Asymptotic symmetries in Carrollian theories of gravity

Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from “magnetic” and “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For the electric contraction, because the lapse function does not appear in the boundary term needed to ensure a well-defined action principle, the asymptotic symmetry algebra is truncated, for Regge-Teitelboim parity conditions, to the semidirect sum of spatial rotations and spatial translations. Similarly, with Henneaux-Troessaert parity conditions, the asymptotic symmetries are given by the semidirect sum of spatial rotations and an infinite number of parity odd supertranslations. Thus, from the point of view of the asymptotic symmetries, the magnetic contraction can be seen as a smooth limit of General Relativity, in contrast to its electric counterpart.

Coordinate-time lapse function of FLRW accelerated expanding universe in dRGT massive gravity theory

In this paper, we discuss the behavior of coordinate-time dependent lapse function of FLRW metric of an accelerated expanding universe in the de Rham–Gabadadze–Tolley massive gravity theory. Physically, this function is considered to connect a general observer coordinate-time to the related proper-time and also to another normal observer under specific condition. We find that in the standard dRGT formalism, the corresponding lapse function can exhibit unphysical behavior in the parameter space region with a negative cosmological-constant-like term. To solve this problem, we reconsider the cosmological constant energy density which induces negative pressure. It turns out that this setup could overcome the existence of singular and negative square lapse function in the related parameter space and restore all the parameter space to admit only the accelerated expanding universe model.

A remark on black holes of Chern–Simons gravities in 2n + 1 dimensions: n = 1,2,3

A systematic prescription for constructing Chern–Simons gravities in all odd dimensions is given, and it is shown that Chern–Simons gravities in [Formula: see text] dimensions admit solutions described by the same lapse function which describes the BTZ black hole in the [Formula: see text] case. This has been carried out explicitly for [Formula: see text]. Moreover, it is seen that these solutions are unique.

Trajectories of photons in modified Hayward black hole spacetime

We study the trajectories of photons in modified Hayward black hole spacetime. Three kinds of horizons are distinguished by analyzing the lapse function of modified Hayward black hole spacetime. Through plotting the effective potential with different values of parameters, it is found that the parameter [Formula: see text] has more conspicuous effects than parameters [Formula: see text] ([Formula: see text] is associated with the time-delay) and [Formula: see text] ([Formula: see text] is related to the 1-loop quantum corrections) for the effective potential. The change of the parameters ([Formula: see text], [Formula: see text] and [Formula: see text]) has an obvious influence on unstable circular orbits. The structure of null geodesic is simpler than that of time-like geodesic. The stable circular orbits and the bound orbits are not included for the photon trajectories. By analyzing the corresponding effective potential, all possible orbits of null geodesic are found. The radius of unstable circular orbit equals 2.8790 for fixed [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

On Sliced Spaces: Global Hyperbolicity Revisited

We give a topological condition for a generic sliced space to be globally hyperbolic without any hypothesis on lapse function, shift function, and spatial metric.

On Sliced Spaces: Global Hyperbolicity Revisited

We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.