The null-surface formulation (NSF) of general relativity differs markedly from the conventional approach. The conventional approach to general relativity is concerned with local fields such as the metric, whereas the NSF focuses on surfaces. The NSF has two distinct but mathematically equivalent interpretations: (a) Future-directed light rays leave a spacetime point and intersect future null-infinity

In principle, the local classification of spacetimes is always possible using the Cartan-Karlhede algorithm. However, in practice, the process of determining equivalence of two spacetimes relies on determining if a set of equations has a solution. Depending on the form of the equations this may be undecideable. Furthemore, if a solution does exist the equations may still be unsolvable in some way.

We elaborate on a model of nonassociative and noncommutative Einstein–Dirac–Maxwell, EDM, theory determined by star product R-flux deformations in string theory. Solutions for nonassociative EDM systems and physical properties not studied in modern physics. For modifications of the four-dimensional, 4-d, Einstein gravity, we work on conventional nonassociative 8-d phase spaces modelled as star-deformed

Beginning from the standard Arnowitt–Deser–Misner (ADM) formulation of general relativity we construct a tentative model of quantum gravity from the point of view of an observer with constant proper acceleration, just outside of a horizon of spacetime. In addition of producing the standard results of black-hole thermodynamics, our model makes an entirely new prediction that there is a certain upper

In this short note we investigate canonical formalism for General Relativity which is formulated with the metric \(f^{ab}=(-g)^\alpha g^{ab}\). We find corresponding Hamiltonian and we show that constraint structure is the same as in the standard formulation. We also analyze another model when the spatial part of metric \(h^{ij}\) is related with the new one by relation \(a^{ij}=(\det h_{ij})^\beta

This paper discusses several functional analytic issues relevant for field theories in the context of the Hamiltonian formulation for a free, massless, scalar field defined on a closed interval of the real line. The fields that we use belong to a Sobolev space with a scalar product. As we show this choice is useful because it leads to an explicit representation of the points in the fibers of the phase

In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid, followed by a fluid with an azimuthally directed pressure, and, finally, by a fluid where the pressure is radially oriented. The perfect fluid configuration has

We examine the model of two-dimensional quadratic gravity as a consequence of symmetry breaking within the framework of background field (BF) theory. This theory is essentially an extension of BF theory, introducing an additional polynomial term that operates on both the gauge and background fields. We analyze the theory using the Dirac and Faddeev–Jackiw procedures, determining the form of the gauge

The process of the gravitational collapse might lead not only to a black hole but also to naked singularity formation. In this paper, we consider the generalized Vaidya spacetime with polytropic and generalized polytropic equations of state. We solve the Einstein and Einstein–Maxwell equations to obtain the explicit form of a mass function. We consider the limiting cases of solutions and find out,

We apply the gradient expansion approximation to the light-cone gauge, obtaining a separate universe picture at non-linear order in perturbation theory within this framework. Thereafter, we use it to generalize the \(\delta \mathcal {N}\) formalism in terms of light-cone perturbations. As a consistency check, we demonstrate the conservation of the gauge invariant curvature perturbation on uniform density

In this paper, we study the relativistic correction to Bekenstein–Hawking entropy in the canonical ensemble and isothermal–isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann–Gibbs (BG) statistics with its relativistic generalization, Kaniadakis statistics, or \(\kappa \)-statistics

The triumph of general relativity under the banner “gravity is geometry” began with confirming the crucial effects within the Solar system and proceeded recently to the strong-field shadow effect for the compact object in the center of the Milky Way. Here, we examine some of those phenomena for the Einstein-scalar equations in the antiscalar regime to reveal the difference from vacuum both in weak