Schwarzschild De Sitter Space Research Articles

Hyperelliptic functions and geodesic equations

AbstractA method for solving geodesic equations in Schwarzschild–de Sitter space–times and higher dimensional Schwarzschild space–times is presented. The solutions are derived from Jacobi's inversion problem on a Riemann surface of genus 2 restricted to the set of zeros of the theta function, which is called a theta–divisor. In its final form, the solutions are given in terms of derivatives of Kleinian sigma functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

PSEUDO-NEWTONIAN GRAVITATIONAL POTENTIAL FOR SCHWARZSCHILD–DE SITTER SPACE–TIMES

Pseudo-Newtonian gravitational potential describing the gravitational field of static and spherically symmetric black holes in the universe with a repulsive cosmological constant is introduced. In order to demonstrate the accuracy of the pseudo-Newtonian approach, the related effective potential for test particle motion is constructed and compared with its general-relativistic counterpart given by the Schwarzschild–de Sitter geometry. The results indicate that such an approach could be useful in applications of developed Newtonian theories of accretion disks in astrophysically interesting situations in large galactic structures for the Schwarzschild–de Sitter space–times with the cosmological parameter y = Λ M2/3 ≤ 10-6.

De Sitter thermodynamics: A glimpse into nonequilibrium

In this article it is shown that the thermodynamical evolution of a Schwarzschild de Sitter space is the evaporation of its black hole. The result is extended in higher dimensions to Lovelock theories of gravity with a single positive cosmological constant.

The Schwarzschild–de Sitter solution in five-dimensional general relativity briefly revisited

We briefly revisit the Schwarzschild–de Sitter solution in the context of five-dimensional general relativity. We obtain a class of five-dimensional solutions of Einstein vacuum field equations into which the four-dimensional Schwarzschild–de Sitter space can be locally and isometrically embedded. We show that this class of solutions is well behaved in the limit of Λ → 0. Applying the same procedure to the de Sitter cosmological model in five dimensions, we obtain a class of embedding spaces which are similarly well behaved in this limit. These examples demonstrate that the presence of a non-zero cosmological constant does not, in general, impose a rigid relation between the (3 + 1)- and (4 + 1)-dimensional spacetimes, with degenerate limiting behaviour.

Solar system effects in Schwarzschild–de Sitter space–time

The Schwarzschild–de Sitter space–time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant Λ. Based on this space–time we calculate Solar system effects like gravitational redshift, light deflection, gravitational time delay, perihelion shift, geodetic or de Sitter precession, as well as the influence of Λ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For Λ=Λ0∼10−52 m−2 the cosmological constant plays no role for all of these effects, while a value of Λ∼−10−37 m−2, if hypothetically held responsible for the Pioneer anomaly, is not compatible with the perihelion shift.

Massive particles' black hole tunneling and de Sitter tunneling

Hawking radiation is viewed as a tunneling process. The behavior of the tunneling massive particles is investigated, and the emission rates at which massive particles tunnel across the event horizon and the de Sitter cosmological horizon of the Schwarzschild–de Sitter space–time are calculated. The results are consistent with an underlying unitary theory and take the same functional form as that of massless particles.

Smooth transitions from the Schwarzschild vacuum to de Sitter space

We provide an infinity of spacetimes which contain part of both the Schwarzschild vacuum and de Sitter space. The transition, which occurs below the Schwarzschild event horizon, involves only boundary surfaces (no surface layers). An explicit example is given in which the weak and strong energy conditions are satisfied everywhere (except in the de Sitter section) and the dominant energy condition is violated only in the vicinity of the boundary to the Schwarzschild section. The singularity is avoided by way of a change in topology in accord with a theorem due to Borde..

THE ENTROPY CALCULATED VIA BRICK-WALL METHOD COMES FROM A THIN FILM NEAR THE EVENT HORIZON

The brick-wall method put forward by 't Hooft has contributed a great deal to the understanding and calculating of the entropy of a black hole. However, there are some drawbacks in it such as little mass approximation, neglecting logarithm terms, and taking the term including L3as a contribution of the vacuum surrounding the black hole. Moreover, the fundamental problem is why the entropy of scalar field or Dirac field surrounding a black hole is the entropy of the black hole itself. It is well known that the event horizon is the characteristic of a black hole. The entropy calculation of a black hole should be only related to its horizon. Due to this analysis, we improve the brick-wall model by taking that the entropy of a black hole is only contributed by a thin film near the event horizon. This improvement not only gives us a satisfied result, but also avoids the drawbacks in the original brick-wall method. It is found that there is an intrinsic relation between the event horizon and the entropy. We also calculate the entropy of Schwarzschild–de Sitter space–time via the improved method, which can hardly be resolved via the original model.

Black Hole and Cosmic Entropy for Schwarzschild–de Sitter Space–Time

We calculate the free energy and the entropy of a scalar field in terms of the brick-wall method in the background of the Schwarzschild–de Sitter space–time. We obtain the entropy of a black hole and the cosmic entropy at nonasymptotic flat space. When the cut-off satisfies the proper condition, the entropy of a black hole is proportional to the area of a black hole horizon, and the cosmic entropy is proportional to the cosmic horizon area.

Erratum: Hadamard renormalization, conformal anomaly, and cosmological event horizons [Phys. Rev. D56, 4633 (1997)

The Hadamard renormalization prescription is used to derive a two dimensional analog of the renormalized stress tensor for a minimally coupled scalar field in Schwarzschild-de Sitter space time. In the two dimensional analog the minimal coupling reduces to the conformal coupling and the stress tensor is found to be determined by the (nonlocal) contribution of the anomalous trace and some additional parameters in close relation to the work [1]. To properly relate the stress tensor to the state of outwards signals coming from the direction of the black hole at late times we propose a cut-off hypothesis which excludes the contribution of the anomalous trace close to the black hole horizon. The corresponding cut-off scale is found to be related to the equilibrium-temperature of the cosmological horizon in a leading order estimate. Finally, we establish a relation between the radiation-temperature of the black hole horizon at large distance from the hole and the the anomalous trace and determine the correction term to the Hawking temperature due to the presence of the cosmological horizon.

Schwarzschild-de Sitter type wormhole

The two Schwarzschild-de Sitter spaces connected by a wormhole according to Visser's method are considered in order to find the effect of the cosmological constant on the Lorentzian wormhole. The roles of the cosmological constant in the classical and quantum stabilities of the dynamics of the Lorentzian wormhole are studied.

Schwarzschild-de Sitter space and its perturbations.

Metric perturbations of Schwarzschild-de Sitter space are examined in the Regge-Wheeler formalism. We demonstrate that both even and odd perturbations can be derived from a Schr\"odinger equation, and establish stability.