayall-Sandage data on red=shifts» It is found that these rule out all but decelerating model=universes unless some further hypotheses are made. The particular hypothesis of varying absolute nebular luminosities is examined and the minimum rate required is found. The last chapter contains e complete analysis of visual horizons in cosmology. Two essentially different types of horizon are recognized end examples are given of models possessing either type, both types at once, or no horizon. In an appendix the tensor significance of the "relativistic" acceleration, as used e.g. in Page's equivalence, is investigated.Imperial Users onl