Introduction

It was not a war to end all wars. It was not a war to destroy or truncate the Roman Empire in the east. The Persian aim at the outset was not even regime change, merely restoration of an ousted regime. But the fighting went on and on. There was a steady escalation in its scope and intensity with the passing years. After a decade of conflict, foreboding came upon contemporaries. The saints were plainly withdrawing their favour from mankind. God was turning his face from the present generation. The world and all things in it were being troubled because of man’s sinfulness, and those few who strove to squeeze out desire, ambition, envy, and other human feelings from their lives should withdraw and pray for a softening of God’s anger. For one distant observer, far to the south of the Fertile Crescent, where the two belligerent great powers were engaged in combat, the war presaged the end of time. The last days were at hand, when the earth would shake and the seas boil, when the sky would be torn apart and the stars scattered, when men would come face to face with the creator and manager of all things....

Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr–Newman–de Sitter and Kerr–Newman black hole geometries

We investigate the redshift and blueshift of light emitted by timelike geodesic particles in orbits around a Kerr–Newman–(anti) de Sitter (KN(a)dS) black hole. Specifically we compute the redshift and blueshift of photons that are emitted by geodesic massive particles and travel along null geodesics towards a distant observer-located at a finite distance from the KN(a)dS black hole. For this purpose we use the killing-vector formalism and the associated first integrals-constants of motion. We consider in detail stable timelike equatorial circular orbits of stars and express their corresponding redshift/blueshift in terms of the metric physical black hole parameters (angular momentum per unit mass, mass, electric charge and the cosmological constant) and the orbital radii of both the emitter star and the distant observer. These radii are linked through the constants of motion along the null geodesics followed by the photons since their emission until their detection and as a result we get closed form analytic expressions for the orbital radius of the observer in terms of the emitter radius, and the black hole parameters. In addition, we compute exact analytic expressions for the frame dragging of timelike spherical orbits in the KN(a)dS spacetime in terms of multivariable generalised hypergeometric functions of Lauricella and Appell. We apply our exact solutions of timelike non-spherical polar KN geodesics for the computation of frame-dragging, pericentre-shift, orbital period for the orbits of S2 and S14 stars within the $$1^{\prime \prime }$$ 1 ″ of SgrA*. We solve the conditions for timelike spherical orbits in KN(a)dS and KN spacetimes. We present new, elegant compact forms for the parameters of these orbits. Last but not least we derive a very elegant and novel exact formula for the periapsis advance for a test particle in a non-spherical polar orbit in KNdS black hole spacetime in terms of Jacobi’s elliptic function sn and Lauricella’s hypergeometric function $$F_D$$ F D .

Which stars can see Earth as a transiting exoplanet?

ABSTRACT Transit observations have found the majority of exoplanets to date. Also spectroscopic observations of transits and eclipses are the most commonly used tool to characterize exoplanet atmospheres and will be used in the search for life. However, an exoplanet’s orbit must be aligned with our line of sight to observe a transit. Here, we ask, from which stellar vantage points would a distant observer be able to search for life on Earth in the same way? We use the TESS Input Catalog and data from Gaia DR2 to identify the closest stars that could see Earth as a transiting exoplanet: We identify 1004 main-sequence stars within 100 parsecs, of which 508 guarantee a minimum 10-h long observation of Earth’s transit. Our star list consists of about 77 percent M-type, 12 percent K-type, 6 percent G-type, 4 percent F-type stars, and 1 percent A-type stars close to the ecliptic. SETI searches like the Breakthrough Listen Initiative are already focusing on this part of the sky. Our catalogue now provides a target list for this search. As part of the extended mission, NASA’s TESS will also search for transiting planets in the ecliptic to find planets that could already have found life on our transiting Earth .

To see the invisible: Image of the event horizon within the black hole shadow

How the supermassive black hole SgrA* in the Milky Way Center looks like for a distant observer? It depends on the black hole highlighting by the surrounding hot matter. The black hole shadow (the photon capture cross-section) would be viewed if there is a stationary luminous background. The black hole event horizon is invisible directly (per se). Nevertheless, a more compact (with respect to black hole shadow) projection of the black hole event horizon on the celestial sphere may be reconstructed by detecting the highly redshifted photons emitted by the nonstationary luminous matter plunging into the black hole and approaching the event horizon. It is appropriate to call this reconstructed projection of the event horizon on the celestial sphere for a distant observer as the “lensed event horizon image”, or simply the “event horizon image”. This event horizon image is placed on the celestial sphere within the position of black hole shadow. Amazingly, the event horizon image is a gravitationally lensed projection on the celestial sphere of the whole surface of the event horizon globe. As a result, the black holes may be viewed at once from both the front and back sides. The lensed event horizon image may be considered as a genuine silhouette of the black hole. For example, a dark northern hemisphere of the event horizon image is the simplest model for a black hole silhouette in the presence of a thin accretion disk.

Neutron stars in frames of R2-gravity and gravitational waves

The realistic models of neutron stars are considered for simple [Formula: see text] gravity and equivalent Brance–Dicke theory with dilaton field in Einsein frame. For negative values of [Formula: see text] we have no acceptable results from astrophysical viewpoint: the resulting solution for spherical stars doesn’t coincide with Schwarzschild solution on spatial infinity. The mass of star from viewpoint of distant observer tends to very large values. For [Formula: see text] it is possible to obtain solutions with required asymptotics and well-defined star mass. The mass confined by stellar surface decreases with increasing of [Formula: see text] but we have some contribution to mass from gravitational sphere appearing outside the star. The resulting effect is increasing of gravitational mass from viewpoint of distant observer. But another interpretation take place in a case of equivalent Brance–Dicke theory with massless dilaton field in Einstein frame. The mass of star increases due to contribution of dilaton field inside the star. We also considered the possible constraints on [Formula: see text] gravity from GW 170817 data. According to results of Bauswein et al. the lower limit on threshold mass is [Formula: see text][Formula: see text][Formula: see text]. This allows to exclude some equations of state (EoS) for dense matter. But in [Formula: see text] gravity the threshold mass increases for given EoS with increasing of [Formula: see text]. In principle it can helps in future discriminate between General Relativity and square gravity (of course one need to know EoS with more accuracy rather than now).

Potential

At any given event gravity accelerates all particles equally—yet gravity is very strong in some places and very weak in others. In this chapter, we learn a powerful thinking tool to help us deal with these variations: the gravitational potential. The potential takes the concept of “acceleration times height” that, we previously found, determines the march of time and generalizes it to cases where the gravitational acceleration varies with position. The potential encodes global relationships, such as the gravitational redshift of light emitted from one point and received by a distant observer, as well as the local acceleration at each point.We also showhow the spacetime metric is affected by the potential. Incorporating the potential into themetric neatly unites gravity with relativity and eliminates any need for a theory of gravity involving forces.

Post- Modern elements in the novels of Chetan Bhagat

Postmodernism is a Western philosophy, a late 20th-century movement characterized by broad skepticism, subjectivism, or relativism; a general suspicion of reason; and an acute sensitivity to the role of ideology in asserting and maintaining political and economic power”.Post-Modernists are independent while expressing their ideas, they never drop their statements and theory. It is more personal than identify with some other categories. The post-modernism was started in America around 16th century later it extended to Europe and other countries.Post-modern civilization fails to accept the modification between high and low class. There is a little place for modernism, originality or individual thinking. Bhagat has concentrated on the preconceptions of toppers, however there is more to life than these things your family, your friends, your internal desires and goals and the grades you get in dealing with each of these areas will define you as a person.The post-modernism has defused the difference between good and bad, moral and immoral, right and wrong. If there is a choice to select modern generation would not hesitate to go for one which is traditionally named as bad. Bhagat imbibed all these qualities in his writing. His characters go against the traditional customs and values. Bhagat represents intricate, deeply engrained socio-cultural complications of multicultural India, light-heartedly. He wishes readers to giggle at themselves, at their stupidities, their partialities, and their wrong-actions; not as a member but as a distant observer. He doesn’t bout them directly, but through fiction he attempts to understand their errors and gives a chance to rectify in the real life. Bhagat’s linking story telling method and the funny situations appeal readers.

Quantum optics approach to radiation from atoms falling into a black hole

We show that atoms falling into a black hole (BH) emit acceleration radiation which, under appropriate initial conditions, looks to a distant observer much like (but is different from) Hawking BH radiation. In particular, we find the entropy of the acceleration radiation via a simple laser-like analysis. We call this entropy horizon brightened acceleration radiation (HBAR) entropy to distinguish it from the BH entropy of Bekenstein and Hawking. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity.