Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms

We investigate multi-dimensional universe with nonlinear scalar curvature terms to evaluate the probability of creation of primordial black holes. For this we obtain Euclidean instanton solution in two different topologies: (a) $S^{D-1}$ - topology which does not accommodate primordial black holes and (b) $S^1\times S^{D-2}$-topology which accommodates a pair of black holes. The probability for quantum creation of an inflationary universe with a pair of black holes has been evaluated assuming a gravitational action which is described by a polynomial function of scalar curvature with or without a cosmological constant ($\Lambda$) using the framework of semiclassical approximation of Hartle-Hawking boundary conditions. We discuss here a class of new gravitational instantons solution in the $R^4$-theory which are relevant for cosmological model building.Comment: 18 pages, no figure. accepted in Phys. Rev.

A simple proof of Birkhoff's theorem for cosmological constant

We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized Birkhoff's theorems are local uniqueness theorems whose corollary is that locally spherically symmetric solutions of Einstein's equations exhibit an additional local killing vector field.Comment: 10 pages, 5 figures References added; typo in eqn. 12 fixe

A Wide Symbiotic Channel to Type Ia Supernovae

As a promising channel to Type Ia supernovae (SNe Ia), we have proposed a symbiotic binary system consisting of a white dwarf (WD) and a low mass red-giant (RG), where strong winds from the accreting WD play a key role to increase the WD mass to the Chandrasekhar mass limit. Here we propose two new evolutionary processes which make the symbiotic channel to SNe Ia much wider. (1) We first show that the WD + RG close binary can form from a wide binary even with such a large initial separation as $a_i \lesssim 40000 R_\odot$. Such a binary consists of an AGB star and a low mass main-sequence (MS) star, where the AGB star is undergoing superwind before becoming a WD. If the superwind at the end of AGB evolution is as fast as or slower than the orbital velocity, the wind outflowing from the system takes away the orbital angular momentum effectively. As a result the wide binary shrinks greatly to become a close binary. Therefore, the WD + RG binary can form from much wider binaries than our earlier estimate. (2) When the RG fills its inner critical Roche lobe, the WD undergoes rapid mass accretion and blows a strong optically thick wind. Our earlier analysis has shown that the mass transfer is stabilized by this wind only when the mass ratio of RG/WD is smaller than 1.15. Our new finding is that the WD wind can strip mass from the RG envelope, which could be efficient enough to stabilize the mass transfer even if the RG/WD mass ratio exceeds 1.15. With the above two new effects (1) and (2), the symbiotic channel can account for the inferred rate of SNe Ia in our Galaxy.Comment: 29 pages including 14 firgures, to be published in ApJ, 521, No.

Solutions of Minimal Four Dimensional de Sitter Supergravity

Pseudo-supersymmetric solutions of minimal $N=2$, $D=4$ de Sitter supergravity are classified using spinorial geometry techniques. We find three classes of solutions. The first class of solution consists of geometries which are fibrations over a 3-dimensional manifold equipped with a Gauduchon-Tod structure. The second class of solution is the cosmological Majumdar-Papapetrou solution of Kastor and Traschen, and the third corresponds to gravitational waves propagating in the Nariai cosmology.Comment: 17 Pages. Minor correction to section 4; equation (4.21) corrected and (old) equation (4.26) deleted; the final result is unchange

The Real Scalar Field Equation for Nariai Black Hole in the 5D Schwarzschild-de Sitter Black String Space

The Nariai black hole, whose two horizons are lying close to each other, is an extreme and important case in the research of black hole. In this paper we study the evolution of a massless scalar field scattered around in 5D Schwarzschild-de Sitter black string space. Using the method shown by Brevik and Simonsen (2001) we solve the scalar field equation as a boundary value problem, where real boundary condition is employed. Then with convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients ($R, T$) are obtained. At last, we also compare the coefficients with usual 4D counterpart.Comment: 10 pages,6 figures.To appear in Int. J. Mod. Phys.

A black hole hologram in de Sitter space

In this paper we show that the entropy of de Sitter space with a black hole in arbitrary dimension can be understood using a modified Cardy-Verlinde entropy formula. We also comment on the observer dependence of the de Sitter entropy.Comment: 13 pages. Final version accepted for publication in JHEP. Added references and improved presentatio

Cosmological solutions from fake N=2 EYM supergravity

We characterise the (fake) supersymmetric solutions of Wick-rotated N=2 d=4 gauged supergravity coupled to non-Abelian vector multiplets. In the time-like case we obtain generalisations of Kastor & Traschen's cosmological black holes: they have a specific time-dependence and the base-space must be 3-dimensional hyperCR/Gauduchon-Tod space. In the null-case, we find that the metric has a holonomy contained in Sim(2), give a general characterisation of the solutions, and give some examples. Finally, we point out that in some cases the solutions we found are non-BPS solutions to N=2 d=4 supergravity coupled to vector multiplets.Comment: 30 pages. Comments and references added, typos correcte

A Non - Singular Cosmological Model with Shear and Rotation

We have investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large value of time.Comment: 10 pages, late

Deformed black strings in 5-dimensional Einstein-Yang-Mills theory

We construct the first examples of deformed non-abelian black strings in a 5-dimensional Einstein-Yang-Mills model. Assuming all fields to be independent of the extra coordinate, we construct deformed black strings, which in the 4-dimensional picture correspond to axially symmetric non-abelian black holes in gravity-dilaton theory. These solutions thus have deformed S^2 x R horizon topology. We study fundamental properties of the black strings and find that for all choices of the gravitational coupling two branches of solutions exist. The limiting behaviour of the second branch of solutions however depends strongly on the choice of the gravitational coupling.Comment: 8 Revtex pages; 4 eps figures; references adde

The Numerical Solution of Scalar Field for Nariai Case in 5D Ricci-flat SdS Black String Space with Polynomial Approximation

As one exact candidate of the higher dimensional black hole, the 5D Ricci-flat Schwarzschild-de Sitter black string space presents something interesting. In this paper, we give a numerical solution to the real scalar field around the Nariai black hole by the polynomial approximation. Unlike the previous tangent approximation, this fitting function makes a perfect match in the leading intermediate region and gives a good description near both the event and the cosmological horizons. We can read from our results that the wave is close to a harmonic one with the tortoise coordinate. Furthermore, with the actual radial coordinate the waves pile up almost equally near the both horizons.Comment: 8 pages, 4 figure