Abstract We seek S-brane solutions in D = 11 supergravity which can be characterized by a harmonic function H on the flat transverse space. It turns out that the Einstein’s equations force H to be a linear function of the transverse coordinates. The codimension one H = 0 hyperplane can be spacelike, timelike or null and the spacelike case reduces to the previously obtained SM2 or SM5 brane solu...

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

A shear-free ray congruence on Minkowski space is a 3-parameter family of null geodesics along which Lie transport of a complementary 2dimensional spacelike subspace (called the screen space) is conformal. Such congruences are defined by complex analytic surfaces in the associated twistor space CP 3 and are the basis of the construction of massless fields. On a more general space-time, it is un...

Quantum mechanics for matter fields moving in an evaporating black hole spacetime is formulated in fully four-dimensional form according to the principles of generalized quantum theory. The resulting quantum theory cannot be expressed in a 3+1 form in terms of a state evolving unitarily or by reduction through a foliating family of spacelike surfaces. That is because evaporating black hole geom...

We study some Weingarten spacelike hypersurfaces in a de Sitter space S 1 (1). If the Weingarten spacelike hypersurfaces have two distinct principal curvatures, we obtain two classification theorems which give some characterization of the Riemannian product H(1−coth ̺)× S(1 − tanh ̺), 1 < k < n − 1 in S 1 (1), the hyperbolic cylinder H(1 − coth ̺) × S(1 − tanh ̺) or spherical cylinder H(1 − coth ̺)×...

We construct an eternally inflating spacelike brane world model. This model is feasible only if the space dimension of the brane is three (SM2) or six (SM5) for M theory or four (SD3) for superstring theory. A time-dependent n-form field would supply a constant energy density and cause eternal expansion of the spacelike brane. On the other hand, the hyperbolic space perpendicular to the brane w...

We construct an eternally inflating spacelike brane world model. If the space dimension of the brane is three (SM2) or six (SM5) for M theory or four (SD3) for superstring theory, a time-dependent n-form field would supply a constant energy density and cause exponentially expansion of the spacelike brane. In these cases, the hyperbolic space perpendicular to the brane would keep its scale facto...

A curve which is called geodesic on a surface M in Lorentz 3-space is a special curve that its acceleration is everywhere normal to M. In this paper, we analyzed the non-linear differential equation to determine the geodesic curves on ruled surfaces which is obtained by a strictly connected spacelike straight line moving with Frenet’s frame along a timelike curve in . When we assume that curvat...

We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ⋆φ : (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of spacespace noncommutativity, it does not vanish at spacelike separation in the noncommutin...