Numerical solutions of Einstein's and scalar-field equations are found for a global defect in a higher-dimensional spacetime. The defect has a $(3+1)$-dimensional core and a ``hedgehog'' scalar-field configuration in $n=3$ extra dimensions. For sufficiently low symmetry-breaking scales $\eta$, the solutions are characterized by a flat worldsheet geometry and a constant solid deficit angle in the extra dimensions, in agreement with previous work. For $\eta$ above the higher-dimensional Planck scale, we find that static-defect solutions are singular. The singularity can be removed if the requirement of staticity is relaxed and defect cores are allowed to inflate. We obtain an analytic solution for the metric of such inflating defects at large distances from the core. The three extra dimensions of the nonsingular solutions have a ``cigar'' geometry. Although our numerical solutions were obtained for defects of codimension $n=3$, we argue that the conclusions are likely to apply to all $n\geq 3$.Comment: 19 pages, revtex, 6 eps figure

We investigate a nonsingular initial state of the Universe which leads to inflation naturally. The model is described by a scalar field with a quadratic potential in Eddington-inspired Born-Infeld gravity. The curvature of this initial state is given by the mass scale of the scalar field, which is much smaller than the Planck scale. Therefore, in this model, quantum gravity is not necessary in understanding this preinflationary stage, no matter how large the energy density becomes. The initial state in this model evolves eventually to a long inflationary period which is similar to the usual chaotic inflation.

We investigate the evolution of the Universe filled with barotropic perfect fluid in Eddingtoninspired Born-Infeld gravity. We consider both the isotropic and the anisotropic universe.At the early stage when the energy density is high, the evolution is modified considerably compared with that in general relativity. For the equation-of-state parameter w > 0, the initial singularity is not accompanied as it was discovered for radiation in earlier work. More interestingly, for pressureless dust (w = 0), the initial state approaches a de Sitter state.This fact opens a new possibility of singularity-free nature of the theory. The anisotropy is mild, and does not develop curvature singularities in spacetime contrary to general relativity. Conclusions 16A Energy-Momentum Conservation 17 B Scale Factor a(t) for p = 0 19

It has been recently shown that topological defects can arise in symmetry breaking models where the scalar field potential $V(\phi)$ has no minima and is a monotonically decreasing function of $|\phi|$. Here we study the gravitational fields produced by such vacuumless defects in the cases of both global and gauge symmetry breaking. We find that a global monopole has a strongly repulsive gravitational field, and its spacetime has an event horizon similar to that in de Sitter space. A gauge monopole spacetime is essentially that of a magnetically charged black hole. The gravitational field of a global string is repulsive and that of a gauge string is attractive at small distances and repulsive at large distances. Both gauge and global string spacetimes have singularities at a finite distance from the string core.Comment: 19 pages, REVTeX, 6 Postscript figure

We investigate black holes formed by static perfect fluid with p = −ρ/3. These represent the black holes in S3 and H3 spatial geometries. There are three classes of black-hole solutions, two S3 types and one H3 type. The interesting solution is the one of S3 type which possesses two singularities. The one is at the north pole behind the horizon, and the other is naked at the south pole. The observers, however, are free from falling to the naked singularity. There are also nonstatic cosmological solutions in S3 and H3, and a singular static solution in H3. In modern cosmology, the spatial topology of the Universe is an unresolved issue. The recent observational data measures the curvature density as Ω k = 0.000 ± 0.005 (95%, Planck TT+lowP+lensing+BAO) [1]. It is never manifest from the current observation to conclude if the Universe is flat, closed, or open. Apart from analyzing the observational data, investigating the primordial density perturbation in different topologies would give an insight for the topology of the Universe. Study of inflation in the closed and the open universe tells that there are models which is viable with the current observational data [2-6]. They predict some peculiar phenomena distinguishable from flat models, but they are still beyond the current observational resolution. Therefore, it is not very possible to rule out any specific topology from the cosmological studies at the current stage.Rather than considering cosmological models, other interesting subject would be considering a relativistic object such as a black hole in different spatial topologies. This might have a very significant feature which can distinguish the spatial topology of the Universe.The metric implying the three spatial topologies is given bywhere k = 0 represents the flat 3-space (R 3 ), and k = ±1 does the closed/open 3-space (S 3 /H 3 ). (The signature of g tt will be chosen so that we have only one time coordinate.) This implies that the curvature of the geometry is provided by the effective energy-momentum tensor,where the signature −/+ is for S 3 /H 3 . This implies thatwhere ρ > 0 for S 3 and ρ < 0 for H 3 . For the closed and the open, with the energy-momentum tensor (2) and the metric ansatzone can show that there is no static solution other than Eq. (1). This is somewhat different from the flat case which is a limit of the Schwarzschild solution characterized by the mass parameter M . In order to achieve a black hole configuration in the closed/open 3-space, therefore, it is suggested to introduce a matter field.In this work, we introduce a static perfect fluid in order to see if a black hole can be formed in the S 3 and H 3 spaces. We introduce the spatial dependence in the energy density, and impose a condition for the equation of state which implies the topology of S 3 /H 3 , as p(r) = − 1 3 ρ(r).(5) * Electronic address: iycho@seoultech.ac.kr † Electronic address: hckim@ut.ac.kr