The lapse function in Friedmann—Lemaître–Robertson–Walker cosmologies

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.

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Solutions with throats in Hořava gravity with cosmological constant

International Journal of Modern Physics D ◽

10.1142/s0218271816500164 ◽

2016 ◽

Vol 25 (02) ◽

pp. 1650016 ◽

Cited By ~ 5

Author(s):

Jorge Bellorín ◽

Alvaro Restuccia ◽

Adrián Sotomayor

Keyword(s):

Cosmological Constant ◽

Effective Action ◽

Naked Singularity ◽

Shift Function ◽

Coupling Constant ◽

De Sitter ◽

Single Side ◽

Horava Gravity ◽

Two Sides ◽

Lapse Function

By combining analytical and numerical methods, we find that the solutions of the complete Hořava theory with negative cosmological constant that satisfy the conditions of staticity, spherical symmetry and vanishing of the shift function are two kinds of geometry: (i) a solution with two sides joined by a throat and (ii) a single side with a naked singularity at the origin. We study the second-order effective action. We consider the case when the coupling constant of the [Formula: see text] term, which is the unique deviation from general relativity (GR) in the effective action, is small. At one side, the solution with the throat acquires a kind of deformed anti-de Sitter (AdS) asymptotia and at the other side, there is an asymptotic essential singularity. The deformation of AdS essentially means that the lapse function [Formula: see text] diverges asymptotically a bit faster than AdS. This can also be interpreted as an anisotropic Lifshitz scaling that the solutions acquire asymptotically.

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INERTIAL FORCES AS VIEWED FROM THE ADM SLICING AND THEIR BEHAVIOUR FOR PARTICLES IN NON-CIRCULAR GEODESICS

Modern Physics Letters A ◽

10.1142/s0217732302008277 ◽

2002 ◽

Vol 17 (28) ◽

pp. 1835-1845 ◽

Cited By ~ 2

Author(s):

A. R. PRASANNA

Keyword(s):

Black Holes ◽

Angular Velocity ◽

Radial Velocity ◽

Centrifugal Force ◽

Test Particle ◽

Physical Parameters ◽

Inertial Forces ◽

Shift Vector ◽

Definition Of ◽

Lapse Function

Considering the definition of inertial forces acting on a test particle, following non-circular geodesics, in static and stationary space–times, we show that the centrifugal force reversal occurs only in the case of particles following prograde orbits around black holes. We first rewrite the covariant expressions for the acceleration components in terms of the lapse function, shift vector and the three-metric γij, using the ADM 3 + 1 splitting and use these, for different cases as given by pure radial motion, pure azimuthal motion and the general non-circular motion. It is found that the reversal occurs between 2m and 3m, only when the azimuthal angular velocity of the particle supersedes the radial velocity, which indeed depends upon the physical parameters E, ℓ and the Kerr parameter a.

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On Sliced Spaces: Global Hyperbolicity Revisited

10.20944/preprints201902.0097.v1 ◽

2019 ◽

Author(s):

Kyriakos Papadopoulos ◽

Nazli Kurt ◽

Basil K. Papadopoulos

Keyword(s):

Shift Function ◽

Global Hyperbolicity ◽

Globally Hyperbolic ◽

Topological Condition ◽

Lapse Function

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x20500220 ◽

2020 ◽

Vol 35 (05) ◽

pp. 2050022 ◽

Cited By ~ 1

Author(s):

D. H. Tchrakian

Keyword(s):

Black Holes ◽

Black Hole ◽

Btz Black Hole ◽

Chern Simons ◽

Lapse Function ◽

Odd Dimensions

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.

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COVARIANT FEATURE OF THE MIXMASTER MODEL INVARIANT MEASURE

International Journal of Modern Physics D ◽

10.1142/s021827180200230x ◽

2002 ◽

Vol 11 (08) ◽

pp. 1321-1330 ◽

Cited By ~ 4

Author(s):

GIOVANNI IMPONENTE ◽

GIOVANNI MONTANI

Keyword(s):

Invariant Measure ◽

Arbitrary Function ◽

Chaotic Behavior ◽

Time Variable ◽

Cosmological Singularity ◽

Constant Of Motion ◽

Set Up ◽

Lapse Function ◽

Mixmaster Model ◽

Hamiltonian Analysis

We provide a Hamiltonian analysis of the Mixmaster Universe dynamics showing the covariant nature of its chaotic behavior with respect to any choice of time variable. Asymptotically to the cosmological singularity, we construct the appropriate invariant measure for the system (which relies on the appearance of an "energy-like" constant of motion) in such a way that its existence is independent of fixing the time gauge, i.e. the corresponding lapse function. The key point in our analysis consists of introducing generic Misner–Chitré-like variables containing an arbitrary function, whose specification allows us to set up the same statistical scheme in any time gauge.

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RESTORING TIME DEPENDENCE INTO QUANTUM COSMOLOGY

International Journal of Modern Physics D ◽

10.1142/s0218271812420114 ◽

2012 ◽

Vol 21 (11) ◽

pp. 1242011 ◽

Cited By ~ 2

Author(s):

AHARON DAVIDSON ◽

BEN YELLIN

Keyword(s):

Quantum Theory ◽

Time Dependence ◽

Quantum Cosmology ◽

Scale Factor ◽

Time Dependent ◽

Hamiltonian Constraint ◽

Canonical Variables ◽

Explicit Time Dependence ◽

Dirac Brackets ◽

Lapse Function

Mini superspace cosmology treats the scale factor a(t), the lapse function n(t) and an optional dilation field ϕ(t) as canonical variables. While pre-fixing n(t) means losing the Hamiltonian constraint, pre-fixing a(t) is serendipitously harmless at this level. This suggests an alternative to the Hartle–Hawking approach, where the pre-fixed a(t) and its derivatives are treated as explicit functions of time, leaving n(t) and a now mandatory ϕ(t) to serve as canonical variables. The naive gauge pre-fix a(t) = const . is clearly forbidden, causing evolution to freeze altogether; so pre-fixing the scale factor, say a(t) = t, necessarily introduces explicit time dependence into the Lagrangian. Invoking Dirac's prescription for dealing with constraints, we construct the corresponding mini superspace time-dependent total Hamiltonian and calculate the Dirac brackets, characterized by {n, ϕ}D ≠ 0, which are promoted to commutation relations in the quantum theory.

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