A simple model of a " black hole interior " , namely a spherically symmetric solution of the Einstein field equations in matter matching the Schwarzschild vacuum at a spacelike hypersurface " R < 2M " is constructed. The model is physically valid: it describes an elastic–solid sphere having a well–defined equation of state and satisfying the weak energy condition. G. Magli, A simple model of a ...

Abstract The dominant energy condition imposes a restriction on initial value pairs found spacelike hypersurface of Lorentzian manifold. In this article, we study the space values that satisfy strictly. To aim, introduce an index difference for and compare it to its classical counterpart Riemannian metrics. Recent non-triviality results latter will then imply has non-trivial homotopy groups.

Let $${{\mathcal {H}}}$$ denote the future outgoing null hypersurface emanating from a spacelike 2-sphere S in vacuum spacetime $$({{\mathcal {M}}},\textbf{g})$$ . In this paper we study so-called canonical foliation on introduced [13, 22] and show that corresponding geometry is controlled locally only terms of initial $$L^2$$ curvature flux through particular, ingoing expansions $${\textrm{tr}...

Abstract We study U-DHOST theories, i.e., higher-order scalar-tensor theories which are degenerate only in the unitary gauge and yield an apparently unstable extra mode a generic coordinate system. show that satisfies three-dimensional elliptic differential equation on spacelike hypersurface, hence it does not propagate. clarify how to treat this “shadowy” at both linear nonlinear levels.

We examine quantum field theory in spacetimes that are time nonorientable but have no other causal pathology. These are Lorentzian universesfrom-nothing, spacetimes with a single spacelike boundary that nevertheless have a smooth Lorentzian metric. A time-nonorientable, spacelike hypersurface serves as a generalized Cauchy surface, a surface on which freely specified initial data for wave equat...

In this study, we study rotational hypersurfaces in 4-dimensional Lorentz-Minkowski space. We find the about spacelike axis according to Gaussian and mean curvatures $E_{1}^{4}$ give some results with aid of curvatures. After that, deal Gauss map hypersurface by obtaining obtain second third Laplace-Beltrami operators on $E_{1}^{4}$. Also, these characterizations for timelike lightlike axes, too.

A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a spacelike and null hypersurface. The development of the data is obtained with the combination of a constrained Cauchy evolution in the interior domain and a characteristic evolution in the exterior, asymptotically flat region. The ...

On any spacelike hypersurface of constant mean curvature of a Generalized Robertson–Walker spacetime, the hyperbolic angle y between the future-pointing unit normal vector field and the universal time axis is considered. It is assumed that y has a local maximum. A physical consequence of this fact is that relative speeds between normal and comoving observers do not approach the speed of light n...

If (M, g) is a Lorentz manifold and S a spacelike hypersurface, let h and k denote the induced metric and second fundamental form of S respectively. The mean curvature of S is the trace trhk. An interesting class of spacelike hypersurfaces are those whose mean curvature is constant (CMC hypersurfaces). The Lorentz manifolds of primary interest in the following are those which possess a compact ...

Modal interpretations of quantum mechanics posit that the state vector obeys linear, unitary evolution at all times, and supplement the state vector with a set of possessed properties sufficiently rich to account for the occurrence of definite events at the macroscopic level, including definite outcomes of experiments, but sufficiently restricted so as to avoid a Kochen-Specker contradiction. T...