Expanding Lorentzian Wormholes in R2 Gravity

Abstract

We present traversable, Lorentzian wormholes in the framework of R 2 gravity. These wormholes are obtained by assuming constant Ricci scalar and trace-less equation of state. The metric is asymptotically RW, and locally that of a Lorentzian wormhole. Dynamics of the cosmological background, as well as the expanding wormhole are discussed. Weak energy condition near the wormhole throat is also examined. It is shown that the positive energy density condition can be satisfied all-over a spacelike hypersurface at large enough cosmological times and small enough, positive cosmological constant.Subject Index: 450, 453 §1. IntroductionThe theory of wormholes goes back to 1916, shortly after Einstein published his general theory, when Ludwig Flamm looked at the simplest possible solution of Einstein's field equation (i.e. the Schwarzschild solution). This solution describes the gravitational field around a spherically-symmetric non-rotating mass. If the mass is sufficiently compact, the solution describes a black hole. Flamm realized that Einstein's equations allowed a second solution, now known as a white hole, and that the two solutions, describing two different regions of spacetime were connected by a tunnel. 1) Because the theory has nothing to say about where these regions of spacetime might be in the real world, the black hole "entrance" and white hole "exit" could be in different parts of the same universe or in different universes.In 1935, Einstein and Rosen further explored the possibility of intra-or interuniverse connections in a paper whose actual purpose was to explain fundamental particles, such as electrons, in terms of spacetime tunnels threaded by electric lines of force. 2) Their work gave rise to the formal name Einstein-Rosen bridge. Later, John Wheeler called such a geometrical structure "wormhole". 3) Wheeler, in his 1955 paper, presented the first diagram of a wormhole as a tunnel connecting two openings in different regions of spacetime. It was proposed that such a hypothetical "tunnel" connecting two different points in spacetime would facilitate a trip between two regions of space which could take much less time than a journey between the same starting and ending points in normal space.The study of traversable wormholes gained a new motive when Morris and Thorne 4) presented a systematic analysis of the so-called traversable wormholes, which allow a safe, two-way journey across the throat. Such static wormholes, however, suffered from a major drawback: when put in the Einstein equations, they * )

Phantom wormhole solutions in a generic cosmological constant background

“…Similar situation arises also in the absence of cosmological constant, as is shown below equation (15) in reference [42]. Then, we have a negative pressure at the throat which provides the geometry with a repulsive character, preventing the wormhole throat from collapsing.…”

“…Thus, the radial pressure will take an asymptotically de Sitter or anti de Sitter behavior p r → ωΛ 8π as r → ∞ where ω should be −1 at spatial infinity. For the lateral pressure, the second term in brackets in equation (8) with respect to equations (15) and (25) will vanish at r → ∞. Then, the lateral pressure also will take an asymptotically de Sitter or anti de Sitter behavior p l → ωΛ 8π as r → ∞ where ω should be −1 at spatial infinity.…”

“…Then, in modified theories of gravity, the effective energy-momentum tensor involving higher order derivatives violates the null energy condition, i.e., T ef f µν k µ k ν < 0 where k µ is a null vector. This approach is widely analysed in the literature as in the fame work of f (R) gravity [14,15], curvature matter couplings [16,17], conformal Weyl gravity [18] and braneworlds [19]. On the other hand, according to the recent discoveries in cosmology, our universe is in accelerated expansion [20][21][22][23].…”

Generalised Ellis–Bronnikov wormholes embedded in warped braneworld background and energy conditions

“…Models of dynamical wormholes [29][30][31][32][33] also provide ways of restricting the violation of energy conditions. Other popular class modified gravity theories, where detailed analysis of wormhole geometries is done with viable matter source, are the so-called f (R) and higher order gravity theories [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Recently, successful modelling and analysis of energy condition satisying wormholes are carried out within the framework of Born-Infeld gravity [51][52][53] and torsional gravity [54][55][56].…”

Generalised Ellis-Bronnikov wormholes embedded in warped braneworld background and energy conditions

“…Models of dynamical wormholes [29][30][31][32][33] also provide ways of restricting the violation of energy conditions. Other popular class modified gravity theories, where detailed analysis of wormhole geometries is done with viable matter source, are the so-called f (R) and higher order gravity theories [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Recently, successful modelling and analysis of energy condition satisying wormholes are carried out within the framework of Born-Infeld gravity [51][52][53] and torsional gravity [54][55][56].…”